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 Title
 The Decision Space Worksheet, the Career Thoughts Inventory, and the Beck Depression InventoryII as Measures of Mental Health in the Career DecisionMaking Process.
 Creator

Solomon, Jennifer L. (Jennifer Lynn), Sampson, James, Kistner, Janet, Peterson, Gary, Lenz, Janet, Department of Educational Psychology and Learning Systems, Florida State...
Show moreSolomon, Jennifer L. (Jennifer Lynn), Sampson, James, Kistner, Janet, Peterson, Gary, Lenz, Janet, Department of Educational Psychology and Learning Systems, Florida State University
Show less  Abstract/Description

At the outset of career counseling, clarifying the nature of an individual's career problem is vital in order to ascertain the appropriate initial steps of the career intervention (Sampson, Peterson, Reardon, & Lenz, 2000; Spokane, 1991). Identifying and assessing client needs at the beginning of the career service delivery process ensures that services are appropriately aligned with these needs (Gati, Gadassi, Saka, Hadadi, Ansenberg, Friedmann, & AsulinPeretz, 1996; Sampson et al., 2000;...
Show moreAt the outset of career counseling, clarifying the nature of an individual's career problem is vital in order to ascertain the appropriate initial steps of the career intervention (Sampson, Peterson, Reardon, & Lenz, 2000; Spokane, 1991). Identifying and assessing client needs at the beginning of the career service delivery process ensures that services are appropriately aligned with these needs (Gati, Gadassi, Saka, Hadadi, Ansenberg, Friedmann, & AsulinPeretz, 1996; Sampson et al., 2000; Sampson & Reardon, 1998; Savickas, 1996; Super, 1983). During the initial client assessment it is also important to address mental health issues, as prior research has shown clients having difficulty making career decisions often endorse items such as depression or anxiety (Saunders, Peterson, Sampson, & Reardon, 2000). The Decision Space Worksheet (DSW) is a projective assessment technique that assists clients in understanding the social and emotional context involved in the career decisionmaking process. In addition, the DSW may also function as a possible indicator of mental health issues out of which a career problem arises (Peterson, Leasure, Carr, & Lenz, 2009). Utilizing the DSW, Career Thoughts Inventory (CTI), and Occupational Alternatives Question (OAQ) at the outset of career counseling could be useful in identifying individuals who are experiencing mental health issues (Lenz, Peterson, Reardon, & Saunders, 2010; Peterson et al., 2009; Walker & Peterson, 2011). This study examines the social and emotional context as portrayed by the DSW in addition to career thoughts and career decidedness as possible indicators of mental health issues in career counseling. Specifically, the question addressed by this study was, "What is the relationship between responses on the DSW and the presence of depressive symptomology?" To answer this question, data were collected for a corelational study from a sample of 151 enrolled in 8 sections of an undergraduate general psychology course (PSY2012) or psychology of personal and social adjustment course (CLP1001) at a midsized city in a southeastern community college in the United States. No significant positive relationship was found between the DSW total score and the BDIII score as well as between the respective DSW domains and the BDIII score. However, there was a contradictory significant inverted relationship between the DSW domain Selfdoubt and the BDIII. Contrary to expectation, Selfdoubt statements were negatively associated with depression. The best predictors of depression were found to be the CTI subscales External Conflict (EC) and Commitment Anxiety (CA). There were no significant differences between high and low groups on the BDIII and DSW responses and no significant differences between the OAQ decided and undecided groups and DSW responses. These findings contribute to the understanding of the DSW's value in assessing the social and emotional context for individuals as they relate to mental health issues, such as depression. Suggestions for modification of the DSW to capture the positive, neutral, or negative value of each statement were provided. The findings of this study implicate other CTI subscales (EC and CA) as significantly capturing unique variation in depression. In addition, these findings support the relationship among the overall CTI and BDIII scores. Lastly, this study suggests that in nonclient populations, who elicit statements on the DSW Selfdoubt domain, are less likely to be depressed. Implications for the use of the DSW in nonclient populations and recommendations for future research are discussed.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd5193
 Format
 Thesis
 Title
 Bibliography: a Cognitive Information Processing (CIP) Approach to Career Development and Services.
 Creator

Sampson, James P., Peterson, Gary, Reardon, Robert C., Lenz, Janet G.
 Abstract/Description

