Current Search: Wang, Xiaoming (x)
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 Title
 An Efficient And Longtime Accurate Thirdorder Algorithm For The Stokesdarcy System.
 Creator

Chen, Wenbin, Gunzburger, Max, Sun, Dong, Wang, Xiaoming
 Abstract/Description

A thirdorder in time numerical IMEXtype algorithm for the StokesDarcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel thirdorder AdamsMoulton scheme is used for the discretization of the dissipative term whereas a thirdorder explicit AdamsBashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. The scheme is efficient in the sense that one needs to solve, at each time step, decoupled...
Show moreA thirdorder in time numerical IMEXtype algorithm for the StokesDarcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel thirdorder AdamsMoulton scheme is used for the discretization of the dissipative term whereas a thirdorder explicit AdamsBashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. The scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. The scheme is also unconditionally stable and, with a mild timestep restriction, longtime accurate in the sense that the error is bounded uniformly in time. Numerical experiments are used to illustrate the theoretical results. To the authors' knowledge, the novel algorithm is the first thirdorder accurate numerical scheme for the StokesDarcy system possessing its favorable efficiency, stability, and accuracy properties.
Show less  Date Issued
 201612
 Identifier
 FSU_libsubv1_wos_000386770800006, 10.1007/s0021101507893
 Format
 Citation
 Title
 EdgeWeighted Centroidal Voronoi Tessellation Based Algorithms for Image Segmentation.
 Creator

Wang, Jie, Wang, Xiaoqiang, Wang, Xiaoming, Gunzburger, Max, Peterson, Janet, ElAzab, Anter, Department of Scientific Computing, Florida State University
 Abstract/Description

Centroidal Voronoi tessellations (CVTs) are special Voronoi tessellations whose generators are also the centers of mass (centroids) of the Voronoi regions with respect to a given density function. CVTbased algorithms have been proved very useful in the context of image processing. However when dealing with the image segmentation problems, classic CVT algorithms are sensitive to noise. In order to overcome this limitation, we develop an edgeweighted centroidal Voronoi Tessellation (EWCVT)...
Show moreCentroidal Voronoi tessellations (CVTs) are special Voronoi tessellations whose generators are also the centers of mass (centroids) of the Voronoi regions with respect to a given density function. CVTbased algorithms have been proved very useful in the context of image processing. However when dealing with the image segmentation problems, classic CVT algorithms are sensitive to noise. In order to overcome this limitation, we develop an edgeweighted centroidal Voronoi Tessellation (EWCVT) model by introducing a new energy term related to the boundary length which is called "edge energy". The incorporation of the edge energy is equivalent to add certain form of compactness constraint in the physical space. With this compactness constraint, we can effectively control the smoothness of the clusters' boundaries. We will provide some numerical examples to demonstrate the effectiveness, efficiency, flexibility and robustness of EWCVT. Because of its simplicity and flexibility, we can easily embed other mechanisms with EWCVT to tackle more sophisticated problems. Two models based on EWCVT are developed and discussed. The first one is "local variation and edgeweighted centroidal Voronoi Tessellation" (LVEWCVT) model by encoding the information of local variation of colors. For the classic CVTs or its generalizations (like EWCVT), pixels inside a cluster share the same centroid. Therefore the set of centroids can be viewed as a piecewise constant function over the computational domain. And the resulting segmentation have to be roughly the same with respect to the corresponding centroids. Inspired by this observation, we propose to calculate the centroids for each pixel separately and locally. This scheme greatly improves the algorithms' tolerance of withincluster feature variations. By extensive numerical examples and quantitative evaluations, we demonstrate the excellent performance of LVEWCVT method compared with several stateofart algorithms. LVEWCVT model is especially suitable for detection of inhomogeneous targets with distinct color distributions and textures. Based on EWCVT, we build another model for "Superpixels" which is in fact a "regularization" of highly inhomogeneous images. We call our algorithm for superpixels as "VCells" which is the abbreviation of "Voronoi cells". For a wide range of images, VCells is capable to generate roughly uniform subregions and meanwhile nicely preserves local image boundaries. The undersegmentation error is effectively limited in a controllable manner. Moreover, VCells is very efficient. The computational cost is roughly linear in image size with small constant coefficient. For megapixel sized images, VCells is able to generate very dense superpixels in a matter of seconds. We demonstrate that VCells outperforms several stateofart algorithms through extensive qualitative and quantitative results on a wide range of complex images. Another important contribution of this work is the "DetectingSegmentBreaking" (DSB) algorithm which can be used to guarantee the spatial connectedness of resulting segments generated by CVT based algorithms. Since the metric is usually defined on the color space, the resulting segments by CVT based algorithms are not necessarily spatially connected. For some applications, this feature is useful and conceptually meaningful, e.g., the foreground objects are not spatially connected. But for some other applications, like the superpixel problem, this "good" feature becomes unacceptable. By simple "extractingconnectedcomponent" and "relabeling" schemes, DSB successfully overcomes the above difficulty. Moreover, the computational cost of DSB is roughly linear in image size with a small constant coefficient. From the theoretical perspective, the innovative idea of EWCVT greatly enriches the methodology of CVTs. (The idea of EWCVT has already been used for variational curve smoothing and reconstruction problems.) For applications, this work shows the great power of EWCVT for image segmentation related problems.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd1244
 Format
 Thesis
 Title
 Numerical Methods for TwoPhase Jet Flow.
 Creator

Wang, Yaohong, Sussman, Mark, Alvi, Farrukh S., Ewald, Brian, Quine, Jack, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

Two numerical methods are developed and analyzed for studying twophase jet flows. The first numerical method solves the eigenvalue problem for the matrix system that is constructed from the pseudospectral discretization of the 3D linearized, incompressible, perturbed NavierStokes (NS) equations for twophase flows. This first numerical method will be denoted as LSA for "linear stability analysis." The second numerical method solves the 3D (nonlinear) NS equations for incompressible, two...
Show moreTwo numerical methods are developed and analyzed for studying twophase jet flows. The first numerical method solves the eigenvalue problem for the matrix system that is constructed from the pseudospectral discretization of the 3D linearized, incompressible, perturbed NavierStokes (NS) equations for twophase flows. This first numerical method will be denoted as LSA for "linear stability analysis." The second numerical method solves the 3D (nonlinear) NS equations for incompressible, twophase flows. The second numerical method will be denoted as DNS for "direct numerical simulation." In this thesis, predictions of jetstability using the LSA method are compared with the predictions using DNS. Researchers have not previously compared LSA with DNS for the coflowing twophase jet problem. Researchers have only recently validated LSA with DNS for the simpler RayleighCapillary stability problem [77] [20] [103] [26]. In this thesis, a DNS method has been developed for cylindrical coordinate systems. Researchers have not previously simulated 3D, twophase, jet flow, in cylindrical coordinate systems. The numerical predictions for jet flow are compared: (1) LSA with DNS (2) DNSCLSVOF with DNSLS, and (3) 3D rectangular with 3D cylindrical. "DNSCLSVOF" denotes the coupled level set and volumeoffluid method for computing solutions to incompressible twophase flows [99]. "DNSLS" denotes a novel hybrid level set and volume constraint method for simulating incompressible twophase flows [89]. The following discoveries have been made in this thesis: (1) the DNSCLSVOF method and the DNSLS method both converge under grid refinement to the same results for predicting the breakup of a liquid jet before and after breakup; (2) computing jet breakup in 3D cylindrical coordinate systems is more efficient than computing jet breakup in 3D rectangular coordinate systems; and (3) the LSA method agrees with the DNS method for the initial growth of instabilities (comparison method made for classical RayleighCapillary problem and coflowing jet problem). It is found that for the classical RayleighCapillary stability problem, the LSA prediction differs from the DNS prediction at later times.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1246
 Format
 Thesis
 Title
 Centroidal Voronoi Tessellations for Mesh Generation: from Uniform to Anisotropic Adaptive Triangulations.
 Creator

Nguyen, Hoa V., Gunzburger, Max D., ElAzab, Anter, Peterson, Janet, Wang, Xiaoming, Wang, Xiaoqiang, Department of Mathematics, Florida State University
 Abstract/Description

Mesh generation in regions in Euclidean space is a central task in computational science, especially for commonly used numerical methods for the solution of partial differential equations (PDEs), e.g., finite element and finite volume methods. Mesh generation can be classified into several categories depending on the element sizes (uniform or nonuniform) and shapes (isotropic or anisotropic). Uniform meshes have been well studied and still find application in a wide variety of problems....
Show moreMesh generation in regions in Euclidean space is a central task in computational science, especially for commonly used numerical methods for the solution of partial differential equations (PDEs), e.g., finite element and finite volume methods. Mesh generation can be classified into several categories depending on the element sizes (uniform or nonuniform) and shapes (isotropic or anisotropic). Uniform meshes have been well studied and still find application in a wide variety of problems. However, when solving certain types of partial differential equations for which the solution variations are large in some regions of the domain, nonuniform meshes result in more efficient calculations. If the solution changes more rapidly in one direction than in others, nonuniform anisotropic meshes are preferred. In this work, first we present an algorithm to construct uniform isotropic meshes and discuss several mesh quality measures. Secondly we construct an adaptive method which produces nonuniform anisotropic meshes that are well suited for numerically solving PDEs such as the convection diffusion equation. For the uniform Delaunay triangulation of planar regions, we focus on how one selects the positions of the vertices of the triangulation. We discuss a recently developed method, based on the centroidal Voronoi tessellation (CVT) concept, for effecting such triangulations and present two algorithms, including one new one, for CVTbased grid generation. We also compare several methods, including CVTbased methods, for triangulating planar domains. Furthermore, we define several quantitative measures of the quality of uniform grids. We then generate triangulations of several planar regions, including some having complexities that are representative of what one may encounter in practice. We subject the resulting grids to visual and quantitative comparisons and conclude that all the methods considered produce highquality uniform isotropic grids and that the CVTbased grids are at least as good as any of the others. For more general grid generation settings, e.g., nonuniform and/or anistropic grids, such quantitative comparisons are much more difficult, if not impossible, to either make or interpret. This motivates us to develop CVTbased adaptive nonuniform anisotropic mesh refinement in the context of solving the convectiondiffusion equation with emphasis on convectiondominated problems. The challenge in the numerical approximation of this equation is due to large variations in the solution over small regions of the physical domain. Our method not only refines the underlying grid at these regions but also stretches the elements according to the solution variation. Three main ingredients are incorporated to improve the accuracy of numerical solutions and increase the algorithm's robustness and efficiency. First, a streamline upwind Petrov Galerkin method is used to produce a stabilized solution. Second, an adapted metric tensor is computed from the approximate solution. Third, optimized anisotropic meshes are generated from the computed metric tensor. Our algorithm has been tested on a variety of 2dimensional examples. It is robust in detecting layers and efficient in resolving nonphysical oscillations in the numerical approximation.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd2616
 Format
 Thesis
 Title
 Inference for Semiparametric TimeVarying Covariate Effect Relative Risk Regression Models.
 Creator

Ye, Gang, McKeague, Ian W., Wang, Xiaoming, Huffer, Fred W., Song, KaiSheng, Department of Statistics, Florida State University
 Abstract/Description

A major interest of survival analysis is to assess covariate effects on survival via appropriate conditional hazard function regression models. The Cox proportional hazards model, which assumes an exponential form for the relative risk, has been a popular choice. However, other regression forms such as Aalen's additive risk model may be more appropriate in some applications. In addition, covariate effects may depend on time, which can not be reflected by a Cox proportional hazards model. In...
Show moreA major interest of survival analysis is to assess covariate effects on survival via appropriate conditional hazard function regression models. The Cox proportional hazards model, which assumes an exponential form for the relative risk, has been a popular choice. However, other regression forms such as Aalen's additive risk model may be more appropriate in some applications. In addition, covariate effects may depend on time, which can not be reflected by a Cox proportional hazards model. In this dissertation, we study a class of timevarying covariate effect regression models in which the link function (relative risk function) is a twice continuously differentiable and prespecified, but otherwise general given function. This is a natural extension of the PrenticeSelf model, in which the link function is general but covariate effects are modelled to be time invariant. In the first part of the dissertation, we focus on estimating the cumulative or integrated covariate effects. The standard martingale approach based on counting processes is utilized to derive a likelihoodbased iterating equation. An estimator for the cumulative covariate effect that is generated from the iterating equation is shown to be ¡Ìnconsistent. Asymptotic normality of the estimator is also demonstrated. Another aspect of the dissertation is to investigate a new test for the above timevarying covariate effect regression model and study consistency of the test based on martingale residuals. For Aalen's additive risk model, we introduce a test statistic based on the HufferMcKeague weightedleastsquares estimator and show its consistency against some alternatives. An alternative way to construct a test statistic based on Bayesian Bootstrap simulation is introduced. An application to real lifetime data will be presented.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd0949
 Format
 Thesis
 Title
 4D Var Data Assimilation and POD Model Reduction Applied to Geophysical Dynamics Models.
 Creator

Chen, Xiao, Navon, Ionel Michael, Sussman, Mark, Hart, Robert, Wang, Xiaoming, Gordon, Erlebacher, Department of Mathematics, Florida State University
 Abstract/Description

