Current Search: Sussman, Mark (x)
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 Title
 Investigation of drop impact on dry and wet surfaces with consideration of surrounding air.
 Creator

Guo, Yisen, Lian, Yongsheng, Sussman, Mark
 Abstract/Description

Numerical simulations were conducted to investigate drop impingement and splashing on both dry and wet surfaces at impact velocities greater than 50 m/s with the consideration of the effect of surrounding air. The NavierStokes equations were solved using the variable density pressure projection method on a dynamic block structured adaptive grid. The moment of fluid method was used to reconstruct interfaces separating different phases. A dynamic contact angle model was used to define the...
Show moreNumerical simulations were conducted to investigate drop impingement and splashing on both dry and wet surfaces at impact velocities greater than 50 m/s with the consideration of the effect of surrounding air. The NavierStokes equations were solved using the variable density pressure projection method on a dynamic block structured adaptive grid. The moment of fluid method was used to reconstruct interfaces separating different phases. A dynamic contact angle model was used to define the boundary condition at the moving contact line. Simulations showed that lowering the ambient gas density can suppress dry surface splashing, which is in agreement with the experiments. A recirculation zone was observed inside the drop after contact: a larger recirculation zone was formed earlier in the higher gas density case than in the lower gas density case. Increasing gas density also enhances the creation of secondary droplets from the lamella breakup. For high speed impact on a dry surface, lowering ambient gas density attenuates splashing. However, ambient air does not significantly affect splashing on a wet surface. Simulations showed that the splashed droplets are primarily from the exiting liquid film. Published by AIP Publishing.
Show less  Date Issued
 201607
 Identifier
 FSU_libsubv1_wos_000382446200015, 10.1063/1.4958694
 Format
 Citation
 Title
 A Comparison Study of Principal Component Analysis and Nonlinear Principal Component Analysis.
 Creator

Wu, Rui, Magnan, Jerry F., Bellenot, Steven, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

In the field of data analysis, it is important to reduce the dimensionality of data, because it will help to understand the data, extract new knowledge from the data, and decrease the computational cost. Principal Component Analysis (PCA) [1, 7, 19] has been applied in various areas as a method of dimensionality reduction. Nonlinear Principal Component Analysis (NLPCA) [1, 7, 19] was originally introduced as a nonlinear generalization of PCA. Both of the methods were tested on various...
Show moreIn the field of data analysis, it is important to reduce the dimensionality of data, because it will help to understand the data, extract new knowledge from the data, and decrease the computational cost. Principal Component Analysis (PCA) [1, 7, 19] has been applied in various areas as a method of dimensionality reduction. Nonlinear Principal Component Analysis (NLPCA) [1, 7, 19] was originally introduced as a nonlinear generalization of PCA. Both of the methods were tested on various artificial and natural datasets sampled from: "F(x) = sin(x) + x", the Lorenz Attractor, and sunspot data. The results from the experiments have been analyzed and compared. Generally speaking, NLPCA can explain more variance than a neural network PCA (NN PCA) in lower dimensions. However, as a result of increasing the dimension, the NLPCA approximation will eventually loss its advantage. Finally, we introduce a new combination of NN PCA and NLPCA, and analyze and compare its performance.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd0704
 Format
 Thesis
 Title
 Steady Dynamics in Shearing Flows of Nematic Liquid Crystalline Polymers.
 Creator

Liu, Fangyu, Wang, Qi, Sussman, Mark, Song, Kaisheng, Department of Mathematics, Florida State University
 Abstract/Description

The biaxiality of the steady state solutions and their stability to inplane disturbances in shearing flows of nematic liquid crystalline polymers are studied by using simplified Wang (2002) model. We obtain all the steady states of Wang model exhibit biaxial symmetry in which two directors are confined to the shearing plane and analysis their stability with respect to inplane disturbances at isolated Debra numbers and polymer concentration values.
 Date Issued
 2004
 Identifier
 FSU_migr_etd1190
 Format
 Thesis
 Title
 Binary White Dwarf Mergers: Weak Evidence for Prompt Detonations in HighResolution Adaptive Mesh Simulations.
 Creator

Fenn, Daniel, Plewa, Tomasz, Sussman, Mark, Erlebacher, Gordon, Department of Scientific Computing, Florida State University
 Abstract/Description

The origins of thermonuclear supernovae remain poorly understooda troubling fact, given their importance in astrophysics and cosmology. A leading theory posits that these events arise from the merger of white dwarfs in a close binary system. In this study we examine the possibility of prompt ignition, in which a runaway fusion reaction is initiated in the early stages of the merger. We present a set of threedimensional white dwarf merger simulations performed with the help of a high...
Show moreThe origins of thermonuclear supernovae remain poorly understooda troubling fact, given their importance in astrophysics and cosmology. A leading theory posits that these events arise from the merger of white dwarfs in a close binary system. In this study we examine the possibility of prompt ignition, in which a runaway fusion reaction is initiated in the early stages of the merger. We present a set of threedimensional white dwarf merger simulations performed with the help of a highresolution adaptive mesh refinement hydrocode. We consider three binary systems of different mass ratios composed of carbon/oxygen white dwarfs with total mass exceeding the Chandrasekhar mass. We additionally explore the effects of mesh resolution on important simulation parameters. We find that two distinct behaviors emerge depending on the progenitor mass ratio. For systems of components with differing masses, a boundary layer forms around the accretor. For systems of nearly equal mass, the merger product displays deep entraintment of each star into the other. We closely monitor thermonuclear burning that begins when sufficiently dense material is shocked during early stages of the merger process. Analysis of ignition times lead us to conclude that for binary systems with components of unequal mass whose combined mass is close to the Chandrasekhar limit, there is a negligible chance of prompt ignition. Simulations of similar systems with a combined mass of 2 solar masses suggest that prompt ignition may be possible, but require further study using higherresolution. The system with components of nearly equal mass does not seem likely to undergo prompt ignition, and higher resolution simulations are unlikely to change this conclusion. We additionally find that white dwarf merger simulations require high resolution. Insufficient resolution can qualitatively change simulation outcomes, either by smoothing important fluctuations in density and temperature, or by altering the dynamics of the system such that additional physics processes, such as gravity, are incorrectly represented.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8779
 Format
 Thesis
 Title
 Numerical Methods for Multiphase Systems with Applications to Biology.
 Creator

Whidden, Mark E., Cogan, Nicholas, Wang, Xiaoqiang, Bertram, Richard, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation is comprised of a variety of efforts towards the development of fast numerical methods and their applications, particularly in the context of simulating biological systems. Scientific computing of these problems requires many considerations bridging gaps between computer science, applied mathematics, and the biology of the specific application. This dissertation spans these fields, with the formulation of heterogeneous mixture descriptions in one chapter, the study and...
Show moreThis dissertation is comprised of a variety of efforts towards the development of fast numerical methods and their applications, particularly in the context of simulating biological systems. Scientific computing of these problems requires many considerations bridging gaps between computer science, applied mathematics, and the biology of the specific application. This dissertation spans these fields, with the formulation of heterogeneous mixture descriptions in one chapter, the study and implementation of efficient and robust numerical techniques in the next, and the application of this modeling framework and computational procedure to specific biological problems in the remaining chapters. The first of these efforts is the construction of multiphase models for macroscopic descriptions of biophysical problems. The second is the development of fast and flexible methods for simulating models derived from this modeling framework. The third is the revelation of this modeling framework to exhibit spatiotemporal patterns that can be initiated by localized perturbations in space. The fourth is the simulation of a fourphase model of biofilm formation implicated in Pierce's Disease.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8661
 Format
 Thesis
 Title
 SO(10) Supersymmetric Grand Unified Theories: from Cosmology to Colliders.
 Creator

Summy, Heaya Ann, Baer, Howard, Sussman, Mark, Reina, Laura, Wahl, Horst, Manousakis, Efstratios, Department of Physics, Florida State University
 Abstract/Description

Simple SUSY GUT models based on the gauge group SO(10) require tbt Yukawa coupling unification, in addition to gauge coupling and matter unification. The Yukawa coupling unification places a severe constraint on the expected spectrum of superpartners, with scalar masses ~ 10 TeV while gaugino masses are quite light. For Yukawaunified models with μ > 0, the spectrum is characterized by three mass scales: i). first and second generation scalars in the multiTeV range, ii). third generation...
Show moreSimple SUSY GUT models based on the gauge group SO(10) require tbt Yukawa coupling unification, in addition to gauge coupling and matter unification. The Yukawa coupling unification places a severe constraint on the expected spectrum of superpartners, with scalar masses ~ 10 TeV while gaugino masses are quite light. For Yukawaunified models with μ > 0, the spectrum is characterized by three mass scales: i). first and second generation scalars in the multiTeV range, ii). third generation scalars, μ and mA in the fewTeV range and iii). gluinos in the ~ 350−500 GeV range with chargino masses around 100−160 GeV. In such a scenario, gluino pair production should occur at large rates at the CERN LHC, followed by gluino threebody decays into neutralinos or charginos. Discovery of Yukawaunified SUSY at the LHC should hence be possible with only 1 fb−1 of integrated luminosity, by tagging multijet events with 2–3 isolated leptons, without relying on missing ET . A characteristic dilepton mass edge should easily be apparent above Standard Model background. Combining dileptons with bjets, along with the gluino pair production cross section information, should allow for gluino and neutralino mass reconstruction. A secondary corroborative signal should be visible at higher integrated luminosity in the X1±1X20 → 3l channel, and should exhibit the same dilepton mass edge as in the gluino cascade decay signal. A problem generic to all supergravity models comes from overproduction of gravitinos in the early universe: if gravitinos are unstable, then their late decays may destroy the predictions of Big Bang nucleosynthesis. We also present a Yukawaunified SO(10) SUSY GUT scenario which avoids the gravitino problem, gives rise to the correct matterantimatter asymmetry via nonthermal leptogenesis, and is consistent with the WMAPmeasured abundance of cold dark matter due to the presence of an axino LSP. To maintain a consistent cosmology for Yukawaunified SUSY models, we require a reheat temperature TR ~ 106−107 GeV, an axino mass around 0.1−10 MeV, and a PecceiQuinn breaking scale fa ~ 1012 GeV.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0405
 Format
 Thesis
 Title
 Deterministic and Stochastic Aspects of Data Assimilation.
 Creator

Akella, Santharam, Navon, Ionel Michael, O'Brien, James J., Erlebacher, Gordon, Wang, Qi, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

