Current Search: Wang, Xiaoqiang (x)
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 Title
 Fixed Point Theorems For A Class Of Nonlinear Sumtype Operators And Application In A Fractional Differential Equation.
 Creator

Wang, Hui, Zhang, Lingling, Wang, Xiaoqiang
 Abstract/Description

In this paper, we consider the fixed point for a class of nonlinear sumtype operators 'A +B+ C' on an ordered Banach space, where A, B are two mixed monotone operators, C is an increasing operator. Without assuming the existence of upperlower solutions or compactness or continuity conditions, we prove the unique existence of a positive fixed point and also construct two iterative schemes to approximate it. As applications, we research a nonlinear fractional differential equation with multi...
Show moreIn this paper, we consider the fixed point for a class of nonlinear sumtype operators 'A +B+ C' on an ordered Banach space, where A, B are two mixed monotone operators, C is an increasing operator. Without assuming the existence of upperlower solutions or compactness or continuity conditions, we prove the unique existence of a positive fixed point and also construct two iterative schemes to approximate it. As applications, we research a nonlinear fractional differential equation with multipoint fractional boundary conditions. By using the obtained fixed point theorems of sumtype operator, we get the sufficient conditions which guarantee the existence and uniqueness of positive solutions. At last, a specific example is provided to illustrate our result.
Show less  Date Issued
 20180918
 Identifier
 FSU_libsubv1_wos_000446257800001, 10.1186/s136610181059y
 Format
 Citation
 Title
 The Application of Dynamic Models to the Exploration of AR Overactivation as a Cause of Heart Failure.
 Creator

Wang, Xiaoyun, Zhao, Min, Wang, Xiaoqiang, Li, Shuping, Cao, Ning, Liu, Huirong
 Abstract/Description

High titer of adrenoreceptor autoantibodies (AA) has been reported to appear in heart failure patients. It induces sustained adrenergic receptor (AR) activation which leads to heart failure (HF), but the mechanism is as yet unclear. In order to investigate the mechanisms causing AR nondesensitization, we studied the beating frequency of the neonatal rat cardiomyocytes (NRCMs) under different conditions (an injection of isoprenaline (ISO) for one group and AA for the other) and...
Show moreHigh titer of adrenoreceptor autoantibodies (AA) has been reported to appear in heart failure patients. It induces sustained adrenergic receptor (AR) activation which leads to heart failure (HF), but the mechanism is as yet unclear. In order to investigate the mechanisms causing AR nondesensitization, we studied the beating frequency of the neonatal rat cardiomyocytes (NRCMs) under different conditions (an injection of isoprenaline (ISO) for one group and AA for the other) and established three dynamic models in order to best describe the true relationships shown in medical experiments; one model used a control group of healthy rats; then in HF rats one focused on conformation changes in AR; the other examined interaction between AR and adrenergic receptors (AR). Comparing the experimental data and corresponding Akaike information criterion (AIC) values, we concluded that the interaction model was the most likely mechanism. We used mathematical methods to explore the mechanism for the development of heart failure and to find potential targets for prevention and treatment. The aim of the paper was to provide a strong theoretical basis for the clinical development of personalized treatment programs. We also carried out sensitivity analysis of the initial concentration AA and found that they had a noticeable effect on the fitting results.
Show less  Date Issued
 20180730
 Identifier
 FSU_pmch_30154911, 10.1155/2018/1613290, PMC6091447, 30154911, 30154911
 Format
 Citation
 Title
 EdgeWeighted Centroidal Voronoi Tessellation Based Algorithms for Image Segmentation.
 Creator

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

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

Qu, Yenan, Erlebacher, Gordon, Ye, Ming, Wang, Xiaoqiang, Department of Scientific Computing, Florida State University
 Abstract/Description

Over the past decade, Web Services have played a prominent role in the Internet area and in the business world. My interest is focused on developing the toolkits for automatic web service and graphical user interface (GUI) generation, KWATT. The standalone KWATT service generator(KSG) is a C++ application that generates web services from Tcl, Python, and Ruby scripts uploaded by end user with KGT(Kwatt Gui Tools), with minimal user intervention. KSG Parser parses the scripts and extracts...
Show moreOver the past decade, Web Services have played a prominent role in the Internet area and in the business world. My interest is focused on developing the toolkits for automatic web service and graphical user interface (GUI) generation, KWATT. The standalone KWATT service generator(KSG) is a C++ application that generates web services from Tcl, Python, and Ruby scripts uploaded by end user with KGT(Kwatt Gui Tools), with minimal user intervention. KSG Parser parses the scripts and extracts information about procedures and userdefined control statements, embedded as comments. The KSG creates all necessary C++ wrappers, along with the code stubs required by gSOAP, a C++ interface to the SOAP protocol. Initially conceived to translate VTK frontend Tcl scripts into Web Services, the architecture is sufficiently general to accommodate a wide range of input languages. The work is extanded by considering the automatic creation of graphical user interfaces to allow interaction between an end user and the web service generated by the KSG. Kwatt GUI Generator(KGG) was developed to achieve this. The KGG is a web service that runs inside a service of Javabased open source, and it performs four major steps of GUI generation. First, the KGG receives the scripts from KGT (KWATT GUI Tools) after the corresponding web service generated successfully. Comment lines inserted into the scripts provide hints to the XML generator about the interface widgets. Second, the structure of the GUI is encoded into an XML file by parsing those scripts with the XML generator. Third, the KGG extracts information from the generated XML file, then passes them to a plugin. Finally, the plugin generates the corresponding language user interface that is sent back to the user by the KGG.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd2239
 Format
 Thesis
 Title
 Centroidal Voronoi Tessellations for Mesh Generation: from Uniform to Anisotropic Adaptive Triangulations.
 Creator

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

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

Lei, Hongzhuan, Ye, Ming, Wang, Xiaoqiang, Shanbhag, Sachin, Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