Standard spatial discretization schemes for dynamical system (DS), usually lead to largescale, highdimensional, and in general, nonlinear systems of ordinary differential equations.Due to limited computational and storage capabilities, Reduced Order Modeling (ROM) techniques from system and control theory provide an attractive approach to approximate the largescale discretized state equations using lowdimensional models. The objective of 4D variational data assimilation (4D Var) is to...
Show moreStandard spatial discretization schemes for dynamical system (DS), usually lead to largescale, highdimensional, and in general, nonlinear systems of ordinary differential equations.Due to limited computational and storage capabilities, Reduced Order Modeling (ROM) techniques from system and control theory provide an attractive approach to approximate the largescale discretized state equations using lowdimensional models. The objective of 4D variational data assimilation (4D Var) is to obtain the minimum of a cost functional estimating the discrepancy between the model solutions and distributed observations in time and space. A control reduction methodology based on Proper Orthogonal Decomposition (POD), referred to as POD 4D Var, has been widely used for nonlinear systems with tractable computations. However, the appropriate criteria for updating a POD ROM are not yet known in the application to optimal control. This is due to the limited validity of the POD ROM for inverse problems. Therefore, the classical TrustRegion (TR) approach combined with POD (TRPOD) was recently proposed as a way to alleviate the above difficulties. There is a global convergence result for TR, and benefiting from the trustregion philosophy, rigorous convergence results guarantee that the iterates produced by the TRPOD algorithm will converge to the solution of the original optimization problem. In order to reduce the POD basis size and still achieve the global convergence, a method was proposed to incorporate information from the 4D Var system into the ROM procedure by implementing a dual weighted POD (DWPOD) method. The first new contribution in my dissertation consists in studying a new methodology combining the dual weighted snapshots selection and trust region POD adaptivity (DWTRPOD). Another new contribution is to combine the incremental POD 4D Var, balanced truncation techniques and method of snapshots methodology. In the linear DS, this is done by integrating the linear forward model many times using different initial conditions in order to construct an ensemble of snapshots so as to generate the forward POD modes. Then those forward POD modes will serve as the initial conditions for its corresponding adjoint system. We then integrate the adjoint system a large number of times based on different initial conditions generated by the forward POD modes to construct an ensemble of adjoint snapshots. From this ensemble of adjoint snapshots, we can generate an ensemble of socalled adjoint POD modes. Thus we can approximate the controllability Grammian of the adjoint system instead of solving the computationally expensive coupled Lyapunov equations. To sum up, in the incremental POD 4D Var, we can approximate the controllability Grammian by integrating the TLM a number of times and approximate observability Grammian by integrating its adjoint also a number of times. A new idea contributed in this dissertation is to extend the snapshots based POD methodology to the nonlinear system. Furthermore, we modify the classical algorithms in order to save the computations even more significantly. We proposed a novel idea to construct an ensemble of snapshots by integrating the tangent linear model (TLM) only once, based on which we can obtain its TLM POD modes. Then each TLM POD mode will be used as an initial condition to generate a small ensemble of adjoint snapshots and their adjoint POD modes. Finally, we can construct a large ensemble of adjoint POD modes by putting together each small ensemble of adjoint POD modes. To sum up, our idea in a forthcoming study is to test approximations of the controllability Grammian by integrating TLM once and observability Grammian by integrating adjoint model a reduced number of times. Optimal control of a finite element limitedarea shallow water equations model is explored with a view to apply variational data assimilation(VDA) by obtaining the minimum of a functional estimating the discrepancy between the model solutions and distributed observations. In our application, some simplified hypotheses are used, namely the error of the model is neglected, only the initial conditions are considered as the control variables, lateral boundary conditions are periodic and finally the observations are assumed to be distributed in space and time. Derivation of the optimality system including the adjoint state, permits computing the gradient of the cost functional with respect to the initial conditions which are used as control variables in the optimization. Different numerical aspects related to the construction of the adjoint model and verification of its correctness are addressed. The data assimilation setup is tested for various mesh resolutions scenarios and different time steps using a modular computer code. Finally, impact of largescale unconstrained minimization solvers LBFGS is assessed for various lengths of the time windows. We then attempt to obtain a reducedorder model (ROM) of above inverse problem, based on proper orthogonal decomposition(POD), referred to as POD 4D Var. Different approaches of POD implementation of the reduced inverse problem are compared, including a dualweighed method for snapshot selection coupled with a trustregion POD approach. Numerical results obtained point to an improved accuracy in all metrics tested when dualweighing choice of snapshots is combined with POD adaptivity of the trustregion type. Results of adhoc adaptivity of the POD 4D Var turn out to yield less accurate results than trustregion POD when compared with highfidelity model. Finally, we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40yr ECMWF ReAnalysis (ERA40) datasets, in presence of full or incomplete observations being assimilated in a time interval (window of assimilation) presence of background error covariance terms. As an extension of this research, we attempt to obtain a reducedorder model of above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D Var for a finite volume global shallow water equations model based on the LinRood fluxform semiLagrangian semiimplicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dualweighted method for snapshot selection coupled with a trustregion POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4D Var model results combined with the trust region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current research work, we conclude that POD 4D Var certainly warrants further studies, with promising potential for its extension to operational 3D numerical weather prediction models.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd3836
 Format
 Thesis
 Title
 Analysis and Approximation of a TwoBand GinzburgLandau Model of Superconductivity.
 Creator

Chan, WanKan, Gunzburger, Max, Peterson, Janet, Manousakis, Efstratios, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

In 2001, the discovery of the intermetallic compound superconductor MgB2 having a critical temperature of 39K stirred up great interest in using a generalization of the GinzburgLandau model, namely the twoband timedependent GinzburgLandau (2BTDGL) equations, to model the phenomena of twoband superconductivity. In this work, various mathematical and numerical aspects of the twodimensional, isothermal, isotropic 2BTDGL equations in the presence of a timedependent applied magnetic field...
Show moreIn 2001, the discovery of the intermetallic compound superconductor MgB2 having a critical temperature of 39K stirred up great interest in using a generalization of the GinzburgLandau model, namely the twoband timedependent GinzburgLandau (2BTDGL) equations, to model the phenomena of twoband superconductivity. In this work, various mathematical and numerical aspects of the twodimensional, isothermal, isotropic 2BTDGL equations in the presence of a timedependent applied magnetic field and a timedependent applied current are investigated. A new gauge is proposed to facilitate the inclusion of a timedependent current into the model. There are three parts in this work. First, the 2BTDGL model which includes a timedependent applied current is derived. Then, assuming sufficient smoothness of the boundary of the domain, the applied magnetic field, and the applied current, the global existence, uniqueness and boundedness of weak solutions of the 2BTDGL equations are proved. Second, the existence, uniqueness, and stability of finite element approximations of the solutions are shown and error estimates are derived. Third, numerical experiments are presented and compared to some known results which are related to MgB2 or general twoband superconductivity. Some novel behaviors are also identified.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd3923
 Format
 Thesis
 Title
 Partial Differential Equation Methods to Price Options in the Energy Market.
 Creator

Yan, Jinhua, Kopriva, David, Huﬀer, Fred, Case, Bettye Anne, Nolder, Craig, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

We develop partial differential equation methods with wellposed boundary conditions to price average strike options and swing options in the energy market. We use the energy method to develop boundary conditions that make a two space variable model of Asian options wellposed on a finite domain. To test the performance of wellposed boundary conditions, we price an average strike call. We also derive new boundary conditions for the average strike option from the putcall parity. Numerical...
Show moreWe develop partial differential equation methods with wellposed boundary conditions to price average strike options and swing options in the energy market. We use the energy method to develop boundary conditions that make a two space variable model of Asian options wellposed on a finite domain. To test the performance of wellposed boundary conditions, we price an average strike call. We also derive new boundary conditions for the average strike option from the putcall parity. Numerical results show that wellposed boundary conditions are working appropriately and solutions with new boundary conditions match the similarity solution significantly better than those provided in the existing literature. To price swing options, we develop a finite element penalty method on a one factor mean reverting diffusion model. We use the energy method to find wellposed boundary conditions on a finite domain, derive formulas to estimate the size of the numerical domain, develop a priori error estimates for both Dirichlet boundary conditions and Neumann boundary conditions. We verify the results through numerical experiments. Since the optimal exercise price is unknown in advance, which makes the swing option valuation challenging, we use a penalty method to resolve the difficulty caused by the early exercise feature. Numerical results show that the finite element penalty method is thousands times faster than the Binomial tree method at the same level of accuracy. Furthermore, we price a multiple right swing option with different strike prices. We find that a jump discontinuity can occur in the initial condition of a swing right since the exercise of another swing right may force its optimal exercise region to shrink. We develop an algorithm to identify the optimal exercise boundary at each time level, which allows us to record the optimal exercise time. Numerical results are accurate to one cent comparing with the benchmark solutions computed by a Binomial tree method. We extend applications to multiple right swing options with a waiting period restriction. A waiting period exists between two swing rights to be exercised successively, so we cannot exercise the latter right when we see an optimal exercise opportunity within the waiting period, but have to wait for the first optimal exercise opportunity after the waiting period. Therefore, we keep track of the optimal exercise time when pricing each swing right. We also verify an extreme case numerically. When the waiting time decreases, the value of M right swing option price increases to the value of M times an American option price as expected.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7673
 Format
 Thesis
 Title
 An Asymptotically Preserving Method for Multiphase Flow.
 Creator

Jemison, Matthew, Sussman, Mark, Nof, Doron, Cogan, Nick, Gallivan, Kyle, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

A unified, asymptoticallypreserving method for simulating multiphase flows using an exactly mass, momentum, and energy conserving CellIntegrated SemiLagrangian advection algorithm is presented. The new algorithm uses a semiimplicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed. The asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows,...
Show moreA unified, asymptoticallypreserving method for simulating multiphase flows using an exactly mass, momentum, and energy conserving CellIntegrated SemiLagrangian advection algorithm is presented. The new algorithm uses a semiimplicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed. The asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows, including stiff materials, which enables large time steps characteristic of incompressible flow algorithms rather than the small time steps required by explicit methods. Shocks are captured and material discontinuities are tracked, without the aid of any approximate or exact Riemann solvers. The new method enables one to simulate the flow of multiple materials, each possessing a potentially exotic equation of state. Simulations of multiphase flow in one and two dimensions are presented which illustrate the effectiveness of the new algorithm at efficiently computing multiphase flows containing shock waves and material discontinuities with large ''impedance mismatch.'' Additionally, new techniques related to the MomentofFluid interface reconstruction are presented, including a novel, asymptoticallypreserving method for capturing ''filaments,'' and an improved method for initializing the MomentofFluid optimization problem on unstructured, triangular grids.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd9012
 Format
 Thesis
 Title
 Computational Aeroacoustics Cascade Model of Fan Noise.
 Creator

Lepoudre, Philip P., Tam, Christopher, Shih, Chiang, Gallivan, Kyle, Hussaini, Yousuff, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

A Computational Aeroacoustics [CAA] cascade model has been built to study the generation and propagation mechanisms of noise resulting from the interaction of the fan and outlet guide vanes in a highbypass ratio turbofan engine. Also called rotorstator interaction noise, this noise source is a dominant contributor to the total tone and broadband noise levels produced by the engine, and therefore an improved understanding of the noise generation processes will assist in developing successful...
Show moreA Computational Aeroacoustics [CAA] cascade model has been built to study the generation and propagation mechanisms of noise resulting from the interaction of the fan and outlet guide vanes in a highbypass ratio turbofan engine. Also called rotorstator interaction noise, this noise source is a dominant contributor to the total tone and broadband noise levels produced by the engine, and therefore an improved understanding of the noise generation processes will assist in developing successful noise reduction strategies. The CAA cascade model directly solves the nonlinear compressible NavierStokes equations on a twodimensional linear cascade representation of the fan blade rows. The model incorporates real blade geometry and the rotor and stator blade rows are joined together with a sliding interface method. The fullycoupled aerodynamic flow and acoustic field are directly captured in one high resolution simulation, and therefore the noise production and propagation mechanisms can be visualized and measured in detail. The model includes the fullycoupled physics of the nonlinear sound generation and propagation in swirling wake flow, as well as the transmission and reflection of sound through the blade rows. Previous models of rotorstator interaction noise have typically involved some level of decoupling between the blade rows in order to simplify the noise problem. Stateoftheart CAA methodology is used to produce a high quality numerical solution with minimal dissipation and dispersion of supported waves. The multisizemesh multitimestep Dispersion Relation Preserving [DRP] scheme is used for efficient computation of the wide range of length and time scales in the problem. A conformal mapping technique is used to generate bodyfitted grids around the blade shapes, which are overset on a background grid to create the blade rows. An optimized interpolation scheme is employed for data transfer between the overset grids and also to create the sliding interface between the moving rotorfixed grid and stationary statorfixed grid. A completely new computer program was built for efficient implementation of the cascade model on parallel computers using Message Passing Interface [MPI], and the code was shown to have good parallel performance. The program is a general purpose solver for CAA calculations involving complex flow and geometry, and is a valuable resource for future research. A representative rotorstator cascade with three rotor blades and five stator blades was constructed using real fan and outlet guide vane crosssectional shapes from the NASA Glenn 22in. model fan. A fully developed flow was obtained through the blade rows at the approach condition of the model fan. The performance of the sliding interface method was analyzed by comparing the solution on the rotorfixed and statorfixed grids at the coincident sliding interface mesh line, and the error in grid transfer interpolation was found to be comparable to the low error levels of the underlying DRP scheme. The simulation was used to produce animations of pressure and Mach contour, which provided a wealth of visual information about the flow field and noise generation and propagation behaviour in the cascade. The ability of the CAA cascade model to produce a high fidelity picture of the interaction noise has been demonstrated. In addition, the velocity and pressure fields were measured at various axial locations in the domain to quantify the mean and fluctuating components of the swirling wake flow between the blade rows and after the stator. The tone noise results were compared with interaction tone linear theory. The theory predicted the existence of a small number of propagating spinning wave modes at harmonics of rotor blade passing frequency [BPF]. In particular, the dominant interaction tone at BPF, labelled , was predicted to have two wave fronts in the circumferential domain period and to spin counter to the direction of the rotor. This interaction tone was clearly visible in animations of the pressure contour as an intense shock wave moving at an oblique spiral angle between the blade rows and after the stator. The wave shape was measured using a moving average, and the high amplitude waveform showed characteristic nonlinear steepening, which calls into question the common assumption that the interaction tones can be adequately represented by single linear wave modes. The spinning modes in the solution were measured at various axial locations using a joint temporalspatial modal decomposition of the fluctuating pressure field, and very good agreement was observed with the modal content predicted by linear theory. The relationship of the mode spiral angle to blade stagger angle and the phase velocity of the spinning modes were shown to govern the transmission and reflection behaviour of the modes through the blade rows. The mode was reflected and frequency shifted by the rotor, and the reflected mode propagated through the stator blade row to the outlet. Only corotating modes were able to propagate through the rotor to the inlet, and hence the sound levels in the inlet were significantly lower than in the outlet. This behaviour is in good agreement with the trends observed in experimental studies of fan noise. The unsteady flow and surface pressure fluctuations around a stator blade were also measured. Spectral analysis of the surface pressure fluctuations revealed the highest sound pressure levels occurred near the blade leading edge and on the upper blade surface near the trailing edge. The sound source mechanisms on the stator blade are related to the fluctuating loading on the blade as it cuts through the rotor wake profile and experiences significant variation in the local angle of attack.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd3115
 Format
 Thesis
 Title
 Investigating Vesicle Adhesions Using Multiple Phase Field Functions.
 Creator