This bibliography contains citations about the cognitive information processing (CIP) approach to career development and career services developed at Florida State University. This application of cognitive information processing theory attempts to integrate theory and practice in order to improve the design and delivery of career services for individuals in educational and related human service settings. The bibliography is organized in terms of general principles, foundations of the CIP...
Show moreThis bibliography contains citations about the cognitive information processing (CIP) approach to career development and career services developed at Florida State University. This application of cognitive information processing theory attempts to integrate theory and practice in order to improve the design and delivery of career services for individuals in educational and related human service settings. The bibliography is organized in terms of general principles, foundations of the CIP approach, comparative theoretical perspectives, CIP research, dysfunctional career thoughts research, CIP applications, Career Thoughts Inventory, additional assessment and intervention resources, materials for client use, training materials, CIP reviews, CTI reviews, and CTI on the Internet. For additional information, contact any of the authors at the address listed above.
Show less  Date Issued
 2016
 Identifier
 FSU_migr_techcenter_biblio0001
 Format
 Citation
 Title
 Improvements in Metadynamics Simulations: The Essential Energy Space Random Walk and the WangLandau Recursion.
 Creator

Liu, Yusong, Yang, Wei, Erlebacher, Gordon, Peterson, Janet, Department of Scientific Computing, Florida State University
 Abstract/Description

Metadynamics is a popular tool to explore free energy landscapes and it has been use to elucidate various chemical or biochemical processes. The height of updating Gaussian function is very important for proper free energy convergence to the target free energy surface. Both higher and lower Gaussian heights have advantages and disadvantages, a balance is required. This thesis presents the implementation of the WangLandau recursion scheme in metadynamics simulations to adjust the height of...
Show moreMetadynamics is a popular tool to explore free energy landscapes and it has been use to elucidate various chemical or biochemical processes. The height of updating Gaussian function is very important for proper free energy convergence to the target free energy surface. Both higher and lower Gaussian heights have advantages and disadvantages, a balance is required. This thesis presents the implementation of the WangLandau recursion scheme in metadynamics simulations to adjust the height of the unit Gaussian function. Compared with classical fixed Gaussian heights, this dynamic adjustable method was demonstrated to efficiently yield better converged free energy surfaces. In addition, through combination with the realization of an energy space random walk, the WangLandau recursion scheme can be readily used to deal with the pseudoergodicity problem in molecular dynamic simulations. The use of this scheme is proven to efficiently and robustly obtain a biased free energy function within this thesis.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd1161
 Format
 Thesis
 Title
 Effects of Vertical Mixing Closures on North Atlantic Overflow Simulations.
 Creator

Jacobsen, Douglas, Gunzburger, Max, Erlebacher, Gordon, Peterson, Janet, Department of Scientific Computing, Florida State University
 Abstract/Description

We are exploring the effect of using various vertical mixing closures on resolving the physical process known as overflow. This is when cold dense water overflows from a basin in the ocean. This process is responsible for the majority of the Ocean's dense water transport, and also creates many of the dense water currents that are part of what is known as the Ocean Conveyor Belt. One of the main places this happens is in the North Atlantic, in the Denmark strait and the Faroe Bank Sea Channel....
Show moreWe are exploring the effect of using various vertical mixing closures on resolving the physical process known as overflow. This is when cold dense water overflows from a basin in the ocean. This process is responsible for the majority of the Ocean's dense water transport, and also creates many of the dense water currents that are part of what is known as the Ocean Conveyor Belt. One of the main places this happens is in the North Atlantic, in the Denmark strait and the Faroe Bank Sea Channel. To simulate this process, two ocean models are used, the Parallel Ocean Program (POP) and the hybridcoordinate Parallel Ocean Program (HyPOP). Using these models, differences are observed in three main vertical mixing schemes Constant, Richardson Number, and KPP. Though, not included in this thesis the research also explores three different vertical griding schemes, ZGrid, Sigma Coordinate, and Isopycnal grids. The goal is to attempt to determine which combination gives the most acceptable results for resolving the overflow process. This is motivated by the large role this process plays in the ocean, as well as the difficulty in modeling this process. If an ocean model cannot accurately simulate overflow, then a large portion of the ocean model will be incorrect and one cannot hope to get reasonable results for long simulations out of it.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd3745
 Format
 Thesis
 Title
 Solution of the NavierStokes Equations by the Finite Element Method Using Reduced Order Modeling.
 Creator