The principles of optimal control of distributed parameter systems are used to derive a powerful class of numerical methods for solutions of inverse problems, called data assimilation (DA) methods. Using these DA methods one can efficiently estimate the state of a system and its evolution. This information is very crucial for achieving more accurate long term forecasts of complex systems, for instance, the atmosphere. DA methods achieve their goal of optimal estimation via combination of all...
Show moreThe principles of optimal control of distributed parameter systems are used to derive a powerful class of numerical methods for solutions of inverse problems, called data assimilation (DA) methods. Using these DA methods one can efficiently estimate the state of a system and its evolution. This information is very crucial for achieving more accurate long term forecasts of complex systems, for instance, the atmosphere. DA methods achieve their goal of optimal estimation via combination of all available information in the form of measurements of the state of the system and a dynamical model which describes the evolution of the system. In this dissertation work, we study the impact of new nonlinear numerical models on DA. High resolution advection schemes have been developed and studied to model propagation of flows involving sharp fronts and shocks. The impact of high resolution advection schemes in the framework of inverse problem solution/ DA has been studied only in the context of linear models. A detailed study of the impact of various slope limiters and the piecewise parabolic method (PPM) on DA is the subject of this work. In 1D we use a nonlinear viscous Burgers equation and in 2D a global nonlinear shallow water model has been used. The results obtained show that using the various advection schemes consistently improves variational data assimilation (VDA) in the strong constraint form, which does not include model error. However, the cost functional included efficient and physically meaningful construction of the background cost functional term, J_b, using balance and diffusion equation based correlation operators. This was then followed by an indepth study of various approaches to model the systematic component of model error in the framework of a weak constraint VDA. Three simple forms, decreasing, invariant, and exponentially increasing in time forms of evolution of model error were tested. The inclusion of model error provides a substantial reduction in forecasting errors, in particular the exponentially increasing form in conjunction with the piecewise parabolic high resolution advection scheme was found to provide the best results. Results obtained in this work can be used to formulate sophisticated forms of model errors, and could lead to implementation of new VDA methods using numerical weather prediction models which involve high resolution advection schemes such as the van Leer slope limiters and the PPM.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd0145
 Format
 Thesis
 Title
 Discontinuous Galerkin Spectral Element Approximations on Moving Meshes for Wave Scattering from Reflective Moving Boundaries.
 Creator

AcostaMinoli, Cesar Augusto, Kopriva, David, Srivastava, Anuj, Hussaini, M. Yousuﬀ, Sussman, Mark, Ewald, Brian, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation develops and evaluates a high order method to compute wave scattering from moving boundaries. Specifically, we derive and evaluate a Discontinuous Galerkin Spectral elements method (DGSEM) with Arbitrary Lagrangian Eulerian (ALE) mapping to compute conservation laws on moving meshes and numerical boundary conditions for Maxwell's equations, the linear Euler equations and the nonlinear Euler gasdynamics equations to calculate the numerical flux on reflective moving...
Show moreThis dissertation develops and evaluates a high order method to compute wave scattering from moving boundaries. Specifically, we derive and evaluate a Discontinuous Galerkin Spectral elements method (DGSEM) with Arbitrary Lagrangian Eulerian (ALE) mapping to compute conservation laws on moving meshes and numerical boundary conditions for Maxwell's equations, the linear Euler equations and the nonlinear Euler gasdynamics equations to calculate the numerical flux on reflective moving boundaries. We use one of a family of explicit time integrators such as AdamsBashforth or low storage explicit RungeKutta. The approximations preserve the discrete metric identities and the Discrete Geometric Conservation Law (DGCL) by construction. We present timestep refinement studies with moving meshes to validate the moving mesh approximations. The test problems include propagation of an electromagnetic gaussian plane wave, a cylindrical pressure wave propagating in a subsonic flow, and a vortex convecting in a uniform inviscid subsonic flow. Each problem is computed on a timedeforming mesh with three methods used to calculate the mesh velocities: From exact differentiation, from the integration of an acceleration equation, and from numerical differentiation of the mesh position. In addition, we also present four numerical examples using Maxwell's equations, one example using the linear Euler equations and one more example using nonlinear Euler equations to validate these approximations. These are: reflection of light from a constantly moving mirror, reflection of light from a constantly moving cylinder, reflection of light from a vibrating mirror, reflection of sound in linear acoustics and dipole sound generation by an oscillating cylinder in an inviscid flow.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0111
 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
 Precomputed Global Illumination of Isosurfaces.
 Creator

Beason, Kevin M., Banks, David C., Sussman, Mark, Liu, Xiuwen, Department of Computer Science, Florida State University
 Abstract/Description

Three dimensional scalar heightfields, also known as volumetric datasets, abound in science and medicine. Viewing the isosurfaces, or level sets, is one of the two main ways to display these datasets, the other being volume visualization. Typically the isosurfaces are rendered on a personal computer (PC) allowing the scientist or doctor analyzing the dataset to interactively change the isovalue, and rotate or zoom the isosurface. Unfortunately, out of necessity due to the PC's video card,...
Show moreThree dimensional scalar heightfields, also known as volumetric datasets, abound in science and medicine. Viewing the isosurfaces, or level sets, is one of the two main ways to display these datasets, the other being volume visualization. Typically the isosurfaces are rendered on a personal computer (PC) allowing the scientist or doctor analyzing the dataset to interactively change the isovalue, and rotate or zoom the isosurface. Unfortunately, out of necessity due to the PC's video card, current techniques render the isosurfaces with a basic hardwareaccelerated lighting model. This lighting model lacks important features such as shadows, and as a result the isosurfaces are more difficult to interpret than if they had been rendered with a physically based lighting model. My thesis is that isosurfaces can be displayed with realistic illumination at interactive rates on a typical PC. I present a method for applying global illumination to interactively created isosurfaces, using a physically based lighting model, with a negligible increase in the time required to render the isosurfaces. The result is convincing shading that is easy to interpret by the human visual system, including features such as soft shadows, interreflection, caustics, and color bleeding. This is achieved by solving the rendering equation for all isosurfaces within the volume, storing the solutions in a 3D texture, and then texture mapping the result onto a polygonal approximation of the isosurface. This process is called "heightfield rendering".
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd1175
 Format
 Thesis
 Title
 Rheology and Mesoscale Morphology of Flows of Chlesteric and Nematic Liquid Crystal Polymers.
 Creator

Cui, Zhenlu, Wang, Qi, Liu, Guosheng, Magnan, Jerry F., Sussman, Mark, Tam, Christopher, Department of Mathematics, Florida State University
 Abstract/Description

Cholesteric liquid crystals(CLC) are mesophases, where the average direction of molecular orientation exhibits a chiral (twisted) pattern along its normal direction. In the past, the rheological and flow properties of CLC have been studied scarcely. This is due to the natural tendency of a cholesteric to favor its characteric, twisted configuration, which naturally leads to more complex arrangements of the optic axis than in pure nematics and complicated spatial structures. In this...
Show moreCholesteric liquid crystals(CLC) are mesophases, where the average direction of molecular orientation exhibits a chiral (twisted) pattern along its normal direction. In the past, the rheological and flow properties of CLC have been studied scarcely. This is due to the natural tendency of a cholesteric to favor its characteric, twisted configuration, which naturally leads to more complex arrangements of the optic axis than in pure nematics and complicated spatial structures. In this dissertation, we address the issues related to rheology and flow induced structures in CLC and nematic polymers, with emphasis on the role of the anisotropic elasticities. In the first part of this dissertation, we study the permeation flow problem using a mesoscopic theory obtained from the kinetic theory for Cholesteric liquid crystal polymers and resolve the inconsistency issue in the literature. Then we give a systematic study on steady structures and transient behavior in flows of nematic polymers. In the second part of this dissertation, we develop a hydrodynamic theory for flows of CLCPs following the continuum mechanics formulation of McMillan's second order tensor theory for liquid crystals and study phase transition in chiral nematic liquid crystals as well as the rheological hebaviors and the flow properties of CLCPs.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd2952
 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
 All Speed MultiPhase Flow Solvers.
 Creator

Kadioglu, Samet Y., Sussman, Mark, Telotte, John, Hussaini, Yousuﬀ, Wang, Qi, Erlebacher, Gordon, Department of Mathematics, Florida State University
 Abstract/Description

A new second order primitive preconditioner technique (an all speed method) for solving all speed single/multiphase flow is presented. With this technique, one can compute both compressible and incompressible flows with Machuniform accuracy and efficiency (i.e., accuracy and efficiency of the method are independent of Mach numbers). The new primitive preconditioner (all speed/Mach uniform) technique can handle both strong and weak shocks, providing highly resolved shock solutions together...
Show moreA new second order primitive preconditioner technique (an all speed method) for solving all speed single/multiphase flow is presented. With this technique, one can compute both compressible and incompressible flows with Machuniform accuracy and efficiency (i.e., accuracy and efficiency of the method are independent of Mach numbers). The new primitive preconditioner (all speed/Mach uniform) technique can handle both strong and weak shocks, providing highly resolved shock solutions together with correct shock speeds. In addition, the new technique performs very well at the zero Mach limit. In the case of multiphase flow, the new primitive preconditioner technique enables one to accurately treat phase boundaries in which there is a large impedance mismatch. When solving multidimensional all speed multiphase flows, we introduce adaptive solution techniques which exploit the advantages of Machuniform methods. We compute a variety of problems from low (low speed) to high Mach number (high speed) flows including multiphase flow tests, i.e, computing the growth and collapse of adiabatic bubbles for study of underwater explosions
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd3391
 Format
 Thesis
 Title
 Thermal Conductivity and SelfGeneration of Magnetic Fields in Discontinuous Plasmas.
 Creator

Modica, Frank, Plewa, Tomasz, Navon, Michael Ionel, Sussman, Mark, Department of Scientific Computing, Florida State University
 Abstract/Description

Hydrodynamic instabilities are the driving force behind complex fluid processes that occur from everyday scenarios to the most extreme physical conditions of the universe. The RayleighTaylor instability (RTI) develops when a heavy fluid is accelerated by a light fluid, resulting in sinking spikes, rising bubbles, and material mixing. Laser experiments have observed features of RTI that cannot be explained with pure hydrodynamic models. For this computational study we have implemented and...
Show moreHydrodynamic instabilities are the driving force behind complex fluid processes that occur from everyday scenarios to the most extreme physical conditions of the universe. The RayleighTaylor instability (RTI) develops when a heavy fluid is accelerated by a light fluid, resulting in sinking spikes, rising bubbles, and material mixing. Laser experiments have observed features of RTI that cannot be explained with pure hydrodynamic models. For this computational study we have implemented and verified extended physics mod ules for anisotropic thermal conduction and selfgenerated magnetic fields in the FLASH based Proteus code using the Braginskii plasma theory. We have used this code to simulate RTI in a basic plasma physics context. We obtain results up to 35 nanoseconds (ns) at various resolutions and discuss convergence and computational challenges. We find that magnetic fields as high as 110 megagauss (MG) are genereated near the fluid interface. Thermal conduction turns out to be essentially isotropic in these conditions, but plays the dominant role in the evolution of the system by smearing out smallscale structure and reducing the RT growth rate. This may account for the relatively feature less RT spikes seen in experiments. We do not, however, observe mass extensions in our simulations. Without thermal conductivity, the magnetic field has the effect of generating what appears to be an additional RT mode which results in new structure at later times, when compared to pure hydro models. Additional physics modules and 3D simulations are needed to complete our Braginskii model of RTI.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5841
 Format
 Thesis
 Title
 NonIntrusive Methods for Probablistic Uncertainty Quantification and Global Sensitivity Analysis in Nonlinea Stochastic Phenomena.
 Creator