Gu, Rui, Wang, Xiaoqiang, Gunzburger, Max D., Wang, Xiaoming, Peterson, Janet S., Ye, Ming, Florida State University, College of Arts and Sciences, Department of Scientific...
Show moreGu, Rui, Wang, Xiaoqiang, Gunzburger, Max D., Wang, Xiaoming, Peterson, Janet S., Ye, Ming, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

We construct a phase field model for simulating the adhesion of a cell membrane to a substrate. The model features two phase field functions which are used to simulate the membrane and the substrate. An energy model is defined which accounts for the elastic bending energy and the contact potential energy as well as, through a penalty method, vesicle volume and surface area constraints. Numerical results are provided to verify our model and to provide visual illustrations of the interactions...
Show moreWe construct a phase field model for simulating the adhesion of a cell membrane to a substrate. The model features two phase field functions which are used to simulate the membrane and the substrate. An energy model is defined which accounts for the elastic bending energy and the contact potential energy as well as, through a penalty method, vesicle volume and surface area constraints. Numerical results are provided to verify our model and to provide visual illustrations of the interactions between a lipid vesicle and substrates having complex shapes. Examples are also provided for the adhesion process in the presence of gravitational and point pulling forces. A comparison with experimental results demonstrates the effectiveness of the two phase field approach. Similarly to simulating vesiclesubstrate adhesion, we construct a multiphasefield model for simulating the adhesion between two vesicles. Two phase field functions are introduced to simulate each of the two vesicles. An energy model is defined which accounts for the elastic bending energy of each vesicle and the contact potential energy between the two vesicles; the vesicle volume and surface area constraints are imposed using a penalty method. Numerical results are provided to verify the efficacy of our model and to provide visual illustrations of the different types of contact. The method can be adjusted to solve endocytosis problems by modifying the bending rigidity coefficients of the two elastic bending energies. The method can also be extended to simulate multicell adhesions, one example of which is erythrocyte rouleaux. A comparison with laboratory observations demonstrates the effectiveness of the multiphase field approach. Coupled with fluid, we construct a phase field model for simulating vesiclevessel adhesion in a flow. Two phase field functions are introduced to simulate the vesicle and vessel respectively. The fluid is modeled and confined inside the tube by a phase field coupled NavierStokes equation. Both vesicle and vessel are transported by fluid flow inside our computational domain. An energy model regarding the comprehensive behavior of vesiclefluid interaction, vesselfluid interaction, vesiclevessel adhesion is defined. The vesicle volume and surface area constraints are imposed using a penalty method, while the vessel elasticity is modeled under Hooke's Law. Numerical results are provided to verify the efficacy of our model and to demonstrate the effectiveness of our fluidcoupled vesicle vessel adhesion phase field approach by comparison with laboratory observations.
Show less  Date Issued
 2015
 Identifier
 FSU_2015fall_Gu_fsu_0071E_12873
 Format
 Thesis
 Title
 Analysis of Two Partial Differential Equation Models in Fluid Mechanics: Nonlinear Spectral EddyViscosity Model of Turbulence and InfinitePrandtlNumber Model of Mantle Convection.
 Creator

Saka, Yuki, Gunzburger, Max D., Wang, Xiaoming, ElAzab, Anter, Peterson, Janet, Wang, Xiaoqiang, Department of Mathematics, Florida State University
 Abstract/Description

This thesis presents two problems in the mathematical and numerical analysis of partial differential equations modeling fluids. The first is related to modeling of turbulence phenomena. One of the objectives in simulating turbulence is to capture the large scale structures in the flow without explicitly resolving the small scales numerically. This is generally accomplished by adding regularization terms to the NavierStokes equations. In this thesis, we examine the spectral viscosity models...
Show moreThis thesis presents two problems in the mathematical and numerical analysis of partial differential equations modeling fluids. The first is related to modeling of turbulence phenomena. One of the objectives in simulating turbulence is to capture the large scale structures in the flow without explicitly resolving the small scales numerically. This is generally accomplished by adding regularization terms to the NavierStokes equations. In this thesis, we examine the spectral viscosity models in which only the highfrequency spectral modes are regularized. The objective is to retain the largescale dynamics while modeling the turbulent fluctuations accurately. The spectral regularization introduces a host of parameters to the model. In this thesis, we rigorously justify effective choices of parameters. The other problem is related to modeling of the mantle flow in the Earth's interior. We study a model equation derived from the Boussinesq equation where the Prandtl number is taken to infinity. This essentially models the flow under the assumption of a large viscosity limit. The novelty in our problem formulation is that the viscosity depends on the temperature field, which makes the mathematical analysis nontrivial. Compared to the constant viscosity case, variable viscosity introduces a secondorder nonlinearity which makes the mathematical question of wellposedness more challenging. Here, we prove this using tools from the regularity theory of parabolic partial differential equations.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd2108
 Format
 Thesis
 Title
 SparseGrid Methods for Several Types of Stochastic Differential Equations.
 Creator

Zhang, Guannan, Gunzburger, Max D., Wang, Xiaoming, Peterson, Janet, Wang, Xiaoqiang, Ye, Ming, Webster, Clayton, Burkardt, John, Department of Scientific Computing, Florida...
Show moreZhang, Guannan, Gunzburger, Max D., Wang, Xiaoming, Peterson, Janet, Wang, Xiaoqiang, Ye, Ming, Webster, Clayton, Burkardt, John, Department of Scientific Computing, Florida State University
Show less  Abstract/Description

This work focuses on developing and analyzing novel, efficient sparsegrid algorithms for solving several types of stochastic ordinary/partial differential equations and corresponding inverse problem, such as parameter identification. First, we consider linear parabolic partial differential equations with random diffusion coefficients, forcing term and initial condition. Error analysis for a stochastic collocation method is carried out in a wider range of situations than previous literatures,...
Show moreThis work focuses on developing and analyzing novel, efficient sparsegrid algorithms for solving several types of stochastic ordinary/partial differential equations and corresponding inverse problem, such as parameter identification. First, we consider linear parabolic partial differential equations with random diffusion coefficients, forcing term and initial condition. Error analysis for a stochastic collocation method is carried out in a wider range of situations than previous literatures, including input data that depend nonlinearly on the random variables and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate the exponential decay of the interpolation error in the probability space for both semidiscrete and fullydiscrete solutions. Second, we consider multidimensional backward stochastic differential equations driven by a vector of white noise. A sparsegrid scheme are proposed to discretize the target equation in the multidimensional timespace domain. In our scheme, the time discretization is conducted by the multistep scheme. In the multidimensional spatial domain, the conditional mathematical expectations derived from the original equation are approximated using sparsegrid GaussHermite quadrature rule and adaptive hierarchical sparsegrid interpolation. Error estimates are rigorously proved for the proposed fullydiscrete scheme for multidimensional BSDEs with certain types of simplified generator functions. Third, we investigate the propagation of input uncertainty through nonlocal diffusion models. Since the stochastic local diffusion equations, e.g. heat equations, have already been well studied, we are interested in extending the existing numerical methods to solve nonlocal diffusion problems. In this work, we use sparsegrid stochastic collocation method to solve nonlocal diffusion equations with colored noise and MonteCarlo method to solve the ones with white noise. Our numerical experiments show that the existing methods can achieve the desired accuracy in the nonlocal setting. Moreover, in the white noise case, the nonlocal diffusion operator can reduce the variance of the solution because the nonlocal diffusion operator has "smoothing" effect on the random field. At last, stochastic inverse problem is investigated. We propose sparsegrid Bayesian algorithm to improve the efficiency of the classic Bayesian methods. Using sparsegrid interpolation and integration, we construct a surrogate posterior probability density function and determine an appropriate alternative density which can capture the main features of the true PPDF to improve the simulation efficiency in the framework of indirect sampling. By applying this method to a groundwater flow model, we demonstrate its better accuracy when compared to bruteforce MCMC simulation results.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5298
 Format
 Thesis
 Title
 Numerical Methods for Deterministic and Stochastic Nonlocal Problem in Diffusion and Mechanics.
 Creator

Chen, Xi, Gunzburger, Max, Wang, Xiaoming, Peterson, Janet, Wang, Xiaoqiang, Ye, Ming, Burkardt, John, Department of Scientific Computing, Florida State University
 Abstract/Description

In this dissertation, the recently developed peridynamic nonlocal continuum model for solid mechanics is extensively studied, specifically, the numerical methods for the deterministic and stochastic steadystate peridynamics models. In contrast to the classical partial differential equation models, peridynamic model is an integrodifferential equation that does not involve spatial derivatives of the displacement field. As a result, the peridynamic model admits solutions having jump...
Show moreIn this dissertation, the recently developed peridynamic nonlocal continuum model for solid mechanics is extensively studied, specifically, the numerical methods for the deterministic and stochastic steadystate peridynamics models. In contrast to the classical partial differential equation models, peridynamic model is an integrodifferential equation that does not involve spatial derivatives of the displacement field. As a result, the peridynamic model admits solutions having jump discontinuities so that it has been successfully applied to the fracture problems. This dissentation consists of three major parts. The first part focuses on the onedimensional steadystate peridynamics model. Based on a variational formulation, continuous and discontinuous Galerkin finite element methods are developed for the peridynamic model. Optimal convergence rates for different continuous and discontinuous manufactured solutions are obtained. A strategy for identifying the discontinuities of the solution is developed and implemented. The convergence of peridynamics model to classical elasticity model is studied. Some relevant nonlocal problems are also considered. In the second part, we focus on the twodimensional steadystate peridynamics model. Based on the numerical strategies and results from the onedimensional peridynamics model, we developed and implemented the corresponding approaches for the twodimensional case. Optimal convergence rates for different continuous and discontinuous manufactured solutions are obtained. In the third part, we study the stochastic peridynamics model. We focus on a version of peridynamics model whose forcing terms are described by a finitedimensional random vector, which is often called the finitedimensional noise assumption. Monte Carlo methods, stochastic collocation with full tensor product and sparse grid methods based on this stochastic peridynamics model are implemented and compared.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4753
 Format
 Thesis
 Title
 High Order LongTime Accurate Methods for the StokesDarcy System and Uncertainty Quantification of Contaminant Transport.
 Creator

Sun, Dong, Wang, Xiaoming, Gunzburger, Max D., Wang, Xiaoqiang, Ewald, Brian D., Cogan, Nicholas G., Florida State University, College of Arts and Sciences, Department of...
Show moreSun, Dong, Wang, Xiaoming, Gunzburger, Max D., Wang, Xiaoqiang, Ewald, Brian D., Cogan, Nicholas G., Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

The dissertation includes two parts. The first part consists of designing and analyzing high order longtime accurate numerical methods for StokesDarcy system. We propose second and thirdorder efficient and longtime accurate numerical methods, called IMplicitEXplicit methods (IMEX) for the coupled StokesDarcy system. Although the original continuum StokesDarcy PDE system is fully coupled, our algorithm is capable of decoupling the system into two subsystems so that a single Stokes and...
Show moreThe dissertation includes two parts. The first part consists of designing and analyzing high order longtime accurate numerical methods for StokesDarcy system. We propose second and thirdorder efficient and longtime accurate numerical methods, called IMplicitEXplicit methods (IMEX) for the coupled StokesDarcy system. Although the original continuum StokesDarcy PDE system is fully coupled, our algorithm is capable of decoupling the system into two subsystems so that a single Stokes and a single Darcy system can be computed in a parallel fashion without iteration. All the schemes we proposed are proven to be unconditionally stable and longtime stable. The bound on the error is uniformintime, which is among the first of this kind for second and thirdorder methods of StokesDarcy system. Error estimates for the second order BackwardDifferentiation scheme are proved. The second part concerns the Uncertainty of Quantification (UQ) of the contaminant transport. We compute the convectiondiffusion equation with Streamline Upwind PetrovGalerkin (SUPG) method. The quantity of interest is acquired using Monte Carlo and Sparse Grid methods in order to study the sensitivity with respect to the random parameters.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9692
 Format
 Thesis
 Title
 Numerical Analysis of Nonlocal Problems.
 Creator

Guan, Qingguang, Gunzburger, Max D., Wang, Xiaoming, Peterson, Janet S., Burkardt, John V., Wang, Xiaoqiang, Florida State University, College of Arts and Sciences, Department...
Show moreGuan, Qingguang, Gunzburger, Max D., Wang, Xiaoming, Peterson, Janet S., Burkardt, John V., Wang, Xiaoqiang, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