Forinash, Nick, Peterson, Janet, Plewa, Tomasz, Shanbhag, Sachin, Department of Scientific Computing, Florida State University
 Abstract/Description

Reduced Order Models (ROM) provide a lowdimensional alternative form of a system of differential equations. Such a form permits faster computation of solutions. In this paper, Poisson's Equation in two dimensions, the Heat Equation in one dimension, and a Nonlinear ReactionDiffusion equation in one dimension are solved using the Galerkin formulation of the Finite Element Method (FEM) in conjunction with Newton's Method. Reduced Order Modeling (ROM) by Proper Orthogonal Decomposition (POD)...
Show moreReduced Order Models (ROM) provide a lowdimensional alternative form of a system of differential equations. Such a form permits faster computation of solutions. In this paper, Poisson's Equation in two dimensions, the Heat Equation in one dimension, and a Nonlinear ReactionDiffusion equation in one dimension are solved using the Galerkin formulation of the Finite Element Method (FEM) in conjunction with Newton's Method. Reduced Order Modeling (ROM) by Proper Orthogonal Decomposition (POD) is then used to accelerate the solution of successive linear systems required by Newton's Method. This is done to show the viability of the method on a simple problem. The NavierStokes (NS) Equations are introduced and solved by FEM. A ROM using both POD and clustering by Centroidal Voronoi Tesselation (CVT) are then used to solve the NS equations, and the results are compared with the FEM solution. The specific NS problem we consider has inhomogeneous Dirichlet boundary conditions and the treatment of the boundary conditions is explained. The resulting decrease in computation time required for solving the various equations are compared with ROM methods.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5352
 Format
 Thesis
 Title
 Reduced Order Modeling Using the WaveletGalerkin Approximation of Differential Equations.
 Creator

Witman, David, Peterson, Janet, Gunzburger, Max, Ye, Ming, Department of Scientific Computing, Florida State University
 Abstract/Description

Over the past few decades an increased interest in reduced order modeling approaches has led to its application in areas such as real time simulations and parameter studies among many others. In the context of this work reduced order modeling seeks to solve differential equations using substantially fewer degrees of freedom compared to a standard approach like the finite element method. The finite element method is a Galerkin method which typically uses piecewise polynomial functions to...
Show moreOver the past few decades an increased interest in reduced order modeling approaches has led to its application in areas such as real time simulations and parameter studies among many others. In the context of this work reduced order modeling seeks to solve differential equations using substantially fewer degrees of freedom compared to a standard approach like the finite element method. The finite element method is a Galerkin method which typically uses piecewise polynomial functions to approximate the solution of a differential equation. Wavelet functions have recently become a relevant topic in the area of computational science due to their attractive properties including differentiability and multiresolution. This research seeks to combine a waveletGalerkin method with a reduced order approach to approximate the solution to a differential equation with a given set of parameters. This work will focus on showing that using a reduced order approach in a waveletGalerkin setting is a viable option in determining a reduced order solution to a differential equation.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8663
 Format
 Thesis
 Title
 Quasirandom Optimization.
 Creator

Azoulay, Ariel, Peterson, Janet, Gunzburger, Max, Erlebacher, Gordon, Burkardt, John, Department of Scientific Computing, Florida State University
 Abstract/Description

In this work we apply quasirandom sequences to develop a derivativefree algorithm for approximating the global maximum of a given function. This work is based on previous results which used a single type of quasirandom sequence in a Brute Force approach and in an approach called Localization of Search. In this work we present several methods for computing quasirandom sequences as well as measures for determining their properties. We discuss the shortcomings of the Brute Force and...
Show moreIn this work we apply quasirandom sequences to develop a derivativefree algorithm for approximating the global maximum of a given function. This work is based on previous results which used a single type of quasirandom sequence in a Brute Force approach and in an approach called Localization of Search. In this work we present several methods for computing quasirandom sequences as well as measures for determining their properties. We discuss the shortcomings of the Brute Force and Localization of Search methods and then present modifications which address these issues which culminate in a new algorithm which we call Modified Localization of Search. Our algorithm is applied to a test suite of problems and the results are discussed. Finally we present some comments on code development for our algorithm.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0271
 Format
 Thesis
 Title
 Counterflow Heat Transfer in He II Contained in Porous Media.
 Creator