Excessive nitrogen loading to surface water bodies has resulted in serious environmental, economical, ecological, and human health problems, such as groundwater contamination and eutrophication in surface water. One important source of nitrogen in the environment, especially in densely populated coastal areas in Florida, is due to wastewater treatment using onsite sewage treatment and disposal systems (OSTDS) (a.k.a., septic systems). Moreover, due to the population expansion, nitrogen loads...
Show moreExcessive nitrogen loading to surface water bodies has resulted in serious environmental, economical, ecological, and human health problems, such as groundwater contamination and eutrophication in surface water. One important source of nitrogen in the environment, especially in densely populated coastal areas in Florida, is due to wastewater treatment using onsite sewage treatment and disposal systems (OSTDS) (a.k.a., septic systems). Moreover, due to the population expansion, nitrogen loads from septic systems are expected to increase. Therefore, sustainable decisionmaking and management of nitrogen pollution due to septic systems are urgently needed. In this thesis, two software are used to simulate the whole process of nitrogen (ammonium and nitrate) transport starting from septic systems to finally reach the surface waterbodies. One software is VZMOD, and the other one is the ArcGISbased Nitrogen Load Estimation Toolkit (ArcNLET). VZMOD is seamlessly integrated with ArcNLET in the way as follows. VZMOD is firstly used to simulate the flow and nitrogen transport in the vadose zone, which is between drain field infiltrative surface and water table, based on the assumption of steadystate, onedimensional vertical reactive transport with constant incoming fluxes of water, ammonium, and nitrate. The ammonium and nitrate concentrations, given by VZMOD at the water table, are then used as the inputs to the modeling of ammonium and nitrate fate and transport in groundwater in ArcNLET, considering heterogeneous hydraulic conductivity and porosity as well as spatial variability of septic system locations, surface water bodies, and distances between septic systems and surface water bodies. In addition, the key mechanisms controlling nitrogen transport, including advection, dispersion, and denitrification, are also considered in ArcNLET. The study sites of this thesis research are the MainSouth Canal (MSC) drainage basin and the City of Sebastian located in Indian River County in southeast Florida. Surface water bodies (e.g., rivers and streams) and groundwater at the two site discharge to the Southern Indian River Lagoon, where the ecological and biological integrity has deteriorated in the last several decades due to the decline in water quality caused in part by nitrogen pollution. There are in total 12,741 septic systems in the MSC area, while in the City of Sebastian, the number of septic systems is 4,883. The process of simulating nitrogen reactive transport from septic tanks to surface water bodies consists of the following three steps: (1) based on the sitespecific data, such as DEM, waterbodies, septic locations, hydraulic conductivity and porosity, forward models of VZMOD and ArcNLET is developed, (2) based on the measured data of system state variables, such as water level and nitrogen concentration, the forward models are calibrated, and (3) the calibrated models are used to simulate nitrogen plumes and to estimate nitrogen load from the septic systems to surface water bodies. Considering the modeling ability and the site complexity, two questions, (1) what are the nitrogen characteristics of these two sites, (2) can my model be able to capture these nitrogen characteristics, have been investigated in this study, and the major findings are as follows: (1) The simulated nitrogen plumes and load estimates exhibit substantial spatial variability in the both sites, and the depth from drainfields to water table is important to nitrogen reactive transport, especially the ammonium nitrification to nitrate. (2) Ammonium and nitrate loads for the MainSouth Canal drainage basin are largely located in the south to the South Canal drainage basin. Along the ditches and canals, the ammonium concentration is lower due to the small distance between water table and drainfields. There exists a region located in the southeast drainage basin where ammonium loading is high. (3) Incomplete nitrification process is exposed under the vadose zone while the denitrification process is mostly complete in the saturated zone in the MainSouth Canal area. (4) The nitrification process is largely complete under the unsaturated zone while the denitrification process is incomplete in the saturated zone in the City of Sebastian area. (5) Reduction ratio is lower while nitrogen loading to surface waterbodies per septic system is larger in the City of Sebastian area than in the MainSouth Canal area. (6) The flow model calibration in the City of Sebastian area is not as satisfactory as in the MainSouth Canal area, because of the simplified assumption that water table is a subdued replica of topography used in ArcNLET is not satisfied at the study site. These results can be used to support the ongoing Basin Management Action Plan. More efforts, such as investigating the soil condition (e.g. microbacteria content, dissolved oxygen or dissolved organic carbon and pH) and specific septic system environment, are also needed to verify these results and to develop more insights about the nitrogen processes in the study areas.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Lei_fsu_0071N_14260
 Format
 Thesis
 Title
 Generalized Mahalanobis Depth in Point Process and Its Application in Neural Coding and SemiSupervised Learning in Bioinformatics.
 Creator

Liu, Shuyi, Wu, Wei, Wang, Xiaoqiang, Zhang, Jinfeng, Mai, Qing, Florida State University, College of Arts and Sciences, Department of Statistics
 Abstract/Description

In the first project, we propose to generalize the notion of depth in temporal point process observations. The new depth is defined as a weighted product of two probability terms: 1) the number of events in each process, and 2) the centeroutward ranking on the event times conditioned on the number of events. In this study, we adopt the Poisson distribution for the first term and the Mahalanobis depth for the second term. We propose an efficient bootstrapping approach to estimate parameters...
Show moreIn the first project, we propose to generalize the notion of depth in temporal point process observations. The new depth is defined as a weighted product of two probability terms: 1) the number of events in each process, and 2) the centeroutward ranking on the event times conditioned on the number of events. In this study, we adopt the Poisson distribution for the first term and the Mahalanobis depth for the second term. We propose an efficient bootstrapping approach to estimate parameters in the defined depth. In the case of Poisson process, the observed events are order statistics where the parameters can be estimated robustly with respect to sample size. We demonstrate the use of the new depth by ranking realizations from a Poisson process. We also test the new method in classification problems using simulations as well as real neural spike train data. It is found that the new framework provides more accurate and robust classifications as compared to commonly used likelihood methods. In the second project, we demonstrate the value of semisupervised dimension reduction in clinical area. The advantage of semisupervised dimension reduction is very easy to understand. SemiSupervised dimension reduction method adopts the unlabeled data information to perform dimension reduction and it can be applied to help build a more precise prediction model comparing with common supervised dimension reduction techniques. After thoroughly comparing with dimension embedding methods with label data only, we show the improvement of semisupervised dimension reduction with unlabeled data in breast cancer chemotherapy clinical area. In our semisupervised dimension reduction method, we not only explore adding unlabeled data to linear dimension reduction such as PCA, we also explore semisupervised nonlinear dimension reduction, such as semisupervised LLE and semisupervised Isomap.
Show less  Date Issued
 2018
 Identifier
 2018_Sp_Liu_fsu_0071E_14367
 Format
 Thesis
 Title
 Flocking Implementation for the Blender Game Engine.
 Creator

Serrano, Myrna I. Merced, Erlebacher, Gordon, Ye, Ming, Wang, Xiaoqiang, Department of Scientific Computing, Florida State University
 Abstract/Description