In this work, several nonlocal problems are studied. Analysis and computation have been done for these problems. Firstly, we consider the timedependent nonlocal diffusion and wave equations, formulated in the peridynamics setting. Initial and boundary data are given. For nonlocal diffusion equation, the time derivative is approximated using either an explicit Forward Euler, or implicit Backward Euler scheme. For nonlocal wave equation, we get the dispersion relations and use the Newmark...
Show moreIn this work, several nonlocal problems are studied. Analysis and computation have been done for these problems. Firstly, we consider the timedependent nonlocal diffusion and wave equations, formulated in the peridynamics setting. Initial and boundary data are given. For nonlocal diffusion equation, the time derivative is approximated using either an explicit Forward Euler, or implicit Backward Euler scheme. For nonlocal wave equation, we get the dispersion relations and use the Newmark method to discretize the equation. We have reformulated the standard timestep stability conditions, in light of the peridynamics formulation. Also we have obtained convergence results. Secondly, we consider the spacetime fractional diffusion equation which is used to model anomalous diffusion in physics. Finite difference, finite element and other methods are used to solve it. For finite difference method, the stability of the numerical schemes is well studied. However, for finite element method, we have not found the results for the stability of the θ schemes, especially for the explicit scheme. Here we get the stability and convergence results for all schemes with 0 ≤ θ ≤ 1. Thirdly, an obstacle problem for a nonlocal operator equation is considered; the operator is a nonlocal integral analogue of the Laplacian operator and, as a special case, reduces to the fractional Laplacian. In the analysis of classical obstacle problems for the Laplacian, the obstacle is taken to be a smooth function. For the nonlocal obstacle problem, obstacles are allowed to have jump discontinuities. We cast the nonlocal obstacle problem as a minimization problem wherein the solution is constrained to lie above the obstacle. We prove the existence and uniqueness of a solution in an appropriate function space. Then, the well posedness and convergence of finite element approximations are demonstrated. The results of numerical experiments are provided that illustrate the theoretical results and the differences between solutions of the nonlocal and local obstacle problems. Then we use sparse grid collocation, reduced basis and simplified reduced basis methods to solve nonlocal diffusion equation with random input data. Regularity of the solution and the convergence results for numerical methods are proved. The efficiency of these methods for solving the problem is investigated. As the radius of the spatial interaction zone changes, the computation cost varies due to the density of the stiffness matrix. This is quite different from local problems. Finally, the 1d nonlocal diffusion equation is solved by a continuous piecewiselinear collocation method using a uniform mesh. The time derivative is approximated using any of forward Euler, backward Euler, or CrankNicolson scheme. By developing a technique to deal with the singular integral, we are able to extend the method so that its validity is extended to include the case 1/2 ≤ s [less than] 1. We also derive stability conditions and convergence rates.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Guan_fsu_0071E_13425
 Format
 Thesis
 Title
 A Multiscale Implementation of Finite Element Methods for Nonlocal Models of Mechanics and Diffusion.
 Creator

Xu, Feifei, Gunzburger, Max D., Wang, Xiaoming, Burkardt, John V., Wang, Xiaoqiang, Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

The nonlocal models considered are free of spatial derivatives and thus are suitable for modeling problems with solutions exhibiting defects such as fractures in solids. Those models feature a horizon parameter that specifies the maximum extent of nonlocal interactions. A multiscale finite element implementation in one dimension and two dimensions of the nonlocal models is developed by taking advantage of the proven fact that, for smooth solutions, the nonlocal models reduce, as the horizon...
Show moreThe nonlocal models considered are free of spatial derivatives and thus are suitable for modeling problems with solutions exhibiting defects such as fractures in solids. Those models feature a horizon parameter that specifies the maximum extent of nonlocal interactions. A multiscale finite element implementation in one dimension and two dimensions of the nonlocal models is developed by taking advantage of the proven fact that, for smooth solutions, the nonlocal models reduce, as the horizon parameter tends to zero, to wellknown local partial differential equations models. The implementation features adaptive abrupt mesh refinement based on the detection of defects and resulting in an abrupt transition between refined elements that contain defects and unrefined elements that do not do so. Additional difficulties encountered in the implementation that are overcome are the design of accurate quadrature rules for stiffness matrix construction that are valid for any combination of the grid size and horizon parameter. As a result, the methodology developed can attain optimal accuracy at very modest additional costs relative to situations for which the solution is smooth. Portions of the methodology can also be used for the optimal approximation, by piecewise linear polynomials, of given functions containing discontinuities. Several numerical examples are provided to illustrate the efficacy of the multiscale methodology.
Show less  Date Issued
 2015
 Identifier
 FSU_2016SP_Xu_fsu_0071E_12974
 Format
 Thesis
 Title
 A Spectral Element Method to Price Single and MultiAsset European Options.
 Creator

Zhu, Wuming, Kopriva, David A., Huﬀer, Fred, Case, Bettye Anne, Kercheval, Alec N., Okten, Giray, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

We develop a spectral element method to price European options under the BlackScholes model, Merton's jump diffusion model, and Heston's stochastic volatility model with one or two assets. The method uses piecewise high order Legendre polynomial expansions to approximate the option price represented pointwise on a GaussLobatto mesh within each element. This piecewise polynomial approximation allows an exact representation of the nonsmooth initial condition. For options with one asset under...
Show moreWe develop a spectral element method to price European options under the BlackScholes model, Merton's jump diffusion model, and Heston's stochastic volatility model with one or two assets. The method uses piecewise high order Legendre polynomial expansions to approximate the option price represented pointwise on a GaussLobatto mesh within each element. This piecewise polynomial approximation allows an exact representation of the nonsmooth initial condition. For options with one asset under the jump diffusion model, the convolution integral is approximated by high order GaussLobatto quadratures. A second order implicit/explicit (IMEX) approximation is used to integrate in time, with the convolution integral integrated explicitly. The use of the IMEX approximation in time means that only a block diagonal, rather than full, system of equations needs to be solved at each time step. For options with two variables, i.e., two assets under the BlackScholes model or one asset under the stochastic volatility model, the domain is subdivided into quadrilateral elements. Within each element, the expansion basis functions are chosen to be tensor products of the Legendre polynomials. Three iterative methods are investigated to solve the system of equations at each time step with the corresponding second order time integration schemes, i.e., IMEX and CrankNicholson. Also, the boundary conditions are carefully studied for the stochastic volatility model. The method is spectrally accurate (exponentially convergent) in space and second order accurate in time for European options under all the three models. Spectral accuracy is observed in not only the solution, but also in the Greeks.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0513
 Format
 Thesis
 Title
 Efficient and Accurate Numerical Schemes for Long Time Statistical Properties of the Infinite Prandtl Number Model for Convection.
 Creator

Woodruff, Celestine, Wang, Xiaoming, Sang, QingXiang Amy, Case, Bettye Anne, Ewald, Brian D., Gunzburger, Max D., Florida State University, College of Arts and Sciences,...
Show moreWoodruff, Celestine, Wang, Xiaoming, Sang, QingXiang Amy, Case, Bettye Anne, Ewald, Brian D., Gunzburger, Max D., Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

In our work we analyze and implement numerical schemes for the infinite Prandtl number model for convection. This model describes the convection that is a potential driving force behind the flow and temperature of the Earth's mantle. There are many schemes available, but most are given with no mention of their ability to adequately capture the long time statistical properties of the model. We investigate schemes with the potential to actually capture these statistics. We further show...
Show moreIn our work we analyze and implement numerical schemes for the infinite Prandtl number model for convection. This model describes the convection that is a potential driving force behind the flow and temperature of the Earth's mantle. There are many schemes available, but most are given with no mention of their ability to adequately capture the long time statistical properties of the model. We investigate schemes with the potential to actually capture these statistics. We further show numerically that our schemes align with current knowledge of the model's characteristics at low Rayleigh numbers.
Show less  Date Issued
 2015
 Identifier
 FSU_2015fall_Woodruff_fsu_0071E_12813
 Format
 Thesis
 Title
 SpaceTime Spectral Element Methods in Fluid Dynamics and Materials Science.
 Creator

Pei, Chaoxu, Sussman, Mark, Hussaini, M. Yousuff, Dewar, William K., Cogan, Nicholas G., Wang, Xiaoming, Florida State University, College of Arts and Sciences, Department of...
Show morePei, Chaoxu, Sussman, Mark, Hussaini, M. Yousuff, Dewar, William K., Cogan, Nicholas G., Wang, Xiaoming, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

In this manuscript, we propose spacetime spectral element methods to solve problems arising from fluid dynamics and materials science. Many engineering applications require one to solve complex problems, such as flows containing multiscale structure in either space or time or both. It is straightforward that highorder methods are always more accurate and efficient than loworder ones for solving smooth problems. For example, spectral element methods can achieve a given level of accuracy...
Show moreIn this manuscript, we propose spacetime spectral element methods to solve problems arising from fluid dynamics and materials science. Many engineering applications require one to solve complex problems, such as flows containing multiscale structure in either space or time or both. It is straightforward that highorder methods are always more accurate and efficient than loworder ones for solving smooth problems. For example, spectral element methods can achieve a given level of accuracy with significantly fewer degrees of freedom compared to methods with algebraic convergence rates, e.g., finite difference methods. However, when it comes to complex problems, a high order method should be augmented with, e.g., a level set method or an artificial viscosity method, in order to address the issues caused by either sharp interfaces or shocks in the solution. Complex problems considered in this work are problems with solutions exhibiting multiple scales, i.e., the Stefan problem, nonlinear hyperbolic problems, and problems with smooth solutions but forces exhibiting disparate temporal scales, such as advection, diffusion and reaction processes. Correspondingly, two families of spacetime spectral element methods are introduced in order to achieve spectral accuracy in both space and time. The first category of spacetime methods are the fully implicit spacetime discontinuous Galerkin spectral element methods. In the fully implicit spacetime methods, time is treated as an additional dimension, and the model equation is rewritten into a spacetime formulation. The other category of spacetime methods are specialized for problems exhibiting multiple time scales: multiimplicit spacetime spectral element methods are developed. The method of lines approach is employed in the multiimplicit spacetime methods. The model is first discretized by a discontinuous spectral element method in space, and the resulting ordinary differential equations are then solved by a new multiimplicit spectral deferred correction method. A novel fully implicit spacetime discontinuous Galerkin (DG) spectral element method is presented to solve the Stefan problem in an Eulerian coordinate system. This method employs a level set procedure to describe the timeevolving interface. To deal with the prior unknown interface, a backward transformation and a forward transformation are introduced in the spacetime mesh. By combining an Eulerian description with a Lagrangian description, the issue of dealing with the implicitly defined arbitrary shaped spacetime elements is avoided. The backward transformation maps the unknown timevarying interface in the fixed frame of reference to a known stationary interface in the moving frame of reference. In the moving frame of reference, the transformed governing equations, written in the spacetime framework, are discretized by a DG spectral element method in each spacetime slab. The forward transformation is used to update the level set function and then to project the solution in each phase onto the new corresponding timedependent domain. Two options for calculating the interface velocity are presented, and both options exhibit spectral accuracy. Benchmark tests in one spatial dimension indicate that the method converges with spectral accuracy in both space and time for the temperature distribution and the interface velocity. The interrelation between the interface position and the temperature makes the Stefan problem a nonlinear problem; a Picard iteration algorithm is introduced in order to solve the nonlinear algebraic system of equations and it is found that just a few iterations lead to convergence. We also apply the fully implicit spacetime DG spectral element method to solve nonlinear hyperbolic problems. The spacetime method is combined with two different approaches for treating problems with discontinuous solutions: (i) spacetime dependent artificial viscosity is introduced in order to capture discontinuities/shocks, and (ii) the sharp discontinuity is tracked with spacetime spectral accuracy, as it moves through the grid. To capture the discontinuity whose location is initially unknown, an artificial viscosity term is strategically introduced, and the amount of artificial viscosity varies in time within a given spacetime slab. It is found that spectral accuracy is recovered everywhere except in the "troublesome element(s)'' where the unresolved steep/sharp gradient exists. When the location of a discontinuity is initially known, a spacetime spectrally accurate tracking method has been developed so that the spectral accuracy of the position of the discontinuity and the solution on either side of the discontinuity is preserved. A Picard iteration method is employed to handle nonlinear terms. Within each Picard iteration, a linear system of equations is solved, which is derived from the spacetime DG spectral element discretization. Spectral accuracy in both space and time is first demonstrated for the Burgers' equation with a smooth solution. For tests with discontinuities, the present spacetime method enables better accuracy at capturing the shock strength in the element containing shock when higher order polynomials in both space and time are used. Moreover, the spectral accuracy of the shock speed and location is demonstrated for the solution of the inviscid Burgers' equation obtained by the shock tracking method, and the sensitivity of the number of Picard iterations to the temporal order is discussed. The dynamics of many physical and biological systems involve two or more processes with a wide difference of characteristic time scales, e.g., problems with advection, diffusion and reaction processes. The computational cost of solving a coupled nonlinear system of equations is expensive for a fully implicit (i.e., "monolithic") spacetime method. Thus, we develop another type of a spacetime spectral element method, which is referred to as the multiimplicit spacetime spectral element method. Rather than coupling space and time together, the method of lines is used to separate the discretization of space and time. The model is first discretized by a discontinuous spectral element method in space and the resulting ordinary differential equations are then solved by a new multiimplicit spectral deferred correction method. The present multiimplicit spectral deferred correction method treats processes with disparate temporal scales independently, but couples them iteratively by a series of deferred correction steps. Compared to lower order operator splitting methods, the splitting error in the multiimplicit spectral deferred correction method is eliminated by exploiting an iterative coupling strategy in the deferred correction procedure. For the spectral element discretization in space, two advective flux reconstructions are proposed: extended elementwise flux reconstruction and nonextended elementwise flux reconstruction. A loworder Istable building block time integration scheme is introduced as an explicit treatment for the hyperbolic terms in order to obtain a stable and efficient building block for the spectrally accurate spacetime scheme along with these two advective flux reconstructions. In other words, we compare the extended elementwise reconstruction with Istable building block scheme with the nonextended elementwise reconstruction with Istable building block scheme. Both options exhibit spectral accuracy in space and time. However, the solutions obtained by extended elementwise flux reconstruction are more accurate than those yielded by nonextended elementwise flux reconstruction with the same number of degrees of freedom. The spectral convergence in both space and time is demonstrated for advectiondiffusionreaction problems. Two different coupling strategies in the multiimplicit spectral deferred correction method are also investigated and both options exhibit spectral accuracy in space and time.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Pei_fsu_0071E_13972
 Format
 Thesis
 Title
 NoReference Natural Image/Video Quality Assessment of Noisy, Blurry, or Compressed Images/Videos Based on Hybrid Curvelet, Wavelet and Cosine Transforms.
 Creator