DalbanCanassy, Matthieu, Sciver, Steven W. Van, Peterson, Janet, Luongo, Cesar, Ordonez, Juan, Englander, Ongi, Department of Mechanical Engineering, Florida State University
 Abstract/Description

This dissertation presents a study of steady He II (superfluid helium) counter flow heat transfer in porous media. Porous insulation were suggested as potential alternatives to conventional fully impregnated insulations in superconducting magnet technology. Superconducting magnets are usually cooled with He II. Use of porous insulation requires thus a good knowledge of the behavior of He II within porous materials, when set in motion or exposed to a heat source. The present work was focused...
Show moreThis dissertation presents a study of steady He II (superfluid helium) counter flow heat transfer in porous media. Porous insulation were suggested as potential alternatives to conventional fully impregnated insulations in superconducting magnet technology. Superconducting magnets are usually cooled with He II. Use of porous insulation requires thus a good knowledge of the behavior of He II within porous materials, when set in motion or exposed to a heat source. The present work was focused on the design of an apparatus capable of performing both steady and transient counterflow measurements in He II saturating a porous material with a geometry similar to potential candidate porous insulations. Those will most likely be composed of tapes of preimpregnated woven ceramic fibers, forming a highly anisotropic compound, with a wide pore size distribution. The samples were provided by Composite Technology Development Inc. and are circular pellets (3.08 mm thick and 28.58 mm in diameter) of 20 compressed layers of preimpregnated woven magnet insulation. The porous material was carefully characterized prior to experimental runs in He II. The samples exhibit a porosity and a permeability of respectively 20+1% and 0.95x10^14 m^2 for water measurements. The woven fiber rovings, composing the insulation, were found to be 0.04 mm^2 of average cross sectional area with fibers of average diameter of 10.6 micron. The He II experimental apparatus is composed of a vacuum insulated open channel whose top extremity is closed to a Minco heater. The temperature differences and pressure drops across the porous plug were measured by two Lakeshore barechip Cernox 1050BC thermometers and a Validyne DP1020 differential pressure sensor. Applied heat fluxes ranged up to 0.5 kW/m^2 of sample cross section. Steady temperature differences, up to 570 mK, and pressure drops, up to 1800 Pa (limit of the sensor), measurements were performed at bath temperatures ranging from 1.6 to 2.1 K. In the low heat flux regime, the permeability data corroborate room temperature measurements. In the high heat flux regime however, we show evidence of the failure of previous models based on the inclusion of the tortuosity in the turbulent equation. We propose to include a constriction factor denoting an average maximum change in cross section in the heat path in addition to the increased path length denoted by the tortuosity. In the turbulent regime, this constriction factor is predominant as it enters in the model with a cubic power. Measurements of the critical characteristics, corresponding to the point of transition from the laminar regime, where Darcy law is applicable to the nonlinear regime, where the heat flux adopts its characteristic cubic relationship, corresponding to the appearance of turbulence within He II are also reported. We obtained critical heat fluxes ranging from 20 to 70 W/m^2, Reynolds numbers of 0.5 to 4 and normal fluid velocities from 0.5 to 2.5 mm/s, varying with bath temperature. To confirm the room temperature measurements of permeability, we also conducted a forced flow experiment. Unfortunately, the flow range covered is outside of the laminar regime and does not permit an accurate estimation of the permeability. The results are however favorably comparable to earlier data recorded in the turbulent regime in similar flow conditions but with very different materials.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0855
 Format
 Thesis
 Title
 Spherical Centroidal Voronoi Tessellations: Point Generation and Density Functions via Images.
 Creator

Womeldorff, Geoffrey A., Gunzburger, Max, Peterson, Janet, Erlebacher, Gordon, Department of Scientific Computing, Florida State University
 Abstract/Description

This thesis presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT). First, 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 examine and introduce different schemes for creating their input values, known as generators, and compare the effects of these different initial...
Show moreThis thesis presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT). First, 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 examine and introduce different schemes for creating their input values, known as generators, and compare the effects of these different initial points with respect to their ability to converge and the amount of work required to meet a given tolerance goal. In addition, we describe a method for density functions via images so that we can shape generator density in an intuitive manner and then implement this method with examples to demonstrate it's efficacy.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0843
 Format
 Thesis
 Title
 PVInduced Forcing of Gravity Waves in a Shallow Water Model.
 Creator