Liu, Yaning, Hussaini, M. Yousuff, Okten, Giray, Srivastava, Anuj, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

The objective of this work is to quantify uncertainty and perform global sensitivity analysis for nonlinear models with a moderate or large number of stochastic parameters. We implement nonintrusive methods that do not require modification of the programming code of the underlying deterministic model. To avoid the curse of dimensionality, two methods, namely sampling methods and high dimensional model representation are employed to propagate uncertainty and compute global sensitivity indices...
Show moreThe objective of this work is to quantify uncertainty and perform global sensitivity analysis for nonlinear models with a moderate or large number of stochastic parameters. We implement nonintrusive methods that do not require modification of the programming code of the underlying deterministic model. To avoid the curse of dimensionality, two methods, namely sampling methods and high dimensional model representation are employed to propagate uncertainty and compute global sensitivity indices. Variancebased global sensitivity analysis identifies significant and insignificant model parameters. It also provides basis for reducing a model's stochastic dimension by freezing identified insignificant model parameters at their nominal values. The dimensionreduced model can then be analyzed efficiently. We use uncertainty quantification and global sensitivity analysis in three applications. The first application is to the Rothermel wildland surface fire spread model, which consists of around 80 nonlinear algebraic equations and 24 parameters. We find the reduced models for the selected model outputs and apply efficient sampling methods to quantify the uncertainty. High dimensional model representation is also applied for the Rothermel model for comparison. The second application is to a recently developed biological model that describes inflammatory host response to a bacterial infection. The model involves four nonlinear coupled ordinary differential equations and the dimension of the stochastic space is 16. We compute global sensitivity indices for all parameters and build a dimensionreduced model. The sensitivity results, combined with experiments, can improve the validity of the model. The third application quantifies the uncertainty of weather derivative models and investigates model robustness based on global sensitivity analysis. Three commonly used weather derivative models for the daily average temperature are considered. The one which is least influenced by an increase of parametric uncertainty level is identified as robust. In summary, the following contributions are made in this dissertation: 1. The optimization of sensitivity derivative enhanced sampling that guarantees variance reduction and improved estimation of stochastic moments. 2. The combination of optimized sensitivity derivative enhanced sampling with randomized quasiMonte Carlo sampling, and adaptive Monte Carlo sampling, to achieve higher convergence rates. 3. The construction of cutHDMR component functions based on Gauss quadrature points which results in a more accurate surrogate model, derivation of an integral form of low order partial variances based on cutHDMR, and efficient computation of global sensitivity analysis based on cutHDMR. 4. The application of efficient sampling methods, RSHDMR and cutHDMR for the quantification of Rothermel's wildland fire surface spread model. 5. The uncertainty quantification and global sensitivity analysis of a newly developed immune response model with parametric uncertainty. 6. The uncertainty quantification of weather derivative models and the analysis of model robustness based on global sensitivity analysis.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8681
 Format
 Thesis
 Title
 Uncertainty Quantification and Data Fusion Based on DempsterShafer Theory.
 Creator

He, Yanyan, Hussaini, M. Yousuff, Oates, William S., Kopriva, David A., Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

Quantifying uncertainty in modeling and simulation is crucial since the parameters of the physical system are inherently nondeterministic and knowledge of the system embodied in the model is incomplete or inadequate. The most welldeveloped nonadditivemeasure theory  the DempsterShafer theory of evidence  is explored for uncertainty quantification and propagation. For ''uncertainty quantification," we propose the MinMax method to construct belief functions to represent uncertainty in...
Show moreQuantifying uncertainty in modeling and simulation is crucial since the parameters of the physical system are inherently nondeterministic and knowledge of the system embodied in the model is incomplete or inadequate. The most welldeveloped nonadditivemeasure theory  the DempsterShafer theory of evidence  is explored for uncertainty quantification and propagation. For ''uncertainty quantification," we propose the MinMax method to construct belief functions to represent uncertainty in the information (data set) involving the inseparably mixed type of uncertainties. Using the principle of minimum uncertainty and the concepts of entropy and specificity, the MinMax method specifies a partition of a finite interval on the real line and assigns belief masses to the uniform subintervals. The method is illustrated in a simple example and applied to the total uncertainty quantification in flight plan of two actual flights. For ''uncertainty propagation," we construct belief/probability density functions for the output or the statistics of the output given the belief/probability density functions for the uncertain input variables. Different approaches are introduced for aleatory uncertainty propagation, epistemic uncertainty propagation, and mixed type of uncertainty propagation. The impact of the uncertain input parameters on the model output is studied using these approaches in a simple example of aerodynamic flow: quasionedimensional nozzle flow. In the situation that multiple models are available for the same quantity of interest, the combination rules in the DempsterShafer theory can be utilized to integrate the predictions from the different models. In the present work, we propose a robust and comprehensive procedure to combine multiple bodies of evidence. It is robust in that it can combine multiple bodies of evidence, consistent or otherwise. It is comprehensive in the sense that it examines the bodies of evidence strongly conflicted with others, reconstructs the basic belief mass functions by discounting, and then fuses all the bodies of evidence using an optimally parametrized combination rule. The proposed combination procedure is applied to radiotherapy dose response outcome analysis.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8563
 Format
 Thesis
 Title
 Toward Connecting CoreCollapse Supernova Theory with Observations.
 Creator

Handy, Timothy A., Plewa, Tomasz, Sussman, Mark, MeyerBaese, Anke, Erlebacher, Gordon, Navon, Ionel M., Department of Scientific Computing, Florida State University
 Abstract/Description

We study the evolution of the collapsing core of a 15 solar mass blue supergiant supernova progenitor from the moment shortly after core bounce until 1.5 seconds later. We present a sample of two and threedimensional hydrodynamic models parameterized to match the explosion energetics of supernova SN 1987A. We focus on the characteristics of the flow inside the gain region and the interplay between hydrodynamics, selfgravity, and neutrino heating, taking into account uncertainty in the...
Show moreWe study the evolution of the collapsing core of a 15 solar mass blue supergiant supernova progenitor from the moment shortly after core bounce until 1.5 seconds later. We present a sample of two and threedimensional hydrodynamic models parameterized to match the explosion energetics of supernova SN 1987A. We focus on the characteristics of the flow inside the gain region and the interplay between hydrodynamics, selfgravity, and neutrino heating, taking into account uncertainty in the nuclear equation of state. We characterize the evolution and structure of the flow behind the shock in terms the accretion flow dynamics, shock perturbations, energy transport and neutrino heating effects, and convective and turbulent motions. We also analyze information provided by particle tracers embedded in the flow. Our models are computed with a highresolution finite volume shock capturing hydrodynamic code. The code includes source terms due to neutrinomatter interactions from a lightbulb neutrino scheme that is used to prescribe the luminosities and energies of the neutrinos emerging from the core of the protoneutron star. The protoneutron star is excised from the computational domain, and its contraction is modeled by a timedependent inner boundary condition. We find the spatial dimensionality of the models to be an important contributing factor in the explosion process. Compared to twodimensional simulations, our threedimensional models require lower neutrino luminosities to produce equally energetic explosions. We estimate that the convective engine in our models is $4$% more efficient in three dimensions than in two dimensions. We propose that this is due to the difference of morphology of convection between two and threedimensional models. Specifically, the greater efficiency of the convective engine found in threedimensional simulations might be due to the larger surfacetovolume ratio of convective plumes, which aids in distributing energy deposited by neutrinos. We do not find evidence of the standing accretion shock instability in our models. Instead we identify a relatively long phase of quasisteady convection below the shock, driven by neutrino heating. During this phase, the analysis of the energy transport in the postshock region reveals characteristics closely resembling that of penetrative convection. We find that the flow structure grows from small scales and organizes into large, convective plumes on the size of the gain region. We use tracer particles to study the flow properties, and find substantial differences in residency times of fluid elements in the gain region between twodimensional and threedimensional models. These appear to originate at the base of the gain region and are due to differences in the structure of convection. We also identify differences in the evolution of energy of the fluid elements, how they are heated by neutrinos, and how they become gravitationally unbound. In particular, at the time when the explosion commences, we find that the unbound material has relatively long residency times in twodimensional models, while in three dimensions a significant fraction of the explosion energy is carried by particles with relatively short residency times. We conduct a series of numerical experiments in which we methodically decrease the angular resolution in our threedimensional models. We observe that the explosion energy decreases dramatically once the resolution is inadequate to capture the morphology of convection on large scales. Thus, we demonstrated that it is possible to connect successful, energetic, threedimensional models with unsuccessful threedimensional models just by decreasing numerical resolution, and thus the amount of resolved physics. This example shows that the role of dimensionality is secondary to correctly accounting for the basic physics of the explosion. The relatively low spatial resolution of current threedimensional models allows for only rudimentary insights into the role of turbulence in driving the explosion. However, and contrary to some recent reports, we do not find evidence for turbulence being a key factor in reviving the stalled supernova shock.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8798
 Format
 Thesis
 Title
 Modeling the Effect of Biofilm Production in the Development of Plant Diseases.
 Creator

Donahue, Matthew, Cogan, Nicholas, Wang, Xiaoqiang, Hurdal, Monica, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

Despite multiple bacterial infections causing widespread damage to the citrus, wine, and other fruit industries, there has been little attention paid to modeling the development and progression of the structures formed by the bacteria within these diseases. A biology primer describing the processes involved in biofilm formation will be followed by a description of bacterial infections within plants. To model these diseases a multiphase framework of partial differential equations will be used...
Show moreDespite multiple bacterial infections causing widespread damage to the citrus, wine, and other fruit industries, there has been little attention paid to modeling the development and progression of the structures formed by the bacteria within these diseases. A biology primer describing the processes involved in biofilm formation will be followed by a description of bacterial infections within plants. To model these diseases a multiphase framework of partial differential equations will be used to examine the dynamic behavior and fluid/structure interactions of the biological system. Perturbation analysis will be used to determine potential causes and tendencies of patterns developed by biofilm formed within microfluidic chambers. These patterns represent a dominant mode of instability within the system, and the model equations capture this instability through the use of dispersion relationships. Numerical simulations of the nonlinear system will follow that are consistent with linear results. Further numerical studies will be used to investigate dynamics on a finite domain resembling the behavior of the system in vitro and in planta. First, a simulation using a constant inflow velocity will be used to mimic the properties of biofilms grown in the lab. These simulations also include the effects of added material, such as calcium. Second, a constant pressure drop will be imposed on the fluid similar to the transpiration pressure experienced by the xylem fluid within the plant. In these simulations, the growth of biomass causes a decrease in the flux of fluid able to move through the chamber. These results may provide insight into the ability of biofilm to successfully occlude xylem vessels.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8973
 Format
 Thesis
 Title
 Massively Parallel Algorithms for CFD Simulation and Optimization on Heterogeneous ManyCore Architectures.
 Creator