Shen, Ji, Erlebacher, Gordon, Bellenot, Steve, Bertram, Richard, Sussman, Mark, Wang, Xiaoming, Liu, Xiuwen, Department of Mathematics, Florida State University
 Abstract/Description

In this thesis, we first propose a new Image Quality Assessment (IQA) method based on a hybrid of curvelet, wavelet, and cosine transforms, called the Hybrid Noreference (HNR) model. From the properties of natural scene statistics, the peak coordinates of the transformed coefficient histogram of filtered natural images occupy welldefined clusters in peak coordinate space, which makes noreference possible. Compared to other methods, HNR has three benefits: (1) It is a noreference method...
Show moreIn this thesis, we first propose a new Image Quality Assessment (IQA) method based on a hybrid of curvelet, wavelet, and cosine transforms, called the Hybrid Noreference (HNR) model. From the properties of natural scene statistics, the peak coordinates of the transformed coefficient histogram of filtered natural images occupy welldefined clusters in peak coordinate space, which makes noreference possible. Compared to other methods, HNR has three benefits: (1) It is a noreference method applicable to arbitrary images without compromising the prediction accuracy of fullreference methods; (2) To the best of our knowledge, it is the only general noreference method wellsuited for four types of image filters: noise, blur, JPEG2000 and JPEG compression; (3) It has excellent performance for additional applications such as the classification of images with subtle differences, hard to detect by the human visual system, the classification of image filter types, and prediction of the noise or blur level of a compressed image. HNR was tested on VIVID (our image library) and LIVE(a public library). When tested against VIVID, HNR has an image quality prediction accuracy above 0.97 measured using correlation coefficients with an average RMS below 7%. Despite the fact that HNR does not use reference images, it compares favorably (except JPEG) to stateoftheart fullreference methods such as PSNR, SSIM, VIF, when tested on the LIVE image database. HNR also predicts noisy or blurry compressed images with a correlation above 0.98. In addition, we extend our image quality assessment methodology to three video quality assessment models. VideoHNR (VHNR) uses 3D curvelet and cosine transforms to study the relation between the extracted features and video quality. VelocityVideoHNR (VVHNR) considers video motion speed to further improve the accuracy of the metric. FrameHNR defines the video quality as the average of the image quality of each video frame. These metrics perform much better than PSNR, the most widely used algorithm.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1777
 Format
 Thesis
 Title
 An Optimal Control Problem for a TimeDependent GinzburgLandau Model of Superconductivity.
 Creator

Lin, Haomin, Peterson, Janet, Gunzburger, Max, Schwartz, Justin, Wang, Xiaoming, Horne, Rudy, Trenchea, Catalin, Department of Mathematics, Florida State University
 Abstract/Description

The motion of vortices in a Type II superconductor destroys the material's superconductivity because it dissipates energy and causes resistance. When a transport current is applied to a clean TypeII superconductor in the mixed state, the vortices will go into motion due to the induced Lorentz force and thus the superconductivity of the material is lost. However, various pinning mechanisms, such as normal inclusions, can inhibit vortex motion and pin the vortices to specific sites. We...
Show moreThe motion of vortices in a Type II superconductor destroys the material's superconductivity because it dissipates energy and causes resistance. When a transport current is applied to a clean TypeII superconductor in the mixed state, the vortices will go into motion due to the induced Lorentz force and thus the superconductivity of the material is lost. However, various pinning mechanisms, such as normal inclusions, can inhibit vortex motion and pin the vortices to specific sites. We demonstrate that the placement of the normal inclusion sites has an important effect on the largest electrical current that can be applied to the superconducting material while all vortices remain stationary. Here, an optimal control problem using a time dependent GinzburgLandau model is proposed to seek numerically the optimal locations of the normal inclusion sites. An analysis of this optimal control problem is performed, the existence of an optimal control solution is proved and a sensitivity system is given. We then derive a gradient method to solve this optimal control problem. Numerical simulations are performed and the results are presented and discussed.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd1334
 Format
 Thesis
 Title
 Impulse Control Problems under NonConstant Volatility.
 Creator

Moreno, Juan F. (Juan Felipe), Kercheval, Alec, Huﬀer, Fred, Beaumont, Paul, Nichols, Warren, Nolder, Craig, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

The objective of this dissertation is to study impulse control problems in situations where the volatility of the underlying process is not constant. First, we explore the case where the dynamics of the underlying process are modified for a fixed (or random with known probability distribution) period of time after each intervention of the impulse control. We propose a modified intervention operator to be used in the QuasiVariational Inequalities approach for solving impulse control problems,...
Show moreThe objective of this dissertation is to study impulse control problems in situations where the volatility of the underlying process is not constant. First, we explore the case where the dynamics of the underlying process are modified for a fixed (or random with known probability distribution) period of time after each intervention of the impulse control. We propose a modified intervention operator to be used in the QuasiVariational Inequalities approach for solving impulse control problems, and we formulate and prove a verification theorem for finding the Value Function of the problem and the optimal control. Secondly, we use a perturbation approach to tackle impulse control problems when the volatility of the underlying process is stochastic but meanreverting. The perturbation method permits to approximate the Value Function and the parameters of the optimal control. Finally, we present a numerical scheme to obtain solutions to impulse control problems with constant and stochastic volatility. Throughout the thesis we find explicit solutions to practical applications in financial mathematics; specifically, in optimal central bank intervention of the exchange rate and in optimal policy dividend payments.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd2271
 Format
 Thesis
 Title
 Nonlinear Dynamics Underlying Fast Bursting in Pituitary Cells.
 Creator

Teka, Wondimu Woubante, Bertram, Richard, Trombley, Paul Q., Tabak, Jöel, Cogan, Nick G., Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

Neurons and endocrine cells display various patterns of electrical activity, including periodic bursting. Bursting oscillations are characterized by the alternation between periods of fast spiking (the active phase) and quiescent periods (the silent phase), and are accompanied by slow variations in one or more slowly changing variables. Bursts are often more efficient than periodic spiking in evoking the release of neurotransmitter or hormone. The technique of twofast/oneslow analysis,...
Show moreNeurons and endocrine cells display various patterns of electrical activity, including periodic bursting. Bursting oscillations are characterized by the alternation between periods of fast spiking (the active phase) and quiescent periods (the silent phase), and are accompanied by slow variations in one or more slowly changing variables. Bursts are often more efficient than periodic spiking in evoking the release of neurotransmitter or hormone. The technique of twofast/oneslow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been identified with this technique, plateau and pseudoplateau bursting, are often observed in neurons and endocrine cells, respectively. These two types of bursting have very different properties and likely serve different functions. This latter point is supported by the divergent expression of the bursting patterns into different cell types, and raises the question of whether it is even possible for a model for one type of cell to produce bursting of the type seen in the other type without large changes to the model. Using fast/slow analysis, we show here that this is possible, and we provide a procedure for achieving this transition. This suggests that the mechanisms for bursting in endocrine cells are just quantitative variations of those for bursting in neurons. The twofast/oneslow analysis used to make the transition between plateau and pseudoplateau bursting, and to understand the dynamics of plateau bursting is of limited use for pseudoplateau bursting. Using a onefast/twoslow analysis technique, we show that pseudoplateau bursting is a canardinduced mixed mode oscillation. Using this technique, it is possible to determine the region of parameter space where bursting occurs as well as salient properties of the burst such as the number of spikes in the burst. Finally we show the relationship between the twofast/oneslow analysis and onefast/twoslow analysis techniques.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5219
 Format
 Thesis
 Title
 Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives.
 Creator

Liang, Tianyu, Kercheval, Alec N., Wang, Xiaoming, Liu, Ewald, Brian, Nichols, Warren D., Department of Mathematics, Florida State University
 Abstract/Description

A lot of attention has been paid to the stochastic volatility model where the volatility is randomly fluctuating driven by an additional Brownian motion. In our work, we change the mean level in the meanreverting process from a constant to a function of the underlying process. We apply our models to the pricing of both equity and interest rate derivatives. Throughout the thesis, a singular perturbation method is employed to derive closedform formulas up to first order asymptotic solutions....
Show moreA lot of attention has been paid to the stochastic volatility model where the volatility is randomly fluctuating driven by an additional Brownian motion. In our work, we change the mean level in the meanreverting process from a constant to a function of the underlying process. We apply our models to the pricing of both equity and interest rate derivatives. Throughout the thesis, a singular perturbation method is employed to derive closedform formulas up to first order asymptotic solutions. We also implement multiplicative noise to arithmetic OrnsteinUhlenbeck process to produce a wider variety of effects. Calibration and Monte Carlo simulation results show that the proposed model outperform Fouque's original stochastic volatility model during some particular window in history. A more efficient numerical scheme, the heterogeneous multiscale method (HMM), is introduced to simulate the multiscale differential equations discussed over the chapters.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4990
 Format
 Thesis
 Title
 Diffuse Interface Method for TwoPhase Incompressible Flows.
 Creator

Han, Daozhi, Wang, Xiaoming, Höflich, Peter, Gallivan, Kyle A., Kopriva, David A., Oberlin, Daniel M., Sussman, Mark, Florida State University, College of Arts and Sciences,...
Show moreHan, Daozhi, Wang, Xiaoming, Höflich, Peter, Gallivan, Kyle A., Kopriva, David A., Oberlin, Daniel M., Sussman, Mark, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

In this contribution, we focus on the study of multiphase flow using the phase field approach. Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications. For two fluids with matched density, the CahnHilliardNavierStokes system (CHNS) is a well...
Show moreIn this contribution, we focus on the study of multiphase flow using the phase field approach. Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications. For two fluids with matched density, the CahnHilliardNavierStokes system (CHNS) is a well accepted phase field model. We propose a novel second order in time numerical scheme for solving the CHNS system. The scheme is based on a second order convexsplitting for the CahnHilliard equation and pressureprojection for the NavierStokes equation. We show that the scheme is massconservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme. Thanks to the simple coupling of the scheme, we design an efficient Picard iteration procedure to further decouple the computation of CahnHilliard equation and NavierStokes equation. We implement the scheme by the mixed finite element method. Ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme. In addition, we propose a novel decoupled unconditionally stable numerical scheme for the simulation of twophase flow in a HeleShaw cell which is governed by the CahnHilliardHeleShaw system (CHHS). The temporal discretization of the CahnHilliard equation is based on a convexsplitting of the associated energy functional. Moreover, the capillary forcing term in the Darcy equation is separated from the pressure gradient at the time discrete level by using an operatorsplitting strategy. Thus the computation of the nonlinear CahnHilliard equation is completely decoupled from the update of pressure. Finally, a pressurestabilization technique is used in the update of pressure so that at each time step one only needs to solve a Poisson equation with constant coefficient. We show that the scheme is unconditionally stable. Numerical results are presented to demonstrate the accuracy and efficiency of our scheme. The CHNS system and CHHS system are two widely used phase field models for twophase flow in a single domain (either conduit or HeleShaw cell/porous media). There are applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, where multiphase flows in conduits and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. We present a family of phase field (diffusive interface) models for two phase flow in karstic geometry. These models, the socalled CahnHilliardStokesDarcy system, together with the associated interface boundary conditions are derived by utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws and are consistent with thermodynamics. For the analysis of the CahnHilliardStokesDarcy system, we show that there exists at least a global in time finite energy solution by the compactness argument. A weakstrong uniqueness result is also established, which says that the strong solution, if exists, is unique in the class of weak solutions. Finally, we propose and analyze two unconditionally stable numerical algorithms of first order and second order respectively, for solving the CHSD system. A decoupled numerical procedure for practical implementation of the schemes are also presented. The decoupling is realized through explicit discretization of the velocity in the CahnHilliard equation and extrapolation in time of the interface boundary conditions. At each time step, one only needs to solve a CahnHilliard type equation in the whole domain, a Darcy equation in porous medium, and a Stokes equation in conduit in a separate and sequential fashion. Two numerical experiments, boundary driven and buoyancy driven flows, are performed to illustrate the effectiveness of our scheme. Both numerical simulations are of physical interest for transport processes of twophase flow in karst geometry.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9609
 Format
 Thesis
 Title
 Understanding Climate Feedback Contributions to the Surface Temperature Response.
 Creator

Sejas, Sergio A., Cai, Ming, Wang, Xiaoming, Ellingson, R. G., Sura, Philip, Wu, Zhaohua, Florida State University, College of Arts and Sciences, Department of Earth, Ocean, and...
Show moreSejas, Sergio A., Cai, Ming, Wang, Xiaoming, Ellingson, R. G., Sura, Philip, Wu, Zhaohua, Florida State University, College of Arts and Sciences, Department of Earth, Ocean, and Atmospheric Science
Show less  Abstract/Description