In this thesis, we discuss the development of a new Boids system that simulates flocking behavior inside the Blender Game Engine and within the framework of the RealTime Par ticles System (RTPS) library developed by Ian Johnson. The collective behavior of Boids is characterized as an emergent behavior caused by following three steering behaviors: sep aration, alignment, and cohesion. The implementation leverages OpenCL to maintain the portability of the Blender across different graphics...
Show moreIn this thesis, we discuss the development of a new Boids system that simulates flocking behavior inside the Blender Game Engine and within the framework of the RealTime Par ticles System (RTPS) library developed by Ian Johnson. The collective behavior of Boids is characterized as an emergent behavior caused by following three steering behaviors: sep aration, alignment, and cohesion. The implementation leverages OpenCL to maintain the portability of the Blender across different graphics cards and operating systems. Bench marks of the RTPSFLOCK system show that our implementation speeds up Blender's original Boids implementation (which only runs outside the game engine) by more than an order of magnitude. We demonstrate our boids system in three ways. First, we illustrate how symmetry of the steering behavior is maintained in time. Second, we consider the behavior of a "swarm of bees" approaching their hive. And third, we simulate the motion of a "crowd" constrained to a twodimensional plane.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd2481
 Format
 Thesis
 Title
 Anova for Parameter Dependent Nonlinear PDEs and Numerical Methods for the Stochastic Stokes Equations.
 Creator

Chen, Zheng, Gunzburger, Max, Huï¬€er, Fred, Peterson, Janet, Wang, Xiaoqiang, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation includes the application of analysisofvariance (ANOVA) expansions to analyze solutions of parameter dependent partial differential equations and the analysis and finite element approximations of the Stokes equations with stochastic forcing terms. In the first part of the dissertation, the impact of parameter dependent boundary conditions on the solutions of a class of nonlinear PDEs is considered. Based on the ANOVA expansions of functionals of the solutions, the effects...
Show moreThis dissertation includes the application of analysisofvariance (ANOVA) expansions to analyze solutions of parameter dependent partial differential equations and the analysis and finite element approximations of the Stokes equations with stochastic forcing terms. In the first part of the dissertation, the impact of parameter dependent boundary conditions on the solutions of a class of nonlinear PDEs is considered. Based on the ANOVA expansions of functionals of the solutions, the effects of different parameter sampling methods on the accuracy of surrogate optimization approaches to PDE constrained optimization is considered. The effects of the smoothness of the functional and the nonlinearity in the PDE on the decay of the higherorder ANOVA terms are studied. The concept of effective dimensions is used to determine the accuracy of the ANOVA expansions. Demonstrations are given to show that whenever truncated ANOVA expansions of functionals provide accurate approximations, optimizers found through a simple surrogate optimization strategy are also relatively accurate. The effects of several parameter sampling strategies on the accuracy of the surrogate optimization method are also considered; it is found that for this sparse sampling application, the Latin hypercube sampling method has advantages over other wellknown sampling methods. Although most of the results are presented and discussed in the context of surrogate optimization problems, they also apply to other settings such as stochastic ensemble methods and reducedorder modeling for nonlinear PDEs. In the second part of the dissertation, we study the numerical analysis of the Stokes equations driven by a stochastic process. The random processes we use are white noise, colored noise and the homogeneous Gaussian process. When the process is white noise, we deal with the singularity of matrix Green's functions in the form of mild solutions with the aid of the theory of distributions. We develop finite element methods to solve the stochastic Stokes equations. In the 2D and 3D cases, we derive error estimates for the approximate solutions. The results of numerical experiments are provided in the 2D case that demonstrate the algorithm and convergence rates. On the other hand, the singularity of the matrix Green's functions necessitates the use of the homogeneous Gaussian process. In the framework of theory of abstract Wiener spaces, the stochastic integrals with respect to the homogeneous Gaussian process can be defined on a larger space than L2 . With some conditions on the density function in the definition of the homogeneous Gaussian process, the matrix Green's functions have well defined integrals. We have studied the probability properties of this kind of integral and simulated discretized colored noise.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd3851
 Format
 Thesis
 Title
 Centroidal Voronoi Tesselation of Manifolds Using the GPU.
 Creator

Bollig, Evan F., Erlebacher, Gordon, Gunzburger, Max, Wang, Xiaoqiang, Department of Scientific Computing, Florida State University
 Abstract/Description

Within the last decade, commodity Graphics Processing Units (GPUs) specialized for 2D and 3D scene rendering have seen an explosive growth in processing power compared to their general purpose counterpart, the CPU. Currently capable of near teraflop speeds and sporting gigabytes of onboard memory, GPUs have transformed from accessory video game hardware to truly general purpose computational coprocessors. One of the first applications of GPUs for general computing was 2D Voronoi tessellation...
Show moreWithin the last decade, commodity Graphics Processing Units (GPUs) specialized for 2D and 3D scene rendering have seen an explosive growth in processing power compared to their general purpose counterpart, the CPU. Currently capable of near teraflop speeds and sporting gigabytes of onboard memory, GPUs have transformed from accessory video game hardware to truly general purpose computational coprocessors. One of the first applications of GPUs for general computing was 2D Voronoi tessellationpartitioning a 2D domain into regions based on a set of seed points, such that regions contain all points closer to one seed than to any other. Although the topic has been revisited many times, related work has failed to consider GPU based production of emph{centroidal} Voronoi tessellations, where seed points are also the regional centers of mass. This thesis presents a first look at centroidal Voronoi tessellation computed entirely on the GPU. An extension to centroidal Voronoi tessellation is also considered for partitioning surfaces (2manifolds) of the form $f(u,v) ightarrow (u, v, z(u,v))$ using Euclidean based metrics. To complete these tasks, a highly efficient flooding algorithm is used for the Voronoi tessellation, while a regularized sampling approach is employed to compute the centroids of the Voronoi regions. Seeds are updated by a deterministic Lloyd's method.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd3606
 Format
 Thesis
 Title
 Numerical Implementation of Continuum Dislocation Theory.
 Creator

Xia, Shengxu, ElAzab, Anter, Plewa, Tomasz, Wang, Xiaoqiang, Department of Scientific Computing, Florida State University
 Abstract/Description

This thesis aims at theoretical and computational modeling of the continuum dislocation theory coupled with its internal elastic field. In this continuum description, the spacetime evolution of the dislocation density is governed by a set of hyperbolic partial differential equations. These PDEs must be complemented by elastic equilibrium equations in order to obtain the velocity field that drives dislocation motion on slip planes. Simultaneously, the plastic eigenstrain tensor that serves as...
Show moreThis thesis aims at theoretical and computational modeling of the continuum dislocation theory coupled with its internal elastic field. In this continuum description, the spacetime evolution of the dislocation density is governed by a set of hyperbolic partial differential equations. These PDEs must be complemented by elastic equilibrium equations in order to obtain the velocity field that drives dislocation motion on slip planes. Simultaneously, the plastic eigenstrain tensor that serves as a known field in equilibrium equations should be updated by the motion of dislocations according to Orowan's law. Therefore, a stress dislocation coupled process is involved when a crystal undergoes elastoplastic deformation. The solutions of equilibrium equation and dislocation density evolution equation are tested by a few examples in order to make sure appropriate computational schemes are selected for each. A coupled numerical scheme is proposed, where resolved shear stress and Orowan's law are two passages that connect these two sets of PDEs. The numerical implementation of this scheme is illustrated by an example that simulates the recovery process of a dislocated cubic crystal. The simulated result demonstrates the possibility to couple macroscopic(stress) and microscopic(dislocation density tensor) physical quantity to obtain crystal mechanical response.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd5280
 Format
 Thesis
 Title
 Monte Carlo Simulation of Phonon Transport in Uranium Dioxide.
 Creator