Duffy, Austen C., Sussman, Mark, Hussaini, M. Yousuﬀ, Van Engelen, Robert, Cogan, Nick, Gallivan, Kyle, Department of Mathematics, Florida State University
 Abstract/Description

In this dissertation we provide new numerical algorithms for use in conjunction with simulation based design codes. These algorithms are designed and best suited to run on emerging heterogenous computing architectures which contain a combination of traditional multicore processors and new programmable manycore graphics processing units (GPUs). We have developed the following numerical algorithms (i) a new Multidirectional Search (MDS) method for PDE constrained optimization that utilizes a...
Show moreIn this dissertation we provide new numerical algorithms for use in conjunction with simulation based design codes. These algorithms are designed and best suited to run on emerging heterogenous computing architectures which contain a combination of traditional multicore processors and new programmable manycore graphics processing units (GPUs). We have developed the following numerical algorithms (i) a new Multidirectional Search (MDS) method for PDE constrained optimization that utilizes a Multigrid (MG) strategy to accelerate convergence, this algorithm is well suited for use on GPU clusters due to its parallel nature and is more scalable than adjoint methods (ii) a new GPU accelerated point implicit solver for the NASA FUN3D code (unstructured NavierStokes) that is written in the Compute Unified Device Architecture (CUDA) language, and which employs a novel GPU sharing model, (iii) novel GPU accelerated smoothers (developed using PGI Fortran with accelerator compiler directives) used to accelerate the multigrid preconditioned conjugate gradient method (MGPCG) on a single rectangular grid, and (iv) an improved pressure projection solver for adaptive meshes that is based on the MGPCG method which requires fewer grid point calculations and has potential for better scalability on hetergeneous clusters. It is shown that a multigrid  multidirectional search (MGMDS) method can run up to 5.5X faster than the MDS method when used on a one dimensional data assimilation problem. It is also shown that the new GPU accelerated point implicit solver of FUN3D is up to 5.5X times faster than the CPU version and that the solver can perform up to 40% faster on a single GPU being shared by four CPU cores. It is found that GPU accelerated smoothers for the MGPCG method on uniform grids can run over 2X faster than the nonaccelerated versions for 2D problems, and that the new MGPCG pressure projection solver for adaptive grids is up to 4X faster than the previous MG algorithm.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0651
 Format
 Thesis
 Title
 Uncertainty Quantification of Nonlinear Stochastic Phenomena.
 Creator

Jimenez, Edwin, Hussaini, M. Y., Srivastava, Anuj, Sussman, Mark, Kopriva, David, Department of Mathematics, Florida State University
 Abstract/Description

The present work quantifies uncertainty in two nonlinear problems using efficient sampling methods and polynomial chaos expansions. The first application is to the Rothermel wildland fire spread model. This model consists of a nonlinear system of algebraic and transcendental equations that relates environmental variables (input parameter groups) such as fuel type, fuel moisture, terrain, and wind to describe the fire environment. The second application quantifies aeroacoustic uncertainty of a...
Show moreThe present work quantifies uncertainty in two nonlinear problems using efficient sampling methods and polynomial chaos expansions. The first application is to the Rothermel wildland fire spread model. This model consists of a nonlinear system of algebraic and transcendental equations that relates environmental variables (input parameter groups) such as fuel type, fuel moisture, terrain, and wind to describe the fire environment. The second application quantifies aeroacoustic uncertainty of a Joukowski airfoil in stochastic vortical gusts. The stochastic gusts are described by random variables that model the gust amplitudes and frequency. The quantification of uncertainty is measured in terms of statistical moments. We construct moment estimates using a variance reduction procedure as well as an efficient stochastic collocation method.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd3511
 Format
 Thesis
 Title
 Level Set and Conservative Level Set Methods on Dynamic Quadrilateral Grids.
 Creator

Simakhina, Svetlana, Sussman, Mark, Roper, Michael, Kopriva, David, Ewald, Brian, Peterson, Janet, Department of Mathematics, Florida State University
 Abstract/Description

The work in this thesis is motivated by the application of spray combustion. If one develops algorithms to simulate spray generation, for example the primary breakup of a liquid jet in a gas crossflow, then a bodyfitted or Lagrangian methods would require "surgery" in order to continue a simulation beyond the point at which a droplet is torn into multiple droplets. The liquid volume must also be conserved in simulating spray generation. In this thesis, an Eulerian front tracking method...
Show moreThe work in this thesis is motivated by the application of spray combustion. If one develops algorithms to simulate spray generation, for example the primary breakup of a liquid jet in a gas crossflow, then a bodyfitted or Lagrangian methods would require "surgery" in order to continue a simulation beyond the point at which a droplet is torn into multiple droplets. The liquid volume must also be conserved in simulating spray generation. In this thesis, an Eulerian front tracking method with conserved fluid volume is developed to represent and update an interface between two fluids. It's a level set (LS) method with global volume fix, and the underlying grid is a structured, dynamic, curvilinear grid. We compared our newly developed method to the coupled level set and volume of fluid method (CLSVOF) for two strategic test problems. The first problem, the rotation of a notched disk, tests for robustness. The second problem (proposed in this thesis), the deformation of a circular interface in an incompressible, deforming, velocity field, tests for order of accuracy. We found that for the notched disk problem, the CLSVOF method is superior to the new combined level set method/curvilinear grid method. For a given number of grid points, the CLSVOF method always outperforms the combined level set/curvilinear grid method. On the other hand, for the deformation of a circular interface problem, the combined level set/curvilinear grid method gives better accuracy than the CLSVOF method, for a given number of grid points. Unfortunately the new method is more expensive because a new mesh must be generated periodically. We note that the volume error of the new level set/curvilinear grid algorithm is comparable to that of the CLSVOF method for all test cases tried. We prove that the conservative level set (CLS) method has O(1) local truncation error in an advection scheme. The following developments of the conservative level set (CLS) method are presented in the thesis: new CLS function remapping algorithm and new CLS reinitialization algorithm. The new developments allow one to implement the CLS method on a dynamic quadrilateral grid but don't remedy the order of the method. A new algorithm for quasicubic interpolation is presented. Quasicubic interpolation has been used for local polynomial interpolation on an orthogonal mesh before, but never on a general, nonorthogonal curvilinear mesh. The new (tunnel quasicubic) algorithm enables one to find a global piecewise polynomial interpolation of degree three on an orthogonal mesh, and to find a local polynomial interpolation of degree three on a curvilinear mesh.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1724
 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
 Indexing, Searching, and Mining LargeScale Visualdata via Structured Vector Quantization.
 Creator

Yuan, Jiangbo, Liu, Xiuwen, Sussman, Mark, Kumar, Piyush, Srinivasan, Ashok, Zhao, Peixiang, Department of Computer Science, Florida State University
 Abstract/Description

This dissertation is centered on indexing, searching, and mining methods for largescale and highdimensional visual data. While the processing to such data has been widely acknowledged to be difficult, the problem becomes more serious when we encounter "big data'', which has shifted the focus of many problems in computational science. There are urgent requirements of new approaches to processing the huge collections of visual information, e.g., images/videos on the Internet. The study first...
Show moreThis dissertation is centered on indexing, searching, and mining methods for largescale and highdimensional visual data. While the processing to such data has been widely acknowledged to be difficult, the problem becomes more serious when we encounter "big data'', which has shifted the focus of many problems in computational science. There are urgent requirements of new approaches to processing the huge collections of visual information, e.g., images/videos on the Internet. The study first investigates difficulties of similarity search in highdimensional spaces, and presents a new model of local intrinsic dimensionality that better fits to similarity search problems, e.g., the nearest neighbor search. Then it turns the focus to discussions of the advantages and the problems when various structured vector quantization applying to the largescale visual data processing. While many structured vector quantization models can be found, this study is focused to three families of them, including product quantization (PQ), residual quantization (RQ), and treestructured vector quantization (TSVQ). The main contributions of this work can be seen in following pipelines: 1) Two novel methods have been proposed to tackle a problem that exists in RQ for decades, and they have been used to improve residual kmeans trees for scalable clustering, and to optimize two most advanced ANN search systems; 2) a new inverted index has been proposed for fast approximate nearest neighbor (ANN) search; 3) a systematic framework has been proposed for repetition mining in long video streams; 4) a tree embedding PQ model has been proposed to improve PQ codes quality for ANN search. The experimental results have shown the proposed methods are substantially better than the existing solutions in terms of tradeoff among speeds, memory usage, and accuracy.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd9121
 Format
 Thesis
 Title
 Spatial Optimal Disturbances in Turbulent Boundary Layers.
 Creator

Davis, Timothy B. (Timothy Brian), Alvi, Farrukh S., Sussman, Mark, Kumar, Rajan, Taira, Kunihiko, Oates, William, Uzun, Ali, Florida State University, FAMUFSU College of...
Show moreDavis, Timothy B. (Timothy Brian), Alvi, Farrukh S., Sussman, Mark, Kumar, Rajan, Taira, Kunihiko, Oates, William, Uzun, Ali, Florida State University, FAMUFSU College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

In this dissertation, disturbances leading to optimal energy growth in a spatially developing, zeropressuregradient turbulent boundary layer are examined. The slow development of the turbulent mean flow in the streamwise direction is modeled through a parabolized formulation to enable a spatial marching procedure. In the present framework, the linearized equations subject to a turbulent forcing are solved at particular wavenumber combinations. Conventional spatial optimal disturbance then...
Show moreIn this dissertation, disturbances leading to optimal energy growth in a spatially developing, zeropressuregradient turbulent boundary layer are examined. The slow development of the turbulent mean flow in the streamwise direction is modeled through a parabolized formulation to enable a spatial marching procedure. In the present framework, the linearized equations subject to a turbulent forcing are solved at particular wavenumber combinations. Conventional spatial optimal disturbance then arise naturally as the homogeneous solution whereas the particular solution captures the response to distributed forcing. A wavelike decomposition for the disturbance is considered to incorporate both conventional stationary modes as well as propagating modes formed by nonzero frequency/streamwise wavenumber and representative of convective structures naturally observed in wall turbulence. The optimal streamwise wavenumber, which varies with the spatial development of the turbulent mean flow, is computed locally via an auxiliary optimization constraint. The present approach can then be considered, in part, as an extension of the resolventbased analyses for slowly developing flows. Optimization results reveal highly amplified disturbances for both stationary and propagating modes. In all cases, propagating modes surpass their stationary counterpart in both energy amplification and relative contribution to total fluctuation energy. We identify three classes of energetic modes associated with the inner, logarithmic and wake layers of the turbulent mean flow. The inner scaled modes are associated with the ubiquitous near wall streaks residing in the buffer layer. The outer scaled wake modes agree well with the largescale motions that populate the wake layer. For high Reynolds numbers, however, the log modes increasingly dominate the energy spectra with the predicted streamwise and wallnormal scales in agreement with superstructures observed in turbulent boundary layers. Preliminary experimental measurements are performed to relate the energetic spanwise modes to the reported optimal disturbances.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Davis_fsu_0071E_14249
 Format
 Thesis
 Title
 LowRank Riemannian Optimization Approach to the Role Extraction Problem.
 Creator