Climate feedback mechanisms are known to substantially affect the surface temperature response to an external forcing. This study aims to advance our physical and quantitative understanding of forcing and feedback contributions to the surface temperature response to an external forcing. The dissertation begins with a comprehensive overview of the climate feedback concept and the frameworks used to interpret the effects of forcing and feedbacks on surface temperature. The climate feedback...
Show moreClimate feedback mechanisms are known to substantially affect the surface temperature response to an external forcing. This study aims to advance our physical and quantitative understanding of forcing and feedback contributions to the surface temperature response to an external forcing. The dissertation begins with a comprehensive overview of the climate feedback concept and the frameworks used to interpret the effects of forcing and feedbacks on surface temperature. The climate feedbackresponse analysis method (CFRAM), a relatively new climate feedback framework whose advantages over the traditional climate feedback analysis framework are delineated, is then used to study the seasonal surface temperature response to a doubling of CO2 in a global warming simulation of the NCAR CCSM4. This allows us for the first time to explain the major features of the seasonal warming structure quantitatively. Polar regions, for example, experience the largest warming and the greatest seasonal variation, with maximum warming in fall/winter and minimum warming in summer. In summer, the large cancelations between the shortwave and longwave cloud feedbacks and between the surface albedo feedback warming and the cooling from the ocean heat storage/dynamics feedback lead to a warming minimum. In polar winter, surface albedo and shortwave cloud feedbacks are nearly absent due to a lack of insolation. However, the ocean heat storage feedback relays the polar warming due to the surface albedo feedback from summer to winter, and the longwave cloud feedback warms the polar surface. Therefore, the seasonal variations in the cloud feedback, surface albedo feedback, and ocean heat storage/dynamics feedback, directly caused by the strong annual cycle of insolation, contribute primarily to the large seasonal variation of polar warming. Furthermore, the CO2 forcing, and water vapor and atmospheric dynamics feedbacks add to the maximum polar warming in fall/winter. The CFRAM allows for a processbased decomposition of the temperature response into individual contributions by the forcing and nontemperature feedbacks, which implicitly include the thermalradiative coupling (i.e., temperature feedback) effects between the surface and atmosphere. To uncover this hidden effect in the CFRAM, this study develops and introduces a method known as the surface feedbackresponse analysis method (SFRAM) to isolate the temperature feedback effects on surface temperature, allowing for a physical and quantitative understanding of the temperature feedback effects. The temperature feedback effect is found to be the most important contributor to the surface temperature change, accounting for nearly 76% of the global mean surface warming. From the CFRAM perspective, the temperature feedback effect is just the indirect effects of the forcing and nontemperature feedbacks. The SFRAM analysis, in conjunction with the CFRAM results, indicates that in general the indirect effects of the forcing and nontemperature feedbacks on the surface temperature change are larger than the direct effects; thus demonstrating the influence and strength of the temperature feedback effect in the CFRAM results. By isolating the temperature feedback loop, an understanding of why the indirect effects are generally larger than direct effects is achieved. The SFRAM also serves as a bridge to the traditional TOA feedback analysis. A comparison of the SFRAM results with those of the traditional TOA feedback analysis indicates the largest disparity in interpretation is given for the lapserate feedback, which is shown to just stem from a misinterpretation of the temperature feedback effects on surface temperature. A better and more intuitive explanation is achieved through the surface perspective of the SFRAM than the TOA perspective of the traditional feedback analysis. A reconciliation of the surface and TOA perspectives is achieved once the temperature feedback effects are included with the effects of the forcing and nontemperature feedbacks, as in the CFRAM analysis.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd9244
 Format
 Thesis
 Title
 RankConstrained Optimization: A Riemannian Manifold Approach.
 Creator

Zhou, Guifang, Gallivan, Kyle A., Van Dooren, Paul, Barbu, Adrian G. (Adrian Gheorghe), Ökten, Giray, Wang, Xiaoming, Florida State University, College of Arts and Sciences,...
Show moreZhou, Guifang, Gallivan, Kyle A., Van Dooren, Paul, Barbu, Adrian G. (Adrian Gheorghe), Ökten, Giray, Wang, Xiaoming, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

This dissertation considers optimization problems on a Riemannian matrix manifold ℳ⊆ℝ[superscript m x n] with an additional rank inequality constraint. A novel technique for building new rankrelated geometric objects from known Riemannian objects is developed and used as the basis for new approach to adjusting matrix rank during the optimization process. The new algorithms combine the dynamic update of matrix rank with stateoftheart rapidly converging and wellunderstood Riemannian...
Show moreThis dissertation considers optimization problems on a Riemannian matrix manifold ℳ⊆ℝ[superscript m x n] with an additional rank inequality constraint. A novel technique for building new rankrelated geometric objects from known Riemannian objects is developed and used as the basis for new approach to adjusting matrix rank during the optimization process. The new algorithms combine the dynamic update of matrix rank with stateoftheart rapidly converging and wellunderstood Riemannian optimization algorithms. A rigorous convergence analysis for the new methods addresses the tradeoffs involved in achieving computationally efficient and effective optimization. Conditions that ensure the ranks of all iterates become fixed eventually are given. This guarantees the desirable consequence that the new dynamicrank algorithms maintain the convergence behavior of the fixed rank Riemannian optimization algorithm used as the main computational primitive. The weighted lowrank matrix approximation problem and the lowrank approximation approach to the problem of quantifying the similarity of two graphs are used to empirically evaluate and compare the performance of the new algorithms with that of existing methods. The experimental results demonstrate the significant advantages of the new algorithms and, in particular, the importance of the new rankrelated geometric objects in efficiently determining a suitable rank for the minimizer.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9533
 Format
 Thesis
 Title
 Parameter Estimation for a Stochastic Volatility Model with Coupled Additive and Multiplicative Noise.
 Creator

Amusan, Ibukun O. O., Ewald, Brian, Okten, Giray, Fuelberg, Henry, Kercheval, Alec, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

In this dissertation we look at a stochastic volatility model with coupled additive and multiplicative noise. We begin by explaining the suitability of the model for the logarithm of volatility by looking at the skewness and kurtosis. We then proceed to estimate the five parameters of the model. The first two parameters are found using the method of least squares on successive observation pairs. Then the remaining three parameters are estimated by further using the maximum likelihood method...
Show moreIn this dissertation we look at a stochastic volatility model with coupled additive and multiplicative noise. We begin by explaining the suitability of the model for the logarithm of volatility by looking at the skewness and kurtosis. We then proceed to estimate the five parameters of the model. The first two parameters are found using the method of least squares on successive observation pairs. Then the remaining three parameters are estimated by further using the maximum likelihood method on the least squares residuals. This leads to a minimization problem with a function of three variables. Using the firstorder conditions, we get a system of three equations in three unknowns. After doing a change of variables and making a substitution, we find that the function to be minimized can be expressed as a function of two variables instead of the original three variables. The parameters for some stocks are then estimated for the coupled additive and multiplicative stochastic model and also for the OrnsteinUhlenbeck model. These estimated parameters are used to price European call options, and the prices for the coupled additive and multiplicative model, OrnsteinUhlenbeck model and BlackScholes model are compared.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7692
 Format
 Thesis
 Title
 Modeling, Analysis and Simulation of the StokesDarcy System with BeaversJoseph Interface Condition.
 Creator

Hua, Fei, Gunzburger, Max, Wang, Xiaoming, Hu, Xiaolong, Ewald, Brian, Horne, Rudy, Department of Mathematics, Florida State University
 Abstract/Description

In this dissertation, the coupling phenomenon of porous media flow and free flow is extensively studied, with an application to studying the solute transport in the groundwater system of karst aquifers. This dissertation consists of three major parts. The first part focuses on the modeling and wellposedness of the mathematical equations. The Stokes equations are used for the free flow part and the Darcy's law is used for the porous media flow part. This is called the StokesDarcy system. To...
Show moreIn this dissertation, the coupling phenomenon of porous media flow and free flow is extensively studied, with an application to studying the solute transport in the groundwater system of karst aquifers. This dissertation consists of three major parts. The first part focuses on the modeling and wellposedness of the mathematical equations. The Stokes equations are used for the free flow part and the Darcy's law is used for the porous media flow part. This is called the StokesDarcy system. To couple the two spatially nonoverlapping yet neighboring regions, BeaversJoseph interface condition is used and studied. We show that the transient StokeDarcy system with BeaversJoseph condition is wellposed when a proper scaling parameter is introduced that essentially brings the two physical processes to the same time scale. The steady state problem with BeaversJoseph condition is also studied and the wellpossedness is obtained under some assumptions of the BeaversJoseph parameter α. We then, in the second part, put the StokesDarcy system under finite element analysis. The analysis is conducted under the framework of a Gårding type inequality established in the first part. First, the spatially semidiscretized problem is studied. Then, a Stokes type projection is devised to aid the convergence rate analysis for the fully discretized system. We obtain a rigorous error bound on the L2 norm with suitable regularity assumptions. The rate is then verified by numerical tests using the TaylorHood and quadratic elements pair for the free flow and porous media flow respectively. In the third part, the research is further carried on to compare the StokesDarcy system with conventional models that is used to study the karst aquifer, an important and susceptible groundwater system. In particular, the coupled continuum pipe flow (CCPF) model, the most conventionally used one, is picked as a the counter part to the StokesDarcy model. By using the laboratory experiment results as reference, we compare the two models in the aspects of flow rate, head distribution and ability to predict contaminant transport. We reject the conventional wisdom in choosing the exchange coefficient αex in the CCPF model and propose a new region where the coefficient should fall in. In the new parameter region, we compare the StokesDarcy model and CCFP model with different boundary and geometry setting to motivate the necessity of switching away from the crude and less physically reasonable CCPF model.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd3686
 Format
 Thesis
 Title
 Sparse Approximation and Its Applications.
 Creator

Li, Qin, Erlebacher, Gordon, Wang, Xiaoming, Hart, Robert, Peterson, Janet, Sussman, Mark, Gallivan, Kyle A., Department of Mathematics, Florida State University
 Abstract/Description

In this thesis, we tackle the fundamental problem of how to effectively and reliably calculate sparse solutions to underdetermined systems of equations. This class of problems is found in applied mathematics, electrical engineering, statistics, geophysics, just to name a few. This dissertation concentrates on developing efficient and robust solution algorithms, and applies them in several applications in the field of signal/image processing. The first contribution concerns the development of...
Show moreIn this thesis, we tackle the fundamental problem of how to effectively and reliably calculate sparse solutions to underdetermined systems of equations. This class of problems is found in applied mathematics, electrical engineering, statistics, geophysics, just to name a few. This dissertation concentrates on developing efficient and robust solution algorithms, and applies them in several applications in the field of signal/image processing. The first contribution concerns the development of a new Iterative Shrinkage algorithm based on Surrogate Function, ISSFK, for finding the best Kterm approximation to an image. In this problem, we seek to represent an image with K elements from an overcomplete dictionary. We present a proof that this algorithm converges to a local minimum of the NP hard sparsity constrained optimization problem. In addition, we choose curvelets as the dictionary. The approximation obtained by our approach achieves higher PSNR than that of the best Kterm wavelet (CohenDaubechiesFauraue 97) approximation. We extends ISSF to the application of Morphological Component Analysis, which leads to the second contribution, a new algorithm MCAISSF with an adaptive thresholding strategy. The adaptive MCAISSF algorithm approximates the problem from the synthesis approach, and it is the only algorithm that incorporate an adaptive strategy to update its algorithmic parameter. Compared to the existent MCA algorithms, our method is more efficient and is parameter free in the thresdholding update. The third contribution concerns the nonconvex optimization problems in Compressive Sensing (CS), which is an important extension of sparse approximation. We propose two new iterative reweighted algorithms based on Alternating Direction Method of Multiplier, IR1ADM and IR2ADM, to solve the ellp,0.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd1399
 Format
 Thesis
 Title
 Asymptotic Behaviour of Convection in Porous Media.
 Creator

Parshad, Rana Durga, Wang, Xiaoming, Ye, Ming, Case, Bettye Anne, Ewald, Brian, N.Kercheval, Alec, Nolder, Craig, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation investigates asymptotic behaviour of convection in a fluid saturated porous medium. We analyse the DarcyBoussinesq system under perturbation of the DarcyPrandtl number parameter. In very tightly packed media this parameter is of very large order and can be driven to infinity to yield the infinite DarcyPrandtl number model. We show convergence of global attractors and invariant measures of the DarcyBoussinesq system to that of the infinite DarcyPrandtl number model with...
Show moreThis dissertation investigates asymptotic behaviour of convection in a fluid saturated porous medium. We analyse the DarcyBoussinesq system under perturbation of the DarcyPrandtl number parameter. In very tightly packed media this parameter is of very large order and can be driven to infinity to yield the infinite DarcyPrandtl number model. We show convergence of global attractors and invariant measures of the DarcyBoussinesq system to that of the infinite DarcyPrandtl number model with respect to perturbation of the DarcyPrandtl number parameter.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd2182
 Format
 Thesis
 Title
 Statistical Analysis on Object Spaces with Applications.
 Creator

Yao, Kouadio David, Patrangenaru, Victor, Kercheval, Alec N., Liu, Xiuwen, Mio, Washington, Wang, Xiaoming, Florida State University, College of Arts and Sciences, Department of...
Show moreYao, Kouadio David, Patrangenaru, Victor, Kercheval, Alec N., Liu, Xiuwen, Mio, Washington, Wang, Xiaoming, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

Most of the data encountered is bounded nonlinear data. The Universe is bounded, planets are sphere like shaped objects, and life growing on Earth comes in various shapes and colors that can hardly be represented as points on a linear space, and even if the object space they sit on is embedded in a Euclidean space, their mean vector can not be represented as a point on that object space, except for the case when such space is convex. To address this misgiving, since the mean vector is the...
Show moreMost of the data encountered is bounded nonlinear data. The Universe is bounded, planets are sphere like shaped objects, and life growing on Earth comes in various shapes and colors that can hardly be represented as points on a linear space, and even if the object space they sit on is embedded in a Euclidean space, their mean vector can not be represented as a point on that object space, except for the case when such space is convex. To address this misgiving, since the mean vector is the minimizer of the expected square distance, following Fr\'echet (1948), on a compact metric space, one may consider both minimizers and maximizers of the expected square distance to a given point on the object space as mean, respectively {\bf antimean} of a given random point. Of all distances on a object space, one considers here the chord distance associated with an embedding of the object space, since for such distances one can give a necessary and sufficient condition for the existence of a unique Fr\'echet mean (respectively Fr\'echet antimean). For such distributions these location parameters are called extrinsic mean (respectively extrinsic antimean), and the corresponding sample statistics are consistent estimators of their population counterparts. Moreover one derives the limit distribution of such estimators around a mean located at a smooth extrinsic antimean. Extrinsic analysis is thus a general framework that allows one to run object data analysis on nonlinear object spaces that can be embedded in a numerical space. In particular one focuses on VeroneseWhitney (VW) means and antimeans of 3D projective shapes of configurations extracted from digital camera images. The 3D data extraction is greatly simplified by an RGB based algorithm followed by the FaugerasHartleyGuptaChen 3D reconstruction method. In particular one derives two sample tests for face analysis based on projective shapes, and more generally a MANOVA on manifolds method to be used in 3D projective shape analysis. The manifold based approach is also applicable to financial data analysis for exchange rates.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Yao_fsu_0071E_13605
 Format
 Thesis
 Title
 Nonlinear SchrödingerType Systems: Complex Lattices and NonParaxiality.
 Creator