Deskins, Walter Ryan, ElAzab, Anter, Plewa, Tomasz, Wang, Xiaoqiang, Department of Scientific Computing, Florida State University
 Abstract/Description

Heat is transfered in crystalline semiconductor materials via lattice vibrations. Lattice vibrations are treated with a waveparticle duality just like photons are quantum mechanical representations of electromagnetic waves. The quanta of energy of these lattice waves are called phonons. The Boltzmann Transport Equation (BTE) has proved to be a powerful tool in modeling the phonon heat conduction in crystalline solids. The BTE tracks the phonon number density function as it evolves according...
Show moreHeat is transfered in crystalline semiconductor materials via lattice vibrations. Lattice vibrations are treated with a waveparticle duality just like photons are quantum mechanical representations of electromagnetic waves. The quanta of energy of these lattice waves are called phonons. The Boltzmann Transport Equation (BTE) has proved to be a powerful tool in modeling the phonon heat conduction in crystalline solids. The BTE tracks the phonon number density function as it evolves according to the drift of all phonons and to the phononphonon interactions (or collisions). Unlike Fourier's law which is limited to describing diffusive energy transport, the BTE can accurately predict energy transport in both ballistic (virtually no collisions) and diffuse regimes. Motivated by the need to understand thermal transport in irradiated Uranium Dioxide at the mesoscale, this work investigates phonon transport in UO2 using Monte Carlo simulation. The simulation scheme aims to solve the Boltzmann transport equation for phonons within a relaxation time approximation. In this approximation the Boltzmann transport equation is simplified by assigning time scales to each scattering mechanism associated with phonon interactions. The Monte Carlo method is first benchmarked by comparing to similar models for silicon. Unlike most previous works on solving this equation by Monte Carlo method, the momentum and energy conservation laws for phononphonon interactions in UO2 are treated exactly; in doing so, the magnitude of possible wave vectors and frequency space are all discretized and a numerical routine is then implemented which considers all possible phononphonon interactions and chooses those interactions which obey the conservation laws. The simulation scheme accounts for the acoustic and optical branches of the dispersion relationships of UO2. The six lowest energy branches in the [001] direction are tracked within the Monte Carlo. Because of their predicted low group velocities, the three remaining, highenergy branches are simply treated as a reservoir of phonons at constant energy in Kspace. These phonons contribute to the thermal conductivity only by scattering with the six lower energy branches and not by their group velocities. Using periodic boundary conditions, this work presents results illustrating the diffusion limit of phonon transport in UO2 single crystals, and computes the thermal conductivity of the material in the diffusion limit based on the detailed phonon dynamics. The temperature effect on conductivity is predicted and the results are compared with experimental data available in the literature.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd4796
 Format
 Thesis
 Title
 Phase Field Modeling of Microstructure Evolution in Thermal Barrier Coating Systems.
 Creator

Ahmed, Karim, ElAzab, Anter, MeyerBaese, Anke, Shanbhag, Sachin, Wang, Xiaoqiang, Program in Materials Science, Florida State University
 Abstract/Description

The development of robust thermal barrier coating (TBC) systems is crucial in many hightemperature applications. The performance of a TBC system is significantly limited by microstructural evolution mechanisms, such as sintering at elevated temperatures. Sintering reduces the porosity of TBC and makes it denser which eventually increases the thermal conductivity and reduces the strain compliance of TBC. Understanding how sintering proceeds in TBC systems is thus important in improving the...
Show moreThe development of robust thermal barrier coating (TBC) systems is crucial in many hightemperature applications. The performance of a TBC system is significantly limited by microstructural evolution mechanisms, such as sintering at elevated temperatures. Sintering reduces the porosity of TBC and makes it denser which eventually increases the thermal conductivity and reduces the strain compliance of TBC. Understanding how sintering proceeds in TBC systems is thus important in improving the design of such systems. An elaborate phase field model was developed in order to understand the sintering behavior of columnar TBC structure. The model takes into account different sintering mechanisms, such as volume diffusion, grain boundary diffusion, surface diffusion, and grain boundary migration, coupled with elastic strain arising from the thermal expansion mismatch in thermal barrier coating system. Direct relations between model parameters and material properties were established. Such relations facilitate quantitative studies of the sintering process in any material of interest. The model successfully demonstrates a strong dependence of the sintering process in TBC on the initial morphology and dimensions of coatings, strain, and temperature.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd4684
 Format
 Thesis
 Title
 Computational Modeling of Elastic Fields in Dislocation Dynamics.
 Creator

Mohamed, Mamdouh, ElAzab, Anter, Van Dommelen, Leon, Erlebacher, Gordon, Ye, Ming, Wang, Xiaoqiang, Department of Scientific Computing, Florida State University
 Abstract/Description

In the present work, we investigate the internal fields generated by the dislocation structures that form during the deformation of copper single crystals. In particular, we perform computational modeling of the statistical and morphological characteristics of the dislocation structures obtained by dislocation dynamics simulation method and compare the results with Xray microscopy measurements of the same data. This comparison is performed for both the dislocation structure and their...
Show moreIn the present work, we investigate the internal fields generated by the dislocation structures that form during the deformation of copper single crystals. In particular, we perform computational modeling of the statistical and morphological characteristics of the dislocation structures obtained by dislocation dynamics simulation method and compare the results with Xray microscopy measurements of the same data. This comparison is performed for both the dislocation structure and their internal elastic fields for the cases of homogeneous deformation and indentation of copper single crystals. A direct comparison between dislocation dynamics predictions and Xray measurements plays a key role in demonstrating the fidelity of discrete dislocation dynamics as a predictive computational mechanics tool and in understanding the Xray data. For the homogeneous deformation case, dislocation dynamics simulations were performed under periodic boundary conditions and the internal fields of dislocations were computed by solving an elastic boundary value problem of manydislocation system using the finite element method. The distribution and pair correlation functions of all internal elastic fields and the dislocation density were computed. For the internal stress field, the availability of such statistical information paves the way to the development of a densitybased mobility law of dislocations in continuum dislocation dynamics models, by correlating the internalstress statistics with dislocation velocity statistics. The statistical analysis of the lattice rotation and the dislocation density fields in the deformed crystal made possible the direct comparison with Xray measurements of the same data. Indeed, a comparison between the simulation and experimental measurements has been possible, which revealed important aspects of similarity and differences between the simulation results and the experimental data. In the case of indentation, which represents a highly inhomogeneous deformation, a contact boundary value problem was solved in conjunction with a discretedislocation dynamics simulation model; the discrete dislocation dynamics simulation was thus enabled to handle finite domains under mixed traction/displacement boundary conditions. The loaddisplacement curves for indentation experiments were analyzed with regard to cross slip, indentation speed and indenter shape. The lattice distortion fields obtained by indentation simulations were directly compared with their experimental counterparts. Other indentation simulations were also carried out, giving insight into different aspects of microscale indentation deformation.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd6962
 Format
 Thesis
 Title
 Artificial Prediction Markets for Classification, Regression and Density Estimation.
 Creator