Marchand, Melissa Sue, Gallivan, Kyle A., Dooren, Paul van, Erlebacher, Gordon, Sussman, Mark, Florida State University, College of Arts and Sciences, Department of Mathematics
 Abstract/Description

This dissertation uses Riemannian optimization theory to increase our understanding of the role extraction problem and algorithms. Recent ideas of using the lowrank projection of the neighborhood pattern similarity measure and our theoretical analysis of the relationship between the rank of the similarity measure and the number of roles in the graph motivates our proposal to use Riemannian optimization to compute a lowrank approximation of the similarity measure. We propose two indirect...
Show moreThis dissertation uses Riemannian optimization theory to increase our understanding of the role extraction problem and algorithms. Recent ideas of using the lowrank projection of the neighborhood pattern similarity measure and our theoretical analysis of the relationship between the rank of the similarity measure and the number of roles in the graph motivates our proposal to use Riemannian optimization to compute a lowrank approximation of the similarity measure. We propose two indirect approaches to use to solve the role extraction problem. The first uses the standard twophase process. For the first phase, we propose using Riemannian optimization to compute a lowrank approximation of the similarity of the graph, and for the second phase using kmeans clustering on the lowrank factor of the similarity matrix to extract the role partition of the graph. This approach is designed to be efficient in time and space complexity while still being able to extract good quality role partitions. We use basic experiments and applications to illustrate the time, robustness, and quality of our twophase indirect role extraction approach. The second indirect approach we propose combines the two phases of our first approach into a onephase approach that iteratively approximates the lowrank similarity matrix, extracts the role partition of the graph, and updates the rank of the similarity matrix. We show that the use of Riemannian rankadaptive techniques when computing the lowrank similarity matrix improves robustness of the clustering algorithm.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Marchand_fsu_0071E_14046
 Format
 Thesis
 Title
 Interactive 3D GPUBased Breast Mass Lesion Segmentation Method Based on Level Sets for DceMRI Images.
 Creator

Zavala Romero, Olmo S., MeyerBaese, Anke, Sussman, Mark, Erlebacher, Gordon, Slice, Dennis E., Wang, Xiaoqiang, Florida State University, College of Arts and Sciences,...
Show moreZavala Romero, Olmo S., MeyerBaese, Anke, Sussman, Mark, Erlebacher, Gordon, Slice, Dennis E., Wang, Xiaoqiang, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

A new method for the segmentation of 3D breast lesions in dynamic contrast enhanced magnetic resonance imaging (DCEMRI) images, using parallel programming with general purpose computing on graphics processing units (GPGPUs), is proposed. The method has two main parts: a preprocessing step and a segmentation algorithm. In the preprocessing step, DCEMRI images are registered using an intensitybased rigid transformation algorithm based on gradient descent. After the registration, voxels...
Show moreA new method for the segmentation of 3D breast lesions in dynamic contrast enhanced magnetic resonance imaging (DCEMRI) images, using parallel programming with general purpose computing on graphics processing units (GPGPUs), is proposed. The method has two main parts: a preprocessing step and a segmentation algorithm. In the preprocessing step, DCEMRI images are registered using an intensitybased rigid transformation algorithm based on gradient descent. After the registration, voxels that correspond to breast lesions are enhanced using the Naïve Bayes machine learning classifier. This classifier is trained to identify four different classes inside breast images: lesion, normal tissue, chest and background. Training is performed by manually selecting 150 voxels for each of the four classes from images in which breast lesions have been confirmed by an expert in the field. Thirteen attributes obtained from the kinetic curves of the selected voxels are later used to train the classifier. Finally, the classifier is used to increase the intensity values of voxels labeled as lesions and to decrease the intensities of all other voxels. The postprocessed images are used for volume segmentation of the breast lesions using a level set method based on the active contours without edges (ACWE) algorithm. The segmentation algorithm is implemented in OpenCL for the GPGPUs to accelerate the original model by parallelizing two main steps of the segmentation process: the computation of the signed distance function (SDF) and the evolution of the segmented curve. The proposed framework uses OpenGL to display the segmented volume in real time, allowing the physician to obtain immediate feedback on the current segmentation progress. The proposed implementation of the SDF is compared with an optimal implementation developed in Matlab and achieves speedups of 25 and 12 for 2D and 3D images, respectively. Moreover, the OpenCL implementation of the segmentation algorithm is compared with an optimal implementation of the narrowband ACWE algorithm. Peak speedups of 55 and 40 are obtained for 2D and 3D images, respectively. The segmentation algorithm has been developed as open source software, with different versions for 2D and 3D images, and can be used in different areas of medical imaging as well as in areas within computer vision, such like tracking, robotics and navigation.
Show less  Date Issued
 2015
 Identifier
 FSU_2015fall_ZavalaRomero_fsu_0071E_12893
 Format
 Set of related objects
 Title
 Comparison of Different Noise Forcings, Regularization of Noise, and Optimal Control for the Stochastic NavierStokes Equations.
 Creator

Zhao, Wenju, Gunzburger, Max D., Sussman, Mark, Peterson, Janet S., Quaife, Bryan, Huang, Chen (Professor of Scientific Computing), Florida State University, College of Arts and...
Show moreZhao, Wenju, Gunzburger, Max D., Sussman, Mark, Peterson, Janet S., Quaife, Bryan, Huang, Chen (Professor of Scientific Computing), Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Stochastic NavierStokes equations have been widely applied in various computational fluid dynamics (CFD) fields in recent years. It can be considered as another milestone in CFD. Our work focuses on exploring some theoretical and numerical properties of the stochastic NavierStokes equations and related optimal control problems. In particular, we consider: a numerical comparison of solutions of the stochastic NavierStokes equations perturbed by a large range of random noises in time and...
Show moreStochastic NavierStokes equations have been widely applied in various computational fluid dynamics (CFD) fields in recent years. It can be considered as another milestone in CFD. Our work focuses on exploring some theoretical and numerical properties of the stochastic NavierStokes equations and related optimal control problems. In particular, we consider: a numerical comparison of solutions of the stochastic NavierStokes equations perturbed by a large range of random noises in time and space; effective Martingale regularized methods for the stochastic NavierStokes equations with additive noises; and the stochastic NavierStokes equations constrained stochastic boundary optimal control problems. We systemically provide numerical simulation methods for the stochastic NavierStokes equations with different types of noises. The noises are classified as colored or white based on their autocovariance functions. For each type of noise, we construct a representation and a simulation method. Numerical examples are provided to illustrate our schemes. Comparisons of the influence of different noises on the solution of the NavierStokes system are presented. To improve the simulation accuracy, we impose a Martingale correction regularized method for the stochastic NavierStokes equations with additive noise. The original systems are split into two parts, a linear stochastic Stokes equations with Martingale solution and a stochastic modified NavierStokes equations with smoother noise. In addition, a negative fractional Laplace operator is introduced to regularize the noise term. Stability and convergence of the pathwise modified NavierStokes equations are proved. Numerical simulations are provided to illustrate our scheme. Comparisons of nonregularized and regularized noises for the NavierStokes system are presented to further demonstrate the efficiency of our numerical scheme. As a consequence of the above work, we consider a stochastic optimal control problem constrained by the NavierStokes equations with stochastic Dirichlet boundary conditions. Control is applied only on the boundary and is associated with reduced regularity, compared to interior controls. To ensure the existence of a solution and the efficiency of numerical simulations, the stochastic boundary conditions are required to belong almost surely to H¹(∂D). To simulate the system, state solutions are approximated using the stochastic collocation finite element approach, and sparse grid techniques are applied to the boundary random field. Oneshot optimality systems are derived from Lagrangian functionals. Numerical simulations are then made, using a combination of Monte Carlo methods and sparse grid methods, which demonstrate the efficiency of the algorithm.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Zhao_fsu_0071E_14002
 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
 A Riemannian Approach for Computing Geodesics in Elastic Shape Space and Its Applications.
 Creator

You, Yaqing, Gallivan, Kyle A., Absil, PierreAntoine, Erlebacher, Gordon, Ökten, Giray, Sussman, Mark, Florida State University, College of Arts and Sciences, Department of...
Show moreYou, Yaqing, Gallivan, Kyle A., Absil, PierreAntoine, Erlebacher, Gordon, Ökten, Giray, Sussman, Mark, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

This dissertation proposes a Riemannian approach for computing geodesics for closed curves in elastic shape space. The application of two Riemannian unconstrained optimization algorithms, Riemannian Steepest Descent (RSD) algorithm and Limitedmemory Riemannian BroydenFletcherGoldfarbShanno (LRBFGS) algorithm are discussed in this dissertation. The application relies on the definition and computation for basic differential geometric components, namely tangent spaces and tangent vectors,...
Show moreThis dissertation proposes a Riemannian approach for computing geodesics for closed curves in elastic shape space. The application of two Riemannian unconstrained optimization algorithms, Riemannian Steepest Descent (RSD) algorithm and Limitedmemory Riemannian BroydenFletcherGoldfarbShanno (LRBFGS) algorithm are discussed in this dissertation. The application relies on the definition and computation for basic differential geometric components, namely tangent spaces and tangent vectors, Riemannian metrics, Riemannian gradient, as well as retraction and vector transport. The difference between this Riemannian approach to compute closed curve geodesics as well as accurate geodesic distance, the existing PathStraightening algorithm and the existing Riemannian approach to approximate distances between closed shapes, are also discussed in this dissertation. This dissertation summarizes the implementation details and techniques for both Riemannian algorithms to achieve the most efficiency. This dissertation also contains basic experiments and applications that illustrate the value of the proposed algorithms, along with comparison tests to the existing alternative approaches. It has been demonstrated by various tests that this proposed approach is superior in terms of time and performance compared to a stateoftheart distance computation algorithm, and has better performance in applications of shape distance when compared to the distance approximation algorithm. This dissertation applies the Riemannian geodesic computation algorithm to calculate Karcher mean of shapes. Algorithms that generate less accurate distances and geodesics are also implemented to compute shape mean. Test results demonstrate the fact that the proposed algorithm has better performance with sacrifice in time. A hybrid algorithm is then proposed, to start with the fast, less accurate algorithm and switch to the proposed accurate algorithm to get the gradient for Karcher mean problem. This dissertation also applies Karcher mean computation to unsupervised learning of shapes. Several clustering algorithms are tested with the distance computation algorithm and Karcher mean algorithm. Different versions of Karcher mean algorithm used are compared with tests. The performance of clustering algorithms are evaluated by various performance metrics.
Show less  Date Issued
 2018
 Identifier
 2018_Su_You_fsu_0071E_14686
 Format
 Thesis
 Title
 Flow Physics and Nonlinear Dynamics of Separated Flows Subject to ZNMFBased Control.
 Creator