Cole, Justin, Musslimani, Ziad H., Höflich, Peter A., Wang, Xiaoming, Moore, M. Nicholas J. (Matthew Nicholas J.), Florida State University, College of Arts and Sciences,...
Show moreCole, Justin, Musslimani, Ziad H., Höflich, Peter A., Wang, Xiaoming, Moore, M. Nicholas J. (Matthew Nicholas J.), Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

This thesis investigates nonlinear systems that are dispersive and conservative in nature and wellapproximated by the nonlinear Schrödinger (NLS) equation. The NLS equation is the prototypical equation for describing such phenomena and it has been utilized in a large number of physical systems. This work considers novel applications and exotic parameter regimes that fall inside the class of solutions well described by nonlinear Schrödingertype systems. A brief historical, physical, and...
Show moreThis thesis investigates nonlinear systems that are dispersive and conservative in nature and wellapproximated by the nonlinear Schrödinger (NLS) equation. The NLS equation is the prototypical equation for describing such phenomena and it has been utilized in a large number of physical systems. This work considers novel applications and exotic parameter regimes that fall inside the class of solutions well described by nonlinear Schrödingertype systems. A brief historical, physical, and mathematical introduction to deriving the NLS equation and its variants is presented. The topics considered in detail cover optical systems in various media and are naturally divided into two parts: nonparaxiality through the inclusion of higherorder dispersion/diffraction and beam propagation in the presence of complex lattices. The higherorder dispersion/diffraction effects on soliton solutions are considered in detail. The propagation of a short soliton pulse as it travels down a fiber optic in the presence of a linear timeperiodic potential is considered. Due to the short duration of the pulse fourthorder dispersive effects are relevant. The band gap structure is determined using FloquetBloch theory and the shape of its dispersion curves as a function of the fourthorder dispersion coupling constant β is discussed. Several features not observed in the absence of highorder dispersion (β=0) are highlighted, such as a nonzero threshold value of potential strength below which there is no band gap and the formation of novel localized modes at large potential amplitudes. A higher order two band tight binding model is introduced that captures and intuitively explains most of the numerical results related to the spectral bands. Lattice solitons corresponding to spectral eigenvalues lying in the semiinfinite and first band gaps are constructed. Stability of various localized lattice modes is studied via linear stability analysis and direct numerical simulation. Next the spectral transverse instabilities of onedimensional solitary wave solutions to the twodimensional NLS equation with biharmoinc diffraction and subject to higherdimensional perturbations are studied. Physically, the inclusion of the biharmonic term corresponds to spatial beams with a narrow width in comparison to their wavelength. A linear boundary value problem governing the evolution of the transverse perturbations is derived. The eigenvalues of the perturbations are numerically computed and a finite band of unstable transverse modes is found to exist. In the long wavelength limit an asymptotic formula for the perturbation growth rate that agrees well with the numerical findings. Using a variational formulation based on Lagrangian model reduction, an approximate expression for the perturbation eigenvalues is obtained and its validity is compared with both the asymptotic and numerical results. The dynamics of a onedimensional soliton stripe in the presence of a transverse perturbation is studied using direct numerical simulations. The second half of the dissertation is concerned with beam propagation in the presence of complex lattices, in particular lattices that possess paritytime (PT) symmetries. A new family of nonhermitian optical potentials given in terms of double exponential periodic functions is introduced. The center of PTsymmetry is not around zero and the potential satisfies a shifted PTsymmetry relation at two distinct locations. These novel refractive index modulations are examined from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum and exceptional points in the band structure are studied in detail. In addition, the nonlinear properties of coherent structures in Kerr media is probed. The spatial symmetries of such lattice solitons follow the shifted PTsymmetric relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stability is critically dependent on their spatial symmetry point. In the final chapter a class of exact multicomponent constant energy solutions to a Manakov system in the presence of an external PTsymmetric complex potential is constructed. This type of uniform wave pattern displays a nontrivial phase whose spatial dependence is induced from the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogenous gain and loss. The constantintensity continuous waves are then used to perform a modulational instability analysis in the presence of both nonhermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using FourierFloquetBloch theory. The stability of the selffocusing and defocusing cases is considered and compared to the zeropotential results. Our linear stability results are supplemented with direct (nonlinear) numerical simulations.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Cole_fsu_0071E_13102
 Format
 Thesis
 Title
 Use of Multiple Satellite Total Ozone Observations within and Around Tropical Cyclones.
 Creator

Wang, Hui, Ellingson, R. G., Wang, Xiaoming, Hart, Robert E. (Robert Edward), Misra, Vasubandhu, Liu, Guosheng, Florida State University, College of Arts and Sciences,...
Show moreWang, Hui, Ellingson, R. G., Wang, Xiaoming, Hart, Robert E. (Robert Edward), Misra, Vasubandhu, Liu, Guosheng, Florida State University, College of Arts and Sciences, Department of Earth, Ocean, and Atmospheric Science
Show less  Abstract/Description

This study explores whether or not tropical cyclone (TC) structure information may be retrieved from satellite total ozone observations and how to link total ozone with analysis fields for potential application to TC vortex initialization schemes. Satellite total ozone retrievals from the Atmospheric Infrared Sounder (AIRS), the second Global Ozone Monitoring Experiment (GOME2), the Ozone Monitoring Instrument (OMI), and the Ozone Mapping and Profiler Suite (OMPS) are used in this study. The...
Show moreThis study explores whether or not tropical cyclone (TC) structure information may be retrieved from satellite total ozone observations and how to link total ozone with analysis fields for potential application to TC vortex initialization schemes. Satellite total ozone retrievals from the Atmospheric Infrared Sounder (AIRS), the second Global Ozone Monitoring Experiment (GOME2), the Ozone Monitoring Instrument (OMI), and the Ozone Mapping and Profiler Suite (OMPS) are used in this study. The study is divided into two portions: updating the quality control (QC) scheme for the AIRS total ozone data and examining applications of total ozone data in TC analyses. A modified QC scheme for AIRS total ozone is proposed to identify erroneous data while avoiding removal of potential useful data, as well as to keep the data consistent with a numerical prediction model. The modified QC scheme produces smaller bias and standard deviation of total ozone relative to the original AIRS QC scheme with less data being removed. Since ultraviolet (UV) retrieved total ozone generally suffers less cloud contamination, GOME2 total ozone is used to examine possible TC structures captured by the data. All the TCs in the 20102012 Atlantic Hurricane seasons are used. Detailed comparisons of total ozone from GOME2 and geopotential heights on isentropic surfaces from the European Centre for MediumRange Weather Forecasts (ECMWF) Interim Reanalysis are carried out for the representative case of Hurricane Earl (2010). It is shown that GOME2 total ozone can capture the characteristics of the storm center including the eye region and spiral bands. Changes in total ozone can also reveal the variations of the storm intensity. Alternatively, locally elevated total ozone in the hurricane eye region can be used to identify the upper tropospheric storm center, depending on the stage and the radius of the maximum winds of the storm. Further, the distribution of total ozone shows that the isentropic geopotential heights may have misplaced the vortex center. Total ozone and the 'aligned' geopotential heights at isentropic levels tend to form a linear relationship. Total ozone and geopotential heights correlate better in isentropic level range of 330K to 345K than at other isentropic levels, indicating better inference of the geopotential heights from total ozone at these isentropic levels. Stronger storms tend to have larger correlations of total ozone and geopotential heights at nearly all isentropic levels examined in this study. Intersatellite calibration is shown to be necessary for better use of ozone observations in TC applications. A general intersatellite total ozone calibration is carried out during August of 2012 with total ozone data from the four instruments. Total ozone from different instruments shows a dependence on cloud fraction, solar zenith angle (SZA), geolocation, and possibly aerosols. Overall, GOME2, OMI and OMPS ozone observations agree well globally for both clearsky and cloudy conditions, whereas AIRS shows large relative differences in both the southern Polar Regions and in the 30S30N tropical regions. The large relative errors in the southern Polar Regions are associated with large AIRS SZAs, while the large relative errors in the 30S30N zone may be caused by aerosol contamination and high cirrus clouds. Latitudinally varying coefficients are derived to remove large, zonally varying biases. Hurricane Michael (2012) is chosen to illustrate the resulting impacts of the intersatellite total ozone calibrations on an individual TC's structure information. It is shown that the transformed observations are more comparable spatially and radially than the original ones. The impacts of the calibrated total ozone on the regression models linking isentropic geopotential heights and total ozone formed from all the TCs are examined. The calibration improves the performance of AIRS regression models at nearly all isentropic levels by increasing the explained variance and decreasing the rootmeansquareerror (RMSE), while it does not change much with the regression models for OMI and GOME2. Overall, stronger storms tend to have larger inference of geopotential heights at all the isentropic levels from these total ozone observations before and after the intersatellite calibration. The intersatellite total ozone calibration improves the comparability among different regression models. The resulting more consistent regression models based on TC's intensities can provide more consistent initial analysis fields from different total ozone observations for potential hurricane vortex initialization application.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9481
 Format
 Thesis
 Title
 Embryonic Stem Cells Promoting Macrophage Survival and Function are Crucial for Teratoma Development.
 Creator

Chen, Tianxiang, Wang, Xi, Guo, Lei, Wu, Mingmei, Duan, Zhaoxia, Lv, Jing, Tai, Wenjiao, Renganathan, Hemamalini, Didier, Ruth, Li, Jinhua, Sun, Dongming, Chen, Xiaoming, He,...
Show moreChen, Tianxiang, Wang, Xi, Guo, Lei, Wu, Mingmei, Duan, Zhaoxia, Lv, Jing, Tai, Wenjiao, Renganathan, Hemamalini, Didier, Ruth, Li, Jinhua, Sun, Dongming, Chen, Xiaoming, He, Xijing, Fan, Jianqing, Young, Wise, Ren, Yi
Show less  Abstract/Description

Stem cell therapies have had tremendous potential application for many diseases in recent years. However, the tumorigenic properties of stem cells restrict their potential clinical application; therefore, strategies for reducing the tumorigenic potential of stem cells must be established prior to transplantation. We have demonstrated that syngeneic transplantation of embryonic stem cells (ESCs) provokes an inflammatory response that involves the rapid recruitment of bone marrowderived...
Show moreStem cell therapies have had tremendous potential application for many diseases in recent years. However, the tumorigenic properties of stem cells restrict their potential clinical application; therefore, strategies for reducing the tumorigenic potential of stem cells must be established prior to transplantation. We have demonstrated that syngeneic transplantation of embryonic stem cells (ESCs) provokes an inflammatory response that involves the rapid recruitment of bone marrowderived macrophages (BMDMs). ESCs are able to prevent mature macrophages from macrophage colonystimulating factor (MCSF) withdrawalinduced apoptosis, and thus prolong macrophage lifespan significantly by blocking various apoptotic pathways in an MCSFindependent manner. ESCs express and secrete IL34, which may be responsible for ESCpromoted macrophage survival. This antiapoptotic effect of ESCs involves activation of extracellular signalregulated kinase (ERK)1/2 and PI3K/Akt pathways and thus, inhibition of ERK1/2 and PI3K/AKT activation decreases ESCinduced macrophage survival. Functionally, ESCtreated macrophages also showed a higher level of phagocytic activity. ESCs further serve to polarize BMDMs into M2like macrophages that exhibit most tumorassociated macrophage phenotypic and functional features. ESCeducated macrophages produce high levels of arginase1, Tie2, and TNFα, which participate in angiogenesis and contribute to teratoma progression. Our study suggests that induction of M2like macrophage activation is an important mechanism for teratoma development. Strategies targeting macrophages to inhibit teratoma development would increase the safety of ESCbased therapies, inasmuch as the depletion of macrophages completely inhibits ESCinduced angiogenesis and teratoma development.
Show less  Date Issued
 20140704
 Identifier
 FSU_pmch_25071759, 10.3389/fimmu.2014.00275, PMC4082241, 25071759, 25071759
 Format
 Citation
 Title
 Rescuing macrophage normal function in spinal cord injury with embryonic stem cell conditioned media.
 Creator

Guo, Lei, Rolfe, Alyssa J., Wang, Xi, Tai, Wenjiao, Cheng, Zhijian, Cao, Kai, Chen, Xiaoming, Xu, Yunsheng, Sun, Dongming, Li, Jinhua, He, Xijing, Young, Wise, Fan, Jianqing,...
Show moreGuo, Lei, Rolfe, Alyssa J., Wang, Xi, Tai, Wenjiao, Cheng, Zhijian, Cao, Kai, Chen, Xiaoming, Xu, Yunsheng, Sun, Dongming, Li, Jinhua, He, Xijing, Young, Wise, Fan, Jianqing, Ren, Yi
Show less  Abstract/Description