Lay, Nathan, Barbu, Adrian, MeyerBaese, Anke, Sinha, Debajyoti, Ming, Ye, Wang, Xiaoqiang, Department of Scientific Computing, Florida State University
 Abstract/Description

Prediction markets are forums of trade where contracts on the future outcomes of events are bought and sold. These contracts reward buyers based on correct predictions and thus give incentive to make accurate predictions. Prediction markets have successfully predicted the outcomes of sporting events, elections, scientific hypothesese, foreign affairs, etc... and have repeatedly demonstrated themselves to be more accurate than individual experts or polling [2]. Since prediction markets are...
Show morePrediction markets are forums of trade where contracts on the future outcomes of events are bought and sold. These contracts reward buyers based on correct predictions and thus give incentive to make accurate predictions. Prediction markets have successfully predicted the outcomes of sporting events, elections, scientific hypothesese, foreign affairs, etc... and have repeatedly demonstrated themselves to be more accurate than individual experts or polling [2]. Since prediction markets are aggregation mechanisms, they have garnered interest in the machine learning community. Artificial prediction markets have been successfully used to solve classification problems [34, 33]. This dissertation explores the underlying optimization problem in the classification market, as presented in [34, 33], proves that it is related to maximum log likelihood, relates the classification market to existing machine learning methods and further extends the idea to regression and density estimation. In addition, the results of empirical experiments are presented on a variety of UCI [25], LIAAD [49] and synthetic data to demonstrate the probability accuracy, prediction accuracy as compared to Random Forest [9] and Implicit Online Learning [32], and the loss function.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7461
 Format
 Thesis
 Title
 Sparse Motion Analysis.
 Creator

Ding, Liangjing, Barbu, Adrian, MeyerBaese, Anke, Liu, Xiuwen, Slice, Dennis, Wang, Xiaoqiang, Department of Scientific Computing, Florida State University
 Abstract/Description

Motion segmentation is an essential preprocessing task in many computer vision problems. In this dissertation, the motion segmentation problem is studied and analyzed. At first, we establish a framework for the accurate evaluation of the motion field produced by different algorithms. Based on the framework, we introduce a feature tracking algorithm based on RankBoost which automatically prunes bad trajectories. The algorithm is observed to outperform many feature trackers using different...
Show moreMotion segmentation is an essential preprocessing task in many computer vision problems. In this dissertation, the motion segmentation problem is studied and analyzed. At first, we establish a framework for the accurate evaluation of the motion field produced by different algorithms. Based on the framework, we introduce a feature tracking algorithm based on RankBoost which automatically prunes bad trajectories. The algorithm is observed to outperform many feature trackers using different measures. Second, we develop three different motion segmentation algorithms. The first algorithm is based on spectral clustering. The affinity matrix is built from the angular information between different trajectories. We also propose a metric to select the best dimension of the lower dimensional space onto which the trajectories are projected. The second algorithm is based on learning. Using training examples, it obtains a ranking function to evaluate and compare a number of motion segmentations generated by different algorithms and pick the best one. The third algorithm is based on energy minimization using the SwendsenWang cut algorithm and the simulated annealing. It has a time complexity of $O(N^2)$, comparing to at least $O(N^3)$ for the spectral clustering based algorithms; also it could take generic forms of energy functions. We evaluate all three algorithms as well as several other stateofthe several other stateoftheart methods on a standard benchmark and show competitive performance.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7355
 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
 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
 Identifying Weak and Strong Binding States of Myosin V on FActin in the ADPÂ·Pi Condition.
 Creator

Dai, Aguang, Taylor, Kenneth A., Wang, Xiaoqiang, Li, Hong, Keller, Thomas C. S., Stagg, Scott, Program in Molecular Biophysics, Florida State University
 Abstract/Description

Myosin V, as a member of the myosin family, can "walk" along Factin to transport many "cargos", such as mRNA and secretary vesicles, to its destination. This study is part of a research project that aims to understand the interaction between myosin V with Factin through direct visualization of biochemical states of myosin V that bind weakly to Factin and are thus conformationally heterogeneous. Because of its processivity, it's a good model to illustrate how myosin interacts with Factin...
Show moreMyosin V, as a member of the myosin family, can "walk" along Factin to transport many "cargos", such as mRNA and secretary vesicles, to its destination. This study is part of a research project that aims to understand the interaction between myosin V with Factin through direct visualization of biochemical states of myosin V that bind weakly to Factin and are thus conformationally heterogeneous. Because of its processivity, it's a good model to illustrate how myosin interacts with Factin to fulfill its function (Chapter 1). Specimens of fulllength myosin V with Factin were cryogenically vitrified to maintain the closetonature conformation. ADPÂ·Pi was added into the solution to keep myosin V in the inhibited state in which the heads are folded back onto the cargo binding domain thereby preventing both heads from binding to a single actin filament at the same time. Electron Tomography rather than singleparticle method was used because the relatively low affinity of inhibited myosin V to Factin which makes the decoration far away from saturation. With subsequent subvolume processing, ET can provide molecularlevel information for relatively heterogeneous and/or sparse macromolecule complexes (Chapter 2). New strategies and methods for processing tomographic subvolumes with heterogeneity were designed to extract homogenous and meaningful classaverages. Factin repeats with or without myosin V decoration were extracted to do the subvolume averaging. Multivariate Data Analysis (MDA) and cluster analysis were used to deal with the heterogeneity issue. More homogeneous repeats were clustered into the same classes and corresponding classaverages were generated to improve signaltonoise ratio (SNR). Repeats with myosin V decoration were later identified and grouped together to get the conformational information. Focused classification was used to further separate different conformations of the bound myosin V (Chapter 3). The new data processing methods present much conformational information of inhibited myosin V on Factin. The enumeration of bound myosin V shows that inhibited myosin V mainly is bound to Factin with only one head. Analysis of the binding angle of the leverarm with respect to the Factin filament shows the leverarm angle of most bound myosin V is not close to 90Âº, which means that most bound myosin might be not in the transition state. This could be due to Pi release after myosin V binds to Factin such that Myosin V is in the rigorlike state, even though ADPÂ·Pi is present in the solution. However, for some bound myosin V, the leverarm angle is really close to 90Âº, which means the leverarm is in the "up" position or that the myosin head is binding to actin weakly in a previously unidentified orientation. One explanation is that even though the binding to Factin could accelerate the release of Pi, some bound myosin V might be still frozen with ADPÂ·Pi during fastfreezing. In addition, copies of doublehead bound myosin V were found. The existence of doublehead binding requires that the two heads be bound to actin in different conformations; this could be because of random Brownian motion of the second head and subsequent collision. Further quasiatomic models were built and docked into classaverages to determine the possible nucleotide condition and provide structural information beyond the resolution of the density map. The improved procedure, with quantitative analysis and simulated data verification provides integrated and detailed structural information of inhibited myosin V on Factin (Chapter 4). Here we identified and characterized the conformation of inhibited myosin V bound to the Factin filament. We found most inhibited myosin V bound to Factin with one head. Also we found the leverarm of most myosin V could be in a rigorlike position rather than the transition position. In addition to single head binding, we found some copies of doublehead binding, one head in rigorlike binding state and the other in the transition state. It's the first time to obtain the molecularlevel structural information of inhibited myosin V on Factin, which could fix the missing structural gap for the myosin V ATPase cycle, thus helping us better understand the mechanism of myosin (Chapter 4).
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8969
 Format
 Thesis
 Title
 Statistical Data Analysis of Resting State fMRI: A Study of Nicotine Addiction Treatment.
 Creator