Deem, Eric Anthony, Cattafesta, Louis N., Sussman, Mark, Taira, Kunihiko, Collins, E., Moore, Matthew Nicholas J., Hemati, Maziar, Florida State University, College of...
Show moreDeem, Eric Anthony, Cattafesta, Louis N., Sussman, Mark, Taira, Kunihiko, Collins, E., Moore, Matthew Nicholas J., Hemati, Maziar, Florida State University, College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

Aircraft, turbomachinery, wind turbines, and other systems that generate or rely on aerodynamic forces are designed to operate most efficiently when flows are fully attached. However, especially due to increasing offdesign performance requirements, there is significant risk of inefficient operation or failure due to flow separation. This work formulates a procedure for extending the performance envelope of many fluidic systems by delaying flow separation through real time separated flow...
Show moreAircraft, turbomachinery, wind turbines, and other systems that generate or rely on aerodynamic forces are designed to operate most efficiently when flows are fully attached. However, especially due to increasing offdesign performance requirements, there is significant risk of inefficient operation or failure due to flow separation. This work formulates a procedure for extending the performance envelope of many fluidic systems by delaying flow separation through real time separated flow state estimation and control. The history of active separation control is rich; however the approach presented here is novel in that it employs "real time" dynamical system updates to track nonlinear variations in the flow and provide robustness to flow state conditions. First, the dynamics of the canonical laminar separated flow over a flat plate at Rec=10⁵ are characterized by employing fullfield, timeresolved PIV and unsteady surface pressure measurements. Dynamic Mode Decomposition (DMD) is employed on the high dimensional PIV velocity fields to identify the dynamically relevant spatial structure and temporal characteristics of the separated flow. Then, results of various cases of openloop control using a zeronet mass flux actuator slot located just upstream of separation are presented that show separation reduction occurs for the employed actuation method. Real time estimates of the dynamical characteristics are provided by performing online DMD on measurements from a linear array of unsteady surface pressure transducers. The results show that online DMD of the pressure measurements provides reliable estimates of the modal characteristics of the separated flow subject to forcing. Furthermore, the dynamical estimates are updated at a rate commensurate with the characteristic time scales of the flow. Therefore, as the separated flow reacts to the applied forcing, online DMD applied to the surface pressure measurements provides a timevarying linear estimate of the evolution of the flow. Building upon these results, methods for adaptive control of flow separation based on the model provided by online DMD are formulated and implemented on the separated flow. Feedback control is implemented in which Linear Quadratic Regulator gains are computed recursively as the model provided by online DMD is updated. This physicsmotivated, autonomous approach results in more efficient flow reattachment, requiring approximately 30% less actuator effort as compared with the commensurate open loop forcing case. Since this approach relies solely on observations of the separated flow, it is robust to variable flow conditions. Additionally, this approach does not require prior knowledge of the characteristics of the separated flow.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Deem_fsu_0071E_14530
 Format
 Thesis
 Title
 NetworkTheoretic and DataBased Analysis and Control of Unsteady Fluid Flows.
 Creator

Nair, Aditya Gopimohan, Taira, Kunihiko, Sussman, Mark, Cattafesta, Louis N., Oates, William, Alvi, Farrukh S., Brunton, Steven L. (Steven Lee), Florida State University,...
Show moreNair, Aditya Gopimohan, Taira, Kunihiko, Sussman, Mark, Cattafesta, Louis N., Oates, William, Alvi, Farrukh S., Brunton, Steven L. (Steven Lee), Florida State University, College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

Unsteady fluid flows have complex dynamics due to the nonlinear interactions amongst vortical elements. In this thesis, a networktheoretic framework is developed to describe vortical and modal (coherent structure) interactions in unsteady fluid flows. A sparsifieddynamics model and a networkedoscillator model describe the complex dynamics in fluid flows in terms of vortical and modal networks, respectively. Based on the characterized network interactions, modelbased feedback control laws...
Show moreUnsteady fluid flows have complex dynamics due to the nonlinear interactions amongst vortical elements. In this thesis, a networktheoretic framework is developed to describe vortical and modal (coherent structure) interactions in unsteady fluid flows. A sparsifieddynamics model and a networkedoscillator model describe the complex dynamics in fluid flows in terms of vortical and modal networks, respectively. Based on the characterized network interactions, modelbased feedback control laws are established, particularly for controlling the flow unsteadiness. Furthermore, to characterize modelfree feedback control laws for suppressing flow separation in turbulent flows, a datadriven approach leveraging unsupervised clustering is developed. This approach alters the Markov transition dynamics of fluid flow trajectories in an optimal manner using a clusterbased control strategy. To describe vortical interactions, dense fluid flow graphs are constructed using discrete point vortices as nodes and induced velocity as edge weights. Sparsification techniques are then employed on these graph representations based on spectral graph theory to construct sparse graphs of the overall vortical interactions which maintain similar spectral properties as the original setup. Utilizing the sparse vortical graphs, a sparsifieddynamics model is developed which drastically reduces the computational cost to predict the dynamical behavior of vortices, sharing characteristics of reducedorder models. The model retains the nonlinearity of the interactions and also conserves the invariants of discrete vortex dynamics. The network structure of vortical interactions in twodimensional incompressible homogeneous turbulence is then characterized. The strength distribution of the turbulence network reveals an underlying scalefree structure that describes how vortical structures are interconnected. Strong vortices serve as network hubs with smaller and weaker eddies predominantly influenced by the neighboring hubs. The time evolution of the fluid flow network informs us that the scalefree property is sustained until dissipation overtakes the flow physics. The types of perturbations that turbulence network is resilient against is also examined. To describe modal interactions in fluid flows, a networkedoscillatorbased analysis is performed. The analysis examines and controls the transfer of kinetic energy for periodic bluff body flows. The dynamics of energy fluctuations in the flow field are described by a set of oscillators defined by conjugate pairs of spatial POD modes. To extract the network of interactions among oscillators, impulse responses of the oscillators to amplitude and phase perturbations are tracked. Using linear regression techniques, a networked oscillator model is constructed that reveals energy exchanges among the modes. In particular, a large collection of system responses are aggregated to capture the general network structure of oscillator interactions. The present networked oscillator model describes the modal perturbation dynamics more accurately than the empirical Galerkin reducedorder model. The linear network model for nonlinear dynamics is subsequently utilized to design a modelbased feedback controller. The controller suppresses the modal fluctuations and amplitudes that result in wake unsteadiness leading to drag reduction. The strength of the approach is demonstrated for a canonical example of twodimensional unsteady flow over a circular cylinder. The networkbased formulation enables the characterization and control of modal interactions to control fundamental energy transfers in unsteady bluff body flows. Finally, unsupervised clustering and datadriven optimization of coarsegrained control laws is leveraged to manipulate poststall separated flows. Optimized feedback control laws are deduced in highfidelity simulations in an automated, modelfree manner. The approach partitions the baseline flow trajectories into clusters, which corresponds to a characteristic coarsegrained phase in a lowdimensional feature space constituted by feature variables (sensor measurements). The feedback control law is then sought for each and every cluster state which is iteratively evaluated and optimized to minimize aerodynamic power and actuation power input. The control optimally transforms the Markov transition network associated with the baseline trajectories to achieve desired performance objectives. The approach is applied to two and threedimensional separated flows over a NACA 0012 airfoil at an angle of attack of 9° Reynolds number Re = 23000 and freestream Mach number M∞ = 0.3. The optimized control law minimizes power consumption for flight enabling flow to reach a lowdrag state. The analysis provides insights for feedback flow control of complex systems characterizing global clusterbased control laws based on a datadriven, lowdimensional characterization of fluid flow trajectories. In summary, this thesis develops a novel networktheoretic and databased framework for analyzing and controlling fluid flows. The framework incorporates advanced mathematical principles from network science, graph theory and dynamical systems to extract fundamental interactions in fluid flows. On manipulating these interactions, wake unsteadiness in bluff body flow is reduced leading to drag reduction. Finally, databased methods are developed to deduce optimal feedback control laws for poststall separated flows. The networktheoretic and databased approaches provides insights on fundamental interactions in fluid flows which paves the way for design of novel flow control strategies.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Nair_fsu_0071E_14745
 Format
 Thesis
 Title
 Ensemble Proper Orthogonal Decomposition Algorithms for the Incompressible NavierStokes Equations.
 Creator

Schneier, Michael, Gunzburger, Max D., Sussman, Mark, Peterson, Janet S., Erlebacher, Gordon, Huang, Chen, Florida State University, College of Arts and Sciences, Department of...
Show moreSchneier, Michael, Gunzburger, Max D., Sussman, Mark, Peterson, Janet S., Erlebacher, Gordon, Huang, Chen, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g., optimization, control, uncertainty quantification, and other settings, solutions are needed for many sets of parameter values. We consider the case of the timedependent NavierStokes equations for which a recently developed ensemblebased method allows for...
Show moreThe definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g., optimization, control, uncertainty quantification, and other settings, solutions are needed for many sets of parameter values. We consider the case of the timedependent NavierStokes equations for which a recently developed ensemblebased method allows for the efficient determination of the multiple solutions corresponding to many parameter sets. The method uses the average of the multiple solutions at any time step to define a linear set of equations that determines the solutions at the next time step. In this work we incorporate a proper orthogonal decomposition (POD) reducedorder model into the ensemblebased method to further reduce the computational cost; in total, three algorithms are developed. Initially a first order accurate in time scheme for low Reynolds number flows is considered. Next a second order algorithm useful for applications that require longterm time integration, such as climate and ocean forecasting is developed. Lastly, in order to extend this approach to convection dominated flows a model incorporating a POD spatial filter is presented. For all these schemes stability and convergence results for the ensemblebased methods are extended to the ensemblePOD schemes. Numerical results are provided to illustrate the theoretical stability and convergence results which have been proven.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Schneier_fsu_0071E_14687
 Format
 Thesis
 Title
 New Numerical Procedures for the Lagrangian Analysis of Hierarchical BlockStructured Reactive Flow Simulations.
 Creator