Background: Macrophages play an important role in the inflammatory responses involved with spinal cord injury (SCI). We have previously demonstrated that infiltrated bone marrowderived macrophages (BMDMs) engulf myelin debris, forming myelinladen macrophages (myeM phi). These myeM phi promote disease progression through their proinflammatory phenotype, enhanced neurotoxicity, and impaired phagocytic capacity for apoptotic cells. We thus hypothesize that the excessive accumulation of mye...
Show moreBackground: Macrophages play an important role in the inflammatory responses involved with spinal cord injury (SCI). We have previously demonstrated that infiltrated bone marrowderived macrophages (BMDMs) engulf myelin debris, forming myelinladen macrophages (myeM phi). These myeM phi promote disease progression through their proinflammatory phenotype, enhanced neurotoxicity, and impaired phagocytic capacity for apoptotic cells. We thus hypothesize that the excessive accumulation of myeM phi is the root of secondary injury, and that targeting myeM phi represents an efficient strategy to improve the local inflammatory microenvironment in injured spinal cords and to further motor neuron function recovery. In this study, we administer murine embryonic stem cell conditioned media (ESCM) as a cellfree stem cell based therapy to treat a mouse model of SCI. Results: We showed that BMDMs, but not microglial cells, engulf myelin debris generated at the injury site. Phagocytosis of myelin debris leads to the formation of myeM phi in the injured spinal cord, which are surrounded by activated microglia cells. These myeM phi are proinflammatory and lose the normal macrophage phagocytic capacity for apoptotic cells. We therefore focus on how to trigger lipid efflux from myeM phi and thus restore their function. Using ESCM as an immune modulating treatment for inflammatory damage after SCI, we rescued myeM phi function and improved functional locomotor recovery. ESCM treatment on myeM phi resulted in improved exocytosis of internalized lipids and a normal capacity for apoptotic cell phagocytosis. Furthermore, when ESCM was administered intraperitoneally after SCI, animals exhibited significant improvements in locomotor recovery. Examination of spinal cords of the ESCM treated mice revealed similar improvements in macrophage function as well as a shift towards a more antiinflammatory environment at the lesion and parenchyma. Conclusions: The embryonic stem cell conditioned media can be used as an effective treatment for SCI to resolve inflammation and improve functional recovery while circumventing the complications involved in whole cell transplantation.
Show less  Date Issued
 20160506
 Identifier
 FSU_libsubv1_wos_000376866000001, 10.1186/s1304101602333
 Format
 Citation
 Title
 Rescuing macrophage normal function in spinal cord injury with embryonic stem cell conditioned media.
 Creator

Guo, Lei, Rolfe, Alyssa J, Wang, Xi, Tai, Wenjiao, Cheng, Zhijian, Cao, Kai, Chen, Xiaoming, Xu, Yunsheng, Sun, Dongming, Li, Jinhua, He, Xijing, Young, Wise, Fan, Jianqing, Ren...
Show moreGuo, Lei, Rolfe, Alyssa J, Wang, Xi, Tai, Wenjiao, Cheng, Zhijian, Cao, Kai, Chen, Xiaoming, Xu, Yunsheng, Sun, Dongming, Li, Jinhua, He, Xijing, Young, Wise, Fan, Jianqing, Ren, Yi
Show less  Abstract/Description

Macrophages play an important role in the inflammatory responses involved with spinal cord injury (SCI). We have previously demonstrated that infiltrated bone marrowderived macrophages (BMDMs) engulf myelin debris, forming myelinladen macrophages (myeMϕ). These myeMϕ promote disease progression through their proinflammatory phenotype, enhanced neurotoxicity, and impaired phagocytic capacity for apoptotic cells. We thus hypothesize that the excessive accumulation of myeMϕ is the root of...
Show moreMacrophages play an important role in the inflammatory responses involved with spinal cord injury (SCI). We have previously demonstrated that infiltrated bone marrowderived macrophages (BMDMs) engulf myelin debris, forming myelinladen macrophages (myeMϕ). These myeMϕ promote disease progression through their proinflammatory phenotype, enhanced neurotoxicity, and impaired phagocytic capacity for apoptotic cells. We thus hypothesize that the excessive accumulation of myeMϕ is the root of secondary injury, and that targeting myeMϕ represents an efficient strategy to improve the local inflammatory microenvironment in injured spinal cords and to further motor neuron function recovery. In this study, we administer murine embryonic stem cell conditioned media (ESCM) as a cellfree stem cell based therapy to treat a mouse model of SCI. We showed that BMDMs, but not microglial cells, engulf myelin debris generated at the injury site. Phagocytosis of myelin debris leads to the formation of myeMϕ in the injured spinal cord, which are surrounded by activated microglia cells. These myeMϕ are proinflammatory and lose the normal macrophage phagocytic capacity for apoptotic cells. We therefore focus on how to trigger lipid efflux from myeMϕ and thus restore their function. Using ESCM as an immune modulating treatment for inflammatory damage after SCI, we rescued myeMϕ function and improved functional locomotor recovery. ESCM treatment on myeMϕ resulted in improved exocytosis of internalized lipids and a normal capacity for apoptotic cell phagocytosis. Furthermore, when ESCM was administered intraperitoneally after SCI, animals exhibited significant improvements in locomotor recovery. Examination of spinal cords of the ESCM treated mice revealed similar improvements in macrophage function as well as a shift towards a more antiinflammatory environment at the lesion and parenchyma. The embryonic stem cell conditioned media can be used as an effective treatment for SCI to resolve inflammation and improve functional recovery while circumventing the complications involved in whole cell transplantation.
Show less  Date Issued
 20160506
 Identifier
 FSU_pmch_27153974, 10.1186/s1304101602333, PMC4858887, 27153974, 27153974, 10.1186/s1304101602333
 Format
 Citation
 Title
 Statistical Analysis of Karst Aquifer Pollution, Karst Flow Model Validation at Laboratory Scale, and Development of Seepage Meter.
 Creator

Castro, Roger Benito Pacheco, Ye, Ming (Professor of scientific computing), Chen, Gang, Wang, Xiaoming, Moore, M. Nicholas J. (Matthew Nicholas J.), Quaife, Bryan, Florida State...
Show moreCastro, Roger Benito Pacheco, Ye, Ming (Professor of scientific computing), Chen, Gang, Wang, Xiaoming, Moore, M. Nicholas J. (Matthew Nicholas J.), Quaife, Bryan, Florida State University, College of Arts and Sciences, Program in Geophysical Fluid Dynamics
Show less  Abstract/Description

Karst aquifers are vulnerable to contamination, as conduits and fractures in the aquifers are preferential flow paths where contaminants move fast. On the other hand, the presence of conduits and fractures make groundwater modeling for karst aquifer a challenge. This dissertation addresses several important issues related to groundwater contamination, numerical modeling, and equipment development with potential applications in karst. In Chapter 2, I discuss groundwater contamination in the...
Show moreKarst aquifers are vulnerable to contamination, as conduits and fractures in the aquifers are preferential flow paths where contaminants move fast. On the other hand, the presence of conduits and fractures make groundwater modeling for karst aquifer a challenge. This dissertation addresses several important issues related to groundwater contamination, numerical modeling, and equipment development with potential applications in karst. In Chapter 2, I discuss groundwater contamination in the karst aquifer of Yucatan, which is the only source of drinking water for the population of Yucatan but groundwater in the top of the aquifer has been polluted and cannot be used for human consumption. I developed a new statistical method to analyze temporal and spatial variation of groundwater quality in the aquifer. By using this method, I identified the factors that cause temporal and spatial changes in the groundwater quality as well as the zones of influence. The spatial changes are caused by the following factors: interaction between groundwater and matrix rock, distribution of precipitation, seawater intrusion, mixture of water rich in sulfates, and human pollution in two zones within the study area. The temporal variation is caused by changes in the amount and distribution of precipitation. The new method proves to be important for deriving information about the temporal and spatial processes affecting groundwater quality. Chapter 3 is focused on validating the MODFLOW CFP M1 model developed by the U.S. Geological Survey for simulating groundwater flow in karst aquifers. The model validation process is important to build confidence for using the model. I was interested in quantifying to what extent the model can accurately simulate groundwater flow in karst conduit and surrounding porous media, in other words, if the equation used to simulate the flow exchange between karst conduits and surrounding porous media was suitable for this experiment. The model validation was done using results of lab experiments. A sandbox lab device was developed to understand threedimensional (3D) groundwater flow in a confined karst aquifer with a conduit in the middle of the aquifer. Thirteen lab experiments were performed. Hydraulic heads and flow rates of the conduit and surrounding sand were measured. I used three experimental results to calibrate the roughness of the conduit, hydraulic conductivity of the sand surrounding the conduit, and a coefficient used by MODFLOW CFP M1 for simulating the flow exchange. Using the calibrated model, I evaluated the estimated errors (the difference between model simulations and the corresponding data) along with the 95% confidence intervals for the true error. The errors were calculated for flow rates at the inflow and outflow of the sandbox and the heads in the porous media. The confidence intervals consider measurement error, model calibration error, parameter uncertainty, and propagation of the measurement error in the boundary conditions. The results of model calibration and validation showed that the magnitude of the error was highly correlated with the magnitude of measured flow exchange, indicating that MODFLOW CFP M1 cannot adequately capture the physics of the flow exchange. Therefore, MODFLOW CFP M1 is valid when the flow exchange is small but invalid otherwise for this sandbox experiment. In Chapter 4, I developed a seepage meter to measure groundwater seepage from groundwater to surface waterbodies such as a lake. I was interested in verifying the accuracy of an analytic solution, which estimates the seepage through the bottom of a lake, using measurements from a sandbox experiment. However, existing methods were not useful in this case because of the small scale. Therefore, I proposed a new seepage meter useful for this case. The proposed seepage meter can be used to estimate the hydraulic conductivity as well. Therefore, I tested: (1) the accuracy of the seepage meter using a Darcy column, and (2) the accuracy of the analytic solution using a MODFLOW model and seepage measurements from a sandbox. This sandbox represents an unconfined aquifer with groundwater discharge into a lake. The new seepage meter consists of a cylinder inserted into the lake bed. The groundwater seepage is directed first to the cylinder and then to an external reservoir where seepage measurements are made. The laboratory results show that the seepage meter can be used to measure seepage for the laboratory experiment. However, more tests are needed to further evaluate the accuracy of the seepage meter. The numerical results show that the analytic solution is a good approximation for seepage estimation. Chapter 5 discusses the conclusions of my dissertation research and the research in future studies.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_PachecoCastro_fsu_0071E_14073
 Format
 Thesis
 Title
 Analysis of Regularity and Convergence of Discretization Methods for the Stochastic Heat Equation Forced by SpaceTime White Noise.
 Creator

Wills, Anthony Clinton, Wang, Xiaoming, Ewald, Brian D., Reina, Laura, Bowers, Philip L., Case, Bettye Anne, Ökten, Giray, Florida State University, College of Arts and Sciences...
Show moreWills, Anthony Clinton, Wang, Xiaoming, Ewald, Brian D., Reina, Laura, Bowers, Philip L., Case, Bettye Anne, Ökten, Giray, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

We consider the heat equation forced by a spacetime white noise and with periodic boundary conditions in one dimension. The equation is discretized in space using four different methods; spectral collocation, spectral truncation, finite differences, and finite elements. For each of these methods we derive a spacetime white noise approximation and a formula for the covariance structure of the solution to the discretized equation. The convergence rates are analyzed for each of the methods as...
Show moreWe consider the heat equation forced by a spacetime white noise and with periodic boundary conditions in one dimension. The equation is discretized in space using four different methods; spectral collocation, spectral truncation, finite differences, and finite elements. For each of these methods we derive a spacetime white noise approximation and a formula for the covariance structure of the solution to the discretized equation. The convergence rates are analyzed for each of the methods as the spatial discretization becomes arbitrarily fine and this is confirmed numerically. Dirichlet and Neumann boundary conditions are also considered. We then derive covariance structure formulas for the two dimensional stochastic heat equation using each of the different methods. In two dimensions the solution does not have a finite variance and the formulas for the covariance structure using different methods does not agree in the limit. This means we must analyze the convergence in a different way than the one dimensional problem. To understand this difference in the solution as the spatial dimension increases, we find the Sobolev space in which the approximate solution converges to the solution in one and two dimensions. This result is then generalized to n dimensions. This gives a precise statement about the regularity of the solution as the spatial dimension increases. Finally, we consider a generalization of the stochastic heat equation where the forcing term is the spatial derivative of a spacetime white noise. For this equation we derive formulas for the covariance structure of the discretized equation using the spectral truncation and finite difference method. Numerical simulation results are presented and some qualitative comparisons between these two methods are made.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9488
 Format
 Thesis
 Title
 Local and Global Bifurcations in FiniteDimensional Center Manifold Equations of DoubleDiffusive Convection.
 Creator

Eilertsen, Justin, Magnan, Jeronimo Francisco, Duke, D. W. (Dennis W.), Bertram, R. (Richard), Wang, Xiaoming, Musslimani, Ziad H., Florida State University, College of Arts and...
Show moreEilertsen, Justin, Magnan, Jeronimo Francisco, Duke, D. W. (Dennis W.), Bertram, R. (Richard), Wang, Xiaoming, Musslimani, Ziad H., Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

A finite dimensional amplitude equation model of 2dimensional doublediffusive convection near a quadruplezero (codimension 4) bifurcation point is derived using center manifold reduction. The derivation employs small perturbationtheory to obtain an asymptomatic solution to the 2dimensional NavierStokes equations. The coefficients of the amplitude equations are derived for two parameter regimes corresponding to high and moderate thermal Rayleigh numbers. By numerically approximating the...
Show moreA finite dimensional amplitude equation model of 2dimensional doublediffusive convection near a quadruplezero (codimension 4) bifurcation point is derived using center manifold reduction. The derivation employs small perturbationtheory to obtain an asymptomatic solution to the 2dimensional NavierStokes equations. The coefficients of the amplitude equations are derived for two parameter regimes corresponding to high and moderate thermal Rayleigh numbers. By numerically approximating the Poincare map of the amplitude equations, local and global bifurcations are detected that lead to birth of strange attractors. Specifically, strange attractors are generated by homoclinic explosions in the Poincare map. For high thermal Rayleigh numbers, this route to chaos in the Poincare map is analogous to that route present in the continuous ShimizuMorioka and Rucklidge models, where the bifurcation to periodic convection is supercritical. For low thermal Rayleigh numbers, the route to chaos in the Poincare map is shown to be analogous to the route observed in the Lorenz equations. Additionally, the bifurcations of the strange attractors of the Poincare map are studied, and numerical simulations reveal the presence of period doubling regimes and intermittency, as well as exotic bifurcations which include splitting, and interior crises, of strange attractors.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SU_Eilertsen_fsu_0071E_13410
 Format
 Thesis