Ehtemami, Anahid, MeyerBaese, Anke, Wang, Xiaoqiang, Beerli, Peter, Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

Statistical analysis methods are used by neuroscience researchers to obtain meaningful information from functional magnetic resonance imaging data to learn more about mind and brain. Machine learning, more specifically pattern recognition and classification tools are frequently used to find regularities in brain scans of different people and/or different stages of a illnesses to understand how functional and anatomical structure of the brain changes under different circumstances. Studies have...
Show moreStatistical analysis methods are used by neuroscience researchers to obtain meaningful information from functional magnetic resonance imaging data to learn more about mind and brain. Machine learning, more specifically pattern recognition and classification tools are frequently used to find regularities in brain scans of different people and/or different stages of a illnesses to understand how functional and anatomical structure of the brain changes under different circumstances. Studies have confirmed that nicotine dependence have impacts on human behaviors such as emotions and motivations, ability to focus, and recalling information which proves nicotine dependency alters brain networks. This study was conducted to investigate this alterations and to test if they can be used for fMRI data classification. The two sets of data that are used are fMRI brain scans from before and after a nicotine addiction treatment on patients. Some of the patients received placebo instead of the real treatment and the goal is to develop a method to be able to classify new patients based on receiving the real treatment or the placebo. The success of the two classification methods, support vector machine and decision trees on the processed data, was not significant and they should not be considered as reliable methods for use in medical diagnosis. This might be due to the different challenges that are present in analyzing fMRI data such as feature to instance ratio, signal to noise ratio and redundancy.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Ehtemami_fsu_0071N_13634
 Format
 Thesis
 Title
 Investigating Vesicle Adhesions Using Multiple Phase Field Functions.
 Creator

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Stoyanova, Detelina, Slice, Dennis E., Creswell, Michael H., AlgeeHewitt, Bridget, Beerli, Peter, Wang, Xiaoqiang, Florida State University, College of Arts and Sciences,...
Show moreStoyanova, Detelina, Slice, Dennis E., Creswell, Michael H., AlgeeHewitt, Bridget, Beerli, Peter, Wang, Xiaoqiang, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

The identification of forensic cases often includes the use of skeletal elements to assess the ageatdeath of an individual. The pubic symphysis is the preferred and most often used skeletal age indicator. Standard techniques, such as the SucheyBrooks system, require that the morphology of the pubic symphysis is visually compared to shape characteristics typical for phases with associated age intervals. As individual factors accumulate during the aging process, estimating the ageatdeath...
Show moreThe identification of forensic cases often includes the use of skeletal elements to assess the ageatdeath of an individual. The pubic symphysis is the preferred and most often used skeletal age indicator. Standard techniques, such as the SucheyBrooks system, require that the morphology of the pubic symphysis is visually compared to shape characteristics typical for phases with associated age intervals. As individual factors accumulate during the aging process, estimating the ageatdeath for older individuals becomes increasingly more difficult. In addition, methods based on visual inspection of the bones introduce some level of subjectivity and observerrelated error. This research makes use of about 100 3D laser scans of the pubic symphysis of white male skeletons with known agesatdeath, and proposes several objective, quantitative methods for shape analysis that aim to provide a surface or outline measure of the shape of the scans that minimizes the ageestimation error. The proposed methods include the use of thin plate splines, twodimensional Fourier, wavelet and elliptic Fourier analysis, and a technique that uses the radius of a best fitting circle (in 2D) or sphere (in 3D) as a measure of the curvature of a shape. In addition some refinement and partitioning techniques were implemented. The project investigates the relationship between the exact ageatdeath and the different measures produced by each method. Also included are results of applying a recently proposed computational method, the SAHScore, to new scan data and scan partitions. As a final result, the project proposes multivariate regression models that combine the measures with highest statistical significance to minimize the age estimation error (about 12 years) and maximize the adjusted Rsquared value (over 55%). Furthermore, the results are subjected to two crossvalidation analysis to test for the accuracy of the models when used in practice.
Show less  Date Issued
 2015
 Identifier
 FSU_2015fall_Stoyanova_fsu_0071E_12868
 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 NaÃ¯ve 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
 Modeling of Complex Behaviors of Submarine Debris Flows.
 Creator