Boehner, Philip Scott, Plewa, Tomasz, Sussman, Mark, Erlebacher, Gordon, Shanbhag, Sachin, Ye, Ming, Florida State University, College of Arts and Sciences, Department of...
Show moreBoehner, Philip Scott, Plewa, Tomasz, Sussman, Mark, Erlebacher, Gordon, Shanbhag, Sachin, Ye, Ming, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Chemical evolution of stellar plasma is one of the most critical components of computational models in stellar astrophysics. Nuclear abundance distributions resulting from chains of nuclear reactions serve as a key comparison tool against observations, used to further constrain models. To that end, we focus on improving the accuracy of model abundances. In most cases, abundances are obtained in the course of hydrodynamic simulations performed on Eulerian meshes. Unfortunately, those models...
Show moreChemical evolution of stellar plasma is one of the most critical components of computational models in stellar astrophysics. Nuclear abundance distributions resulting from chains of nuclear reactions serve as a key comparison tool against observations, used to further constrain models. To that end, we focus on improving the accuracy of model abundances. In most cases, abundances are obtained in the course of hydrodynamic simulations performed on Eulerian meshes. Unfortunately, those models are subject to the unphysical mixing of nuclear species due to numerical diffusion effects. For more reliable nucleosynthesis calculations, mass motions are described using passively advected Lagrangian tracer particles. These particles represent fluid elements, recording their thermodynamic histories which are subsequently used to drive detailed nucleosynthesis calculations in a postprocessing procedure performed with large number of relevant isotopes. Accuracy of nucleosynthesis calculations strongly depends on the accurate coupling between fluid represented on the Eulerian mesh and tracer particles. The coupling involves both interpolation of Eulerian data to particles as well as integrating equations of motion of particles. Both steps contribute numerical errors resulting in divergence of particle tracks from fluid streamlines. Here we propose a new particle advection scheme driven by only the hydrodynamics, replacing the interpolation step of particle motion and show preliminary results. We also introduce an interpolation method for mapping our postprocessed nucleosynthesis results back onto our Eulerian mesh. Spatial convergence studies are performed for the Eulerian hydrodynamic nucleosynthesis results and the remapped, postprocessed Lagrangian results using a reactive HawleyZabusky flow.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Boehner_fsu_0071E_14773
 Format
 Thesis
 Title
 On Some Multiphysics Effects of the KelvinHelmholtz Instability in Dense Plasmas.
 Creator

Learn, Ryan Joseph, Plewa, Tomasz, Sussman, Mark, Erlebacher, Gordon, Huang, Chen, Ye, Ming, Florida State University, College of Arts and Sciences, Department of Scientific...
Show moreLearn, Ryan Joseph, Plewa, Tomasz, Sussman, Mark, Erlebacher, Gordon, Huang, Chen, Ye, Ming, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

In various astrophysical and highenergy density plasma flows, the evolution and behavior of the magnetic field can greatly influence flow morphology and result in transient phenomena. Many existing magnetohydrodynamic codes used in astrophysics and high energy density physics often ignore plasma selfmagnetization and treat other physics related to magnetic field such as viscosity, thermal conduction, and resistivity as isotropic. This work is focused on constructing a computational model...
Show moreIn various astrophysical and highenergy density plasma flows, the evolution and behavior of the magnetic field can greatly influence flow morphology and result in transient phenomena. Many existing magnetohydrodynamic codes used in astrophysics and high energy density physics often ignore plasma selfmagnetization and treat other physics related to magnetic field such as viscosity, thermal conduction, and resistivity as isotropic. This work is focused on constructing a computational model based on the Braginskii plasma transport theory, specifically the effects due to the Biermann battery process, and anisotropic resistive, viscous, and thermal transport processes. This model reflects on the ability of the magnetic field to modify the transport processes throughout the plasma, as well as enables the generation of spontaneous magnetic fields. For certain plasma configurations, the magnetic field dynamics brought on through these processes can come to dominate the evolution of the system at very small scales, leading to a stiff system of equations and necessitating an implicit solution to the magnetic induction equation. To relax this stiffness constraint, we implement a multigridbased CrankNicolson implicit solver. We present implementation details of the corresponding computational model and its related verification results. We apply the verified model to the KelvinHelmholtz instability problem under highenergy density conditions. We carry out a series of numerical experiments and compare the obtained instability growth rates to benchmark results. We design a highenergy density shock tube experiment for conditions on the OMEGA laser and compare the obtained magnetic field growth to theoretically predicted results.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Learn_fsu_0071E_14744
 Format
 Thesis
 Title
 HighOrder, Efficient, Numerical Algorithms for Integration in Manifolds Implicitly Defined by Level Sets.
 Creator

Khanmohamadi, Omid, Sussman, Mark, Plewa, Tomasz, Moore, M. Nicholas J. (Matthew Nicholas J.), Ökten, Giray, Florida State University, College of Arts and Sciences, Department...
Show moreKhanmohamadi, Omid, Sussman, Mark, Plewa, Tomasz, Moore, M. Nicholas J. (Matthew Nicholas J.), Ökten, Giray, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

New numerical algorithms are devised for highorder, efficient quadrature in domains arising from the intersection of a hyperrectangle and a manifold implicitly defined by level sets. By casting the manifold locally as the graph of a function (implicitly evaluated through a recurrence relation for the zero level set), a recursion stack is set up in which the interface and integrand information of a single dimension after another will be treated. Efficient means for the resulting dimension...
Show moreNew numerical algorithms are devised for highorder, efficient quadrature in domains arising from the intersection of a hyperrectangle and a manifold implicitly defined by level sets. By casting the manifold locally as the graph of a function (implicitly evaluated through a recurrence relation for the zero level set), a recursion stack is set up in which the interface and integrand information of a single dimension after another will be treated. Efficient means for the resulting dimension reduction process are developed, including maps for identifying lowerdimensional hyperrectangle facets, algorithms for minimal coordinateflip vertex traversal, which, together with our multilinearformbased derivative approximation algorithms, are used for checking a proposed integration direction on a facet, as well as algorithms for detecting interfacefree subhyperrectangles. The multidimensional quadrature nodes generated by this method are inside their respective domains (hence, the method does not require any extension of the integrand) and the quadrature weights inherit any positivity of the underlying singledimensional quadrature method, if present. The accuracy and efficiency of the method are demonstrated through convergence and timing studies for test cases in spaces of up to seven dimensions. The strengths and weaknesses of the method in high dimensional spaces are discussed.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Khanmohamadi_fsu_0071E_14013
 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
 I. A Modified ƙƐ Turbulence Model for High Speed Hets at Elevated Temperatures. II. Modeling and a Computational Study of Spliced Acoustic Liners.
 Creator

Ganesan, Anand, Tam, Christopher K. W., Nh, HonKie, Hunter, Christopher, Navon, Ionel Michael, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

A modification to the kepsilon model aimed to extend its applicability to the computation of the mean flow and noise of highspeed hot jets is proposed. The motivation of the proposal arises from the observation that there is a large density induced increase in the growth rate of spatial instabilities of a mixing layer if the lighter fluid moves faster. This consideration leads to the incorporation of a density gradient related contribution to the turbulent eddy viscosity of the kepsilon...
Show moreA modification to the kepsilon model aimed to extend its applicability to the computation of the mean flow and noise of highspeed hot jets is proposed. The motivation of the proposal arises from the observation that there is a large density induced increase in the growth rate of spatial instabilities of a mixing layer if the lighter fluid moves faster. This consideration leads to the incorporation of a density gradient related contribution to the turbulent eddy viscosity of the kepsilon model. Computed jet mean flow profiles and centerline velocity distributions at elevated temperatures of highspeed jets are found to be in better agreement with experimental measurements if density modification is included. Noise predictions including density effect are also found to be in better agreement with microphone measurements. The good agreements offer strong support to the validity and usefulness of the proposed density correction formula. A timedomain computational methodology has been deveoped to study the propagation and acoustic scattering of fan tones by spliced liners. The front portion of the engine is modelled as a duct. Significant acoustic scattering is observed for a frequency pretty close to cutoff. In this case, total scattered energy was found to be more than the energy in the incident mode. The spliced liners, in such conditions, are found to be less effective than the uniform liners. The performance of the liner was found to be dependent on the frequency. The results of the simulations agree qualitiatively well with the available experimental and theoretical work.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd4368
 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
 MultiGPU Solutions of Geophysical PDEs with Radial Basis FunctionGenerated Finite Differences.
 Creator

Bollig, Evan F., Erlebacher, Gordon, Sussman, Mark, Flyer, Natasha, Slice, Dennis, Ye, Ming, Peterson, Janet, Department of Scientific Computing, Florida State University
 Abstract/Description

Many numerical methods based on Radial Basis Functions (RBFs) are gaining popularity in the geosciences due to their competitive accuracy, functionality on unstructured meshes, and natural extension into higher dimensions. One method in particular, the Radial Basis Functiongenerated Finite Differences (RBFFD), is drawing attention due to its comparatively low computational complexity versus other RBF methods, highorder accuracy (6th to 10th order is common), and parallel nature. Similar to...
Show moreMany numerical methods based on Radial Basis Functions (RBFs) are gaining popularity in the geosciences due to their competitive accuracy, functionality on unstructured meshes, and natural extension into higher dimensions. One method in particular, the Radial Basis Functiongenerated Finite Differences (RBFFD), is drawing attention due to its comparatively low computational complexity versus other RBF methods, highorder accuracy (6th to 10th order is common), and parallel nature. Similar to classical Finite Differences (FD), RBFFD computes weighted differences of stencil node values to approximate derivatives at stencil centers. The method differs from classical FD in that the test functions used to calculate the differentiation weights arendimensional RBFs rather than onedimensional polynomials. This allows for generalization tondimensional space on completely scattered node layouts. Although RBFFD was first proposed nearly a decade ago, it is only now gaining a critical mass to compete against well known competitors in modeling like FD, Finite Volume and Finite Element. To truly contend, RBFFD must transition from single threaded MATLAB environments to largescale parallel architectures. Many HPC systems around the world have made the transition to Graphics Processing Unit (GPU) accelerators as a solution for added parallelism and higher throughput. Some systems offer significantly more GPUs than CPUs. As the problem size,N, grows larger, it behooves us to work on parallel architectures, be it CPUs or GPUs. In addition to demonstrating the ability to scale to hundreds or thousands of compute nodes, this work introduces parallelization strategies that span RBFFD across multiGPU clusters. The stability and accuracy of the parallel implementation is verified through the explicit solution of two PDEs. Additionally, a parallel implementation for implicit solutions is introduced as part of continued research efforts. This work establishes RBFFD as a contender in the arena of distributed HPC numerical methods.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8531
 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
 Detonability of Turbulent White Dwarf Plasma: Hydrodynamical Models at Low Densities.
 Creator