Saha, Bikash C. (Bikash Chandra), Ye, Ming, Niedoroda, Alan W., Misra, Vasubandhu, Shanbhag, Sachin, Wang, Xiaoqiang, Florida State University, College of Arts and Sciences,...
Show moreSaha, Bikash C. (Bikash Chandra), Ye, Ming, Niedoroda, Alan W., Misra, Vasubandhu, Shanbhag, Sachin, Wang, Xiaoqiang, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Submarine debris flows are hazards when they threaten the facilities that are built on sea floor to facilitate submarine transportation. The dynamics of submarine debris flow is simple once the debris material gets in the flow motion and that it can be represented using simple physics. A twodimensional model with twolayer Bingham fluid representations, SDFlow2D, was developed by using an Eulerian frame of reference to predict the consequences of complex submarine debris flows. The model was...
Show moreSubmarine debris flows are hazards when they threaten the facilities that are built on sea floor to facilitate submarine transportation. The dynamics of submarine debris flow is simple once the debris material gets in the flow motion and that it can be represented using simple physics. A twodimensional model with twolayer Bingham fluid representations, SDFlow2D, was developed by using an Eulerian frame of reference to predict the consequences of complex submarine debris flows. The model was viscoplastic in nature based on depthaveraged approximation to the Shallow Water Equations (SWE), and it assumes that the flow consists of a nondeforming upper layer riding on a deforming layer. The model was verified by comparing the numerical solution with experimental observations as well as with an analytical solution. The comparison shows a good agreement with analytical solution and an acceptable agreement with experimental observations. The model was found to be capable of simulating realword submarine debris flows. The consequence of bed material entrainment is worth studying as this process adds antecedent sediment to the debris flow mass that in turn increases the intensity of hazard. The modeling code SDFlow2D was enhanced by using simple physics to include the capability of computing bed material entrainment. It was assumed that no inertial force was involved in the process, and that the entrainment was instantaneous. The modified SDFlow2D was applied to two idealized cases and to a prognostic case. A total variation diminishing (TVD) scheme with flux limiter was applied with MacCormack predictorcorrector scheme to smooth out the spurious solution near the source area of debris flow. While the TVD scheme served that purpose to some extent, it was not helpful to make the model robust as the computational time was 15 times greater than that of using the code without TVD scheme. The Bayesian inverse modeling was implemented to quantify the Bingham parameters uncertainty. The technique helps find not only the most probable pair of Bingham parameters but also the distribution of the parameters by conducting a small number of model simulations. The overall outcome of the study benefits the deep sea explorers as well as the designers and planners in charge of designing the submarine structures.
Show less  Date Issued
 2017
 Identifier
 FSU_2017SP_Saha_fsu_0071E_13595
 Format
 Thesis
 Title
 Spherical Centroidal Voronoi Tessellation Based Unstructured Meshes for Multidomain Multiphysics Applications.
 Creator

Womeldorff, Geoffrey A., Gunzburger, Max, Peterson, Janet, Gallivan, Kyle, Erlebacher, Gordon, Wang, Xiaoqiang, Ringler, Todd, Department of Scientific Computing, Florida State...
Show moreWomeldorff, Geoffrey A., Gunzburger, Max, Peterson, Janet, Gallivan, Kyle, Erlebacher, Gordon, Wang, Xiaoqiang, Ringler, Todd, Department of Scientific Computing, Florida State University
Show less  Abstract/Description

This dissertation presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT) which are to be used for multiphysics, multidomain applications. As an introduction, we discuss grid generation on the sphere in a broad fashion. Next, we discuss the theory of CVTs in general, and specifically on the sphere. Subsequently we consider the iterative processes, such as Lloyd's algorithm, which are used to construct them. Following...
Show moreThis dissertation presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT) which are to be used for multiphysics, multidomain applications. As an introduction, we discuss grid generation on the sphere in a broad fashion. Next, we discuss the theory of CVTs in general, and specifically on the sphere. Subsequently we consider the iterative processes, such as Lloyd's algorithm, which are used to construct them. Following this, we describe a method for density functions via images so that we can shape generator density in an intuitive, yet arbitrary, manner, and then a method by which SCVTs can be easily adapted to conform to arbitrary sets of line segments, or shorelines. Then, we discuss sample meshes, used for various physical and nonphysical applications. Penultimately, we discuss two sample applications, as a proof of concept, where we adapt the Shallow Water Model from Model for Predictions Across Scales (MPAS) to use our grids for a more accurate border, and we also discuss elliptic interface problems both with and without hanging nodes. Finally, we share a few concluding remarks.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd5250
 Format
 Thesis
 Title
 Phasefield Modeling of Void Nucleation and Growth in Irradiated Materials.
 Creator

Rokkam, Srujan K., ElAzab, Anter, Van Dommelen, Leon, Wang, Xiaoqiang, Hellstrom, Eric, Ordonez, Juan, Department of Mechanical Engineering, Florida State University
 Abstract/Description

Irradiation induced voids and associated swelling is one of the most intriguing and technologically relevant problems in the design of structural materials for nuclear reactor components. Traditional approaches model void nucleation and growth as separate processes that are uniform in space, treating them within the framework of classical nucleation theory and chemical rate theory, respectively. However, void formation and myriad other phenomena occurring in materials exposed to irradiation...
Show moreIrradiation induced voids and associated swelling is one of the most intriguing and technologically relevant problems in the design of structural materials for nuclear reactor components. Traditional approaches model void nucleation and growth as separate processes that are uniform in space, treating them within the framework of classical nucleation theory and chemical rate theory, respectively. However, void formation and myriad other phenomena occurring in materials exposed to irradiation are sensitive to the dynamics of point defects and their interaction with other microstructural entities. Motivated by the need to develop a spatially resolved theory of irradiationinduced microstructural evolution in materials, in the present work a phasefield framework has been developed for modeling the evolution of void microstructure under irradiation. The phasefield model treats void nucleation and growth processes simultaneously in a spatially resolved fashion. Using principles of irreversible thermodynamics and gradient description of inhomogeneous systems the temporal evolution equations for field variables characterizing the material system are cast in the form of a set of coupled CahnHilliard and AllenCahn type equations. The point defect fluxes and their distributions follow a CahnHilliard type description for vacancy and interstitial concentration fields. The dynamics of void formation and growth is obtained in terms of the evolution of nonconserved void phasefield, prescribed by a phenomenological AllenCahn type equation. Irradiation induced point defects are modeled as stochastic sources in CahnHilliard equation, which introduces vacancies and interstitials in a spatially segregated fashion similar to the nature of the displacement cascade. The model accounts for mutual interactions between point defects, interactions between point defects and extended defects or sinks, cascade and thermally induced fluctuations. Illustrative results are presented using two dimensional numerical simulations that characterize: (a) void growth or shrinkage due to supersaturated vacancy or interstitial concentrations, (b) voidvoid interactions, (c) void nucleation and growth kinetics due to cascade induced defects, (d) formation of void denuded and void peak zones adjacent to grain boundaries, and (e) dynamics of concurrent swelling, nucleation and growth under irradiation. The model reproduces essential features of void formation in addition to resolving the time and space coupling between the defect field evolution and void phase dynamics. In addition, swelling studies based on the current model reveal that swelling of the material can occur prior to the nucleation of voids, through the buildup of material layers resulting from migrating interstitials reaching the surface.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd7222
 Format
 Thesis
 Title
 Optimization of Groundwater LongTerm Monitoring Network Optimization of Groundwater LongTerm Monitoring Network with Ant Colony Optimization with Ant Colony Optimization.
 Creator

Liu, Xiaoli, Chen, Gang, Ye, Ming, Wang, Xiaoqiang, Hilton, Amy B. Chan, Huang, Wenrui, Tang, Youneng, Florida State University, College of Engineering, Department of Civil and...
Show moreLiu, Xiaoli, Chen, Gang, Ye, Ming, Wang, Xiaoqiang, Hilton, Amy B. Chan, Huang, Wenrui, Tang, Youneng, Florida State University, College of Engineering, Department of Civil and Environmental Engineering
Show less  Abstract/Description

Groundwater remediation is conducted in polluted sites to remove contaminants and to restore ground water quality. After remediation goals are achieved, longterm groundwater monitoring (LTM) that can span decades is required to assess the concentration of residual contaminants and to avoid the risk of human health and environment. On large remediation sites, the cost for maintaining a LTM network, collecting samples, conducting water quality lab analysis can be a significant, persistent and...
Show moreGroundwater remediation is conducted in polluted sites to remove contaminants and to restore ground water quality. After remediation goals are achieved, longterm groundwater monitoring (LTM) that can span decades is required to assess the concentration of residual contaminants and to avoid the risk of human health and environment. On large remediation sites, the cost for maintaining a LTM network, collecting samples, conducting water quality lab analysis can be a significant, persistent and growing financial burden for the private entities and government agencies who are responsible for environmental remediation projects. LTM network optimization offers an opportunity to improve the costeffectiveness of the LTM effort while meeting data accuracy requirements. The optimization includes identifying the redundancy in the monitoring network, and recommending changes to protect against potential impacts to the public and the environment. This study develops a variant ant colony optimization (VACO) method, using ordinary kriging (OK) or inverse distance weighting (IDW) for data interpolation, to identify optimal LTM networks that minimize the cost of LTM by reducing the number of monitoring locations with minimum overall data loss. ACO is a global stochastic search method inspired by the collective problemsolving ability of a colony of ants as they search for the most efficient routes from their nests to food sources. The performance of ACO variant (VACO) developed in this study is evaluated separately in two test cases. In the first case, VACO is used to solve a simplified traveling sales person problem. In the second case, both enumeration method and VACO are employed for optimization of a synthetic long term monitoring network of 73 wells generated from a groundwater transport simulation model. The two sets of test show that the VACO performs well for optimization problems. The VACO is finally adopted for the optimization of a long term monitoring network of 30 wells in Logistic Center, Washington, with the data interpolation methods of inverse distance weighing, ordinary kriging, and modified inverse distance weighing which is developed in this study. The optimization results are analyzed and group of ideal redundant wells identified. The conclusion of this study is summarized at the end, and future work is suggested.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Liu_fsu_0071E_14254
 Format
 Thesis
 Title
 Multiscale Simulation in Material Science and Engineering: Computational Heterogeneous Catalysis and Molecular Design.
 Creator

Shaban Tameh, Maliheh, Huang, Chen, Oates, William, Shanbhag, Sachin, Wang, Xiaoqiang, Hu, Yanyan, Florida State University, College of Arts and Sciences, Department of...
Show moreShaban Tameh, Maliheh, Huang, Chen, Oates, William, Shanbhag, Sachin, Wang, Xiaoqiang, Hu, Yanyan, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Simulation is valuable since it can provide a link between theory and experiment. Whereas, com puter modeling is based on theory and is limited to simple models, we can explore many physical properties in a parallel way to experiment. Advances in computational physics and chemistry have been an important platform to achieve this progress. Ab initio electronic structure methods take advantage of this platform to accomplish accurate electroniclevel calculations in surface science. In the...
Show moreSimulation is valuable since it can provide a link between theory and experiment. Whereas, com puter modeling is based on theory and is limited to simple models, we can explore many physical properties in a parallel way to experiment. Advances in computational physics and chemistry have been an important platform to achieve this progress. Ab initio electronic structure methods take advantage of this platform to accomplish accurate electroniclevel calculations in surface science. In the meanwhile, the link between electronic structure methods and statistical methods is capable of providing a deep description of the science governing the properties of materials under realistic conditions. Here, we address two branches of multiscale approaches emphasizing computational heteroge neous catalysis and design of phosphorescent molecular butterflies. Computational modeling of molecules, material and surfaces is becoming an important tool in the design of heterogeneous catalysts. In this thesis, we aim to investigate computational design of catalytic materials in the atomic scale by means of highly accurate quantum mechanics methods in a reasonable frame of computational cost. Ab initioâ€“based prediction of the underlying mechanisms and active sites describes the physics that govern the catalytic process under realistic reaction conditions. A better understanding of photoinduced chemical and biological processes can be achieved upon detailed studies of the excitedstate properties of molecules, including their structures, energetics, and decay pathways. This is lead to development of new functional materials and devices. First, we start with an overview of density functional theory (DFT) that is widely used in this study. Second, industrial methanol synthesis is explored. Synthesis of methanol from syngases CO/CO2/H2 is a catalytic process that is important in industrial and has many attractive features. Methanol is used primarily as a feedstock or solvent for chemical synthesis and is valuable as a fuel or precursor for synthetic fuels. Methanol synthesis is a wellstudied reaction in heterogeneous catalysis. Despite extensive research on producing methanol of hydrogenation CO/CO2, it is still highly debated that which pathway plays significant role in reality. Substantial efforts lie in the frame work of Density Functional Theory (DFT) to realize the mechanism and catalyst models. We discuss the reliability of DFT to evaluate this catalytic process. Third, we focus on water gas shift (WGS) reaction at low temperature over copper catalyst that is a wellstudied catalytic reaction and is an important industrial process to produce hydrogen from CO and H2O that can be used for applications such as ammonia production and hydrogen fuel cells. Two mechanisms of redox and carboxyl are examined by DFT employing three levels of exchangecorrelation (XC) functionals: PerdewBurke Ernzerhof (PBE) functional, HeydScuseriaErnzerhof (HSE) hybrid functional, and exact exchange (EXX) and RPA correlation functional. To gain insight into ki netic of these catalytic reactions, we combine DFT energies with microkinetic modeling. Lastly, a series of rationally designed butterflyâ€“like phosphorescent binuclear platinum complexes that can generate dual emission with flapping their wings upon photoexcitation are studied. Based on the Bellâ€“Evansâ€“Polanyi principle, the energy barrier of the photoinduced structural change (PSC) of the Ptâ€“Pt distance can be controlled and subsequently, the coexistence of two distinct excited states, one with high energy at a long Ptâ€“Pt distance and the other with low energy at a short Ptâ€“Pt distance can be achieved and then dual emission of molecular systems is engineered.
Show less  Date Issued
 2018
 Identifier
 2018_Fall_ShabanTameh_fsu_0071E_14855
 Format
 Thesis