Fenn, Daniel Fenn, Plewa, Tomasz, Sussman, Mark, Erlebacher, Gordon, Piekarewicz, Jorge, Shanbhag, Sachin, Florida State University, College of Arts and Sciences, Department of...
Show moreFenn, Daniel Fenn, Plewa, Tomasz, Sussman, Mark, Erlebacher, Gordon, Piekarewicz, Jorge, Shanbhag, Sachin, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

The origins of Type Ia supernovae (SNe Ia) remain an unsolved problem of contemporary astrophysics. Decades of research indicate that these supernovae arise from thermonuclear runaway in the degenerate material of white dwarf stars; however, the mechanism of these explosions is unknown. Also, it is unclear what are the progenitors of these objects. These missing elements are vital components of the initial conditions of supernova explosions, and are essential to understanding these events. A...
Show moreThe origins of Type Ia supernovae (SNe Ia) remain an unsolved problem of contemporary astrophysics. Decades of research indicate that these supernovae arise from thermonuclear runaway in the degenerate material of white dwarf stars; however, the mechanism of these explosions is unknown. Also, it is unclear what are the progenitors of these objects. These missing elements are vital components of the initial conditions of supernova explosions, and are essential to understanding these events. A requirement of any successful SN Ia model is that a sufficient portion of the white dwarf plasma must be brought under conditions conducive to explosive burning. Our aim is to identify the conditions required to trigger detonations in turbulent, carbonrich degenerate plasma at low densities. We study this problem by modeling the hydrodynamic evolution of a turbulent region filled with a carbon/oxygen mixture at a density, temperature, and Mach number characteristic of conditions found in the 0.8+1.2 solar mass (CO0812) model discussed by Fenn et al. (2016). We probe the ignition conditions for different degrees of compressibility in turbulent driving. We assess the probability of successful detonations based on characteristics of the identified ignition kernels, using Eulerian and Lagrangian statistics of turbulent flow. We found that material with very short ignition times is abundant in the case that turbulence is driven compressively. This material forms contiguous structures that persist over many ignition time scales, and that we identify as prospective detonation kernels. Detailed analysis of the kernels revealed that their central regions are densely filled with material characterized by short ignition times and contain the minimum mass required for selfsustained detonations to form. It is conceivable that ignition kernels will be formed for lower compressibility in the turbulent driving. However, we found no detonation kernels in models driven 87.5 percent compressively. We indirectly confirmed the existence of the lower limit of the degree of compressibility of the turbulent drive for the formation of detonation kernels by analyzing simulation results of the He0609 model of Fenn et al. (2016), which produces a detonation in a heliumrich boundary layer. We found that the amount of energy in the compressible component of the kinetic energy in this model corresponds to about 96 percent compressibility in the turbulent drive. The fact that no detonation was found in the original CO0812 model for nominally the same problem conditions suggests that models with carbonrich boundary layers may require higher resolution in order to adequately represent the mass distributions in terms of ignition times.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Fenn_fsu_0071E_13617
 Format
 Thesis
 Title
 Entangling Qubits by Heisenberg Spin Exchange and Anyon Braiding.
 Creator

Zeuch, Daniel, Bonesteel, N. E., Sussman, Mark, Hill, S. (Stephen Olof), Piekarewicz, Jorge, Florida State University, College of Arts and Sciences, Department of Physics
 Abstract/Description

As the discovery of quantum mechanics signified a revolution in the world of physics more than one century ago, the notion of a quantum computer in 1981 marked the beginning of a drastic change of our understanding of information and computability. In a quantum computer, information is stored using quantum bits, or qubits, which are described by a quantummechanical superposition of the quantum states 0 and 1. Computation then proceeds by acting with unitary operations on these qubits. These...
Show moreAs the discovery of quantum mechanics signified a revolution in the world of physics more than one century ago, the notion of a quantum computer in 1981 marked the beginning of a drastic change of our understanding of information and computability. In a quantum computer, information is stored using quantum bits, or qubits, which are described by a quantummechanical superposition of the quantum states 0 and 1. Computation then proceeds by acting with unitary operations on these qubits. These operations are referred to as quantum logic gates, in analogy to classical computation where bits are acted on by classical logic gates. In order to perform universal quantum computation it is, in principle, sufficient to carry out singlequbit gates and twoqubit gates, where the former act on individual qubits and the latter, acting on two qubits, are used to entangle qubits with each other. The present thesis is divided into two main parts. In the first, we are concerned with spinbased quantum computation. In a spinbased quantum computer, qubits are encoded into the Hilbert space spanned by spin½ particles, such as electron spins trapped in semiconductor quantum dots. For a suitable qubit encoding, turning onandoff, or "pulsing," the isotropic Heisenberg exchange Hamiltonian JSi · Sj allows for universal quantum computation and it is this scheme, known as exchangeonly quantum computation, which we focus on. In the second part of this thesis, we consider a topological quantum computer in which qubits are encoded using socalled Fibonacci anyons, exotic quasiparticle excitations that obey nonAbelian statistics, and which may emerge in certain twodimensional topological systems such as fractional quantumHall states. Quantum gates can then be carried out by moving these particles around one another, a process that can be viewed as braiding their 2+1 dimensional worldlines. The subject of the present thesis is the development and theoretical understanding of procedures used for entangling qubits. We begin by presenting analytical constructions of pulse sequences which can be used to carry out twoqubit gates that are locally equivalent to a controlledPHASE gate. The corresponding phase can be arbitrarily chosen, and for one particular choice this gate is equivalent to controlledNOT. While the constructions of these sequences are relatively lengthy and cumbersome, we further provide a straightforward and intuitive derivation of the shortest known twoqubit pulse sequence for carrying out a controlledNOT gate. This derivation is carried out completely analytically through a novel "elevation" of a simple threespin pulse sequence to a more complicated fivespin pulse sequence. In the case of topological quantum computation with Fibonacci anyons, we present a new method for constructing entangling twoqubit braids. Our construction is based on an iterative procedure, established by Reichardt, which can be used to systematically generate braids whose corresponding operations quickly converge towards an operation that has a diagonal matrix representation in a particular natural basis. After describing this iteration procedure we show how the resulting braids can be used in two explicit constructions for twoqubit braids. Compared to twoqubit braids that can be found using other methods, the braids generated here are among the most efficient and can be obtained straightforwardly without computational overhead.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SU_Zeuch_fsu_0071E_13323
 Format
 Thesis
 Title
 An Aeroacoustic Characterization of a MultiElement HighLift Airfoil.
 Creator

Pascioni, Kyle A., Cattafesta, Louis N., Sussman, Mark, Alvi, Farrukh S., Xu, Cheryl, Choudhari, Meelan, Florida State University, College of Engineering, Department of...
Show morePascioni, Kyle A., Cattafesta, Louis N., Sussman, Mark, Alvi, Farrukh S., Xu, Cheryl, Choudhari, Meelan, Florida State University, College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

The leading edge slat of a highlift system is known to be a large contributor to the overall radiated acoustic field from an aircraft during the approach phase of the flight path. This is due to the unsteady flow field generated in the slatcove and near the leading edge of the main element. In an effort to understand the characteristics of the flowinduced source mechanisms, a suite of experimental measurements has been performed on a twodimensional multielement airfoil, namely, the MD...
Show moreThe leading edge slat of a highlift system is known to be a large contributor to the overall radiated acoustic field from an aircraft during the approach phase of the flight path. This is due to the unsteady flow field generated in the slatcove and near the leading edge of the main element. In an effort to understand the characteristics of the flowinduced source mechanisms, a suite of experimental measurements has been performed on a twodimensional multielement airfoil, namely, the MD30P30N. Particle image velocimetry provide mean flow field and turbulence statistics to illustrate the differences associated with a change in angle of attack. Phaseaveraged quantities prove shear layer instabilities to be linked to narrowband peaks found in the acoustic spectrum. Unsteady surface pressure are also acquired, displaying strong narrowband peaks and large spanwise coherence at low angles of attack, whereas the spectrum becomes predominately broadband at high angles. Nonlinear frequency interaction is found to occur at low angles of attack, while being negligible at high angles. To localize and quantify the noise sources, phased microphone array measurements are per formed on the two dimensional highlift configuration. A Kevlar wall test section is utilized to allow the mean aerodynamic flow field to approach distributions similar to a freeair configuration, while still capable of measuring the far field acoustic signature. However, the inclusion of elastic porous sidewalls alters both aerodynamic and acoustic characteristics. Such effects are considered and accounted for. Integrated spectra from Delay and Sum and DAMAS beamforming effectively suppress background facility noise and additional noise generated at the tunnel wall/airfoil junction. Finally, temporallyresolved estimates of a lowdimensional representation of the velocity vector fields are obtained through the use of proper orthogonal decomposition and spectral linear stochastic estimation. An estimate of the pressure field is then extracted by Poissons equation. From this, Curles analogy projects the timeresolved pressure forces on the airfoil surface to further establish the connection between the dominating unsteady flow structures and the propagated noise.
Show less  Date Issued
 2017
 Identifier
 FSU_2017SP_Pascioni_fsu_0071E_13776
 Format
 Thesis
 Title
 Neural Rule Ensembles: Encoding Feature Interactions into Neural Networks.
 Creator

Dawer, Gitesh, Barbu, Adrian G., Gallivan, Kyle A., Erlebacher, Gordon, Ökten, Giray, Sussman, Mark, Florida State University, College of Arts and Sciences, Department of...
Show moreDawer, Gitesh, Barbu, Adrian G., Gallivan, Kyle A., Erlebacher, Gordon, Ökten, Giray, Sussman, Mark, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

Artificial Neural Networks form the basis of very powerful learning methods. It has been observed that a naive application of fully connected neural networks often leads to overfitting. In an attempt to circumvent this issue, a prior knowledge pertaining to feature interactions can be encoded into these networks. This defines a taskspecific structure on an underlying representation and helps in reducing the number of learnable parameters. Convolutional Neural Network is such an adaptation of...
Show moreArtificial Neural Networks form the basis of very powerful learning methods. It has been observed that a naive application of fully connected neural networks often leads to overfitting. In an attempt to circumvent this issue, a prior knowledge pertaining to feature interactions can be encoded into these networks. This defines a taskspecific structure on an underlying representation and helps in reducing the number of learnable parameters. Convolutional Neural Network is such an adaptation of artificial neural networks for image datasets which exploits the spatial relationship among the features and explicitly encodes the translational equivariance. Similarly, Recurrent Neural Networks are designed to exploit the temporal relationship inherent in sequential data. However, for tabular datasets, any prior structure on feature relationships is not apparent. In this work, we use decision trees to capture such feature interactions for this kind of datasets and define a mapping to encode extracted relationships into a neural network. This addresses the initialization related concerns of fully connected neural networks and enables learning of compact representations compared to state of the art treebased approaches. Empirical evaluations and simulation studies show the superiority of such an approach over fully connected neural networks and treebased approaches.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Dawer_fsu_0071E_14670
 Format
 Thesis