Ward, Marshall, Cunningham, Philip, Peterson, Janet, Clayson, Carol Anne, Dewar, William K., Krishnamurti, Ruby, Program in Geophysical Fluid Dynamics, Florida State University
 Abstract/Description

The influence of a geostrophically balanced or potential vorticity (PV) background flow on gravity wave propagation is examined using a rotating shallow water model. The system is analyzed in the context of a perturbative expansion that focuses on the dynamics of the resonances within the nonlinear terms of the system. The nonlinearity is reconstructed as a wavewave interaction forcing on an otherwise undisturbed linear wavefield. The principal conclusion is that while the PV flow is...
Show moreThe influence of a geostrophically balanced or potential vorticity (PV) background flow on gravity wave propagation is examined using a rotating shallow water model. The system is analyzed in the context of a perturbative expansion that focuses on the dynamics of the resonances within the nonlinear terms of the system. The nonlinearity is reconstructed as a wavewave interaction forcing on an otherwise undisturbed linear wavefield. The principal conclusion is that while the PV flow is generally undisturbed by the gravity wavefield, the gravity wavefield is forced by the geostrophic flow over moderate timescales. We numerically test these results for the interaction between a single geostrophic mode and a gravity wave, followed by propagation of a single gravity mode through a turbulent PV background. We find that the gravity mode energy is scattered into other modes of similar wavelength but different directions of propagation. The rate of dispersion is in agreement with resonant triad theory, where the rate depends primarily on the initial gravity wavenumber and background PV strength. These results are expected to have relevance to the propagation of coherent internal tides in the open ocean.}
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd1243
 Format
 Thesis
 Title
 A GISBased Model for Estimating Nitrate Fate and Transport from Septic Systems in Surficial Aquifers.
 Creator

Rios, J. Fernando, Ye, Ming, Peterson, Janet, Shanbhag, Sachin, Wilgenbusch, James, Department of Scientific Computing, Florida State University
 Abstract/Description

Estimating groundwater nitrate fate and transport is an important task in water resources and environmental management because excess nitrate loads may have negative impacts on human and environmental health. This work discusses the development of a simplified nitrate transport model and its implementation as a geographic information system (GIS)based screening tool, whose purpose is to estimate nitrate loads to surface water bodies from onsite wastewatertreatment systems (OWTS). Key...
Show moreEstimating groundwater nitrate fate and transport is an important task in water resources and environmental management because excess nitrate loads may have negative impacts on human and environmental health. This work discusses the development of a simplified nitrate transport model and its implementation as a geographic information system (GIS)based screening tool, whose purpose is to estimate nitrate loads to surface water bodies from onsite wastewatertreatment systems (OWTS). Key features of this project are the reduced data demands due to the use of a simplified model, as well as ease of use compared to traditional groundwater flow and transport models, achieved by embedding the model within a GIS. The simplified conceptual model consists of a simplified groundwater flow model in the surficial aquifer, and a simplified transport model that makes use of an analytical solution to the advectiondispersion equation, used for determining nitrate fate and transport. Denitrification is modeled using first order decay in the analytical solution with the decay constant obtained from literature and/or sitespecific data. The groundwater flow model uses readily available topographic data to approximate the hydraulic gradient, which is then used to calculate seepage velocity magnitude and direction. The flow model is evaluated by comparing the results to a previous numerical modeling study of the U.S. Naval Air Station, Jacksonville (NAS) performed by the USGS. The results show that for areas in the vicinity of the NAS, the model is capable of predicting groundwater travel times from a source to a surface water body to within Â±20 years of the USGS model, 75% of the time. The transport model uses an analytical solution based on the one by Domenico and Robbins (1985), the results of which are then further processed so that they may be applied to more general, realworld scenarios. The solution, as well as the processing steps are tested using artificially constructed scenarios, each meant to evaluate a certain aspect of the solution. For comparison purposes, each scenario is solved using a well known numerical contaminant transport model. The results show that the analytical solution provides a reasonable approximation to the numerical result. However, it generally underestimates the concentration distribution to varying degrees depending on choice of parameters, especially along the plume centerline. These results are in agreement with previous studies (Srinivasan et al., 2007; West et al., 2007). The adaptation of the analytical solution to more realistic scenarios results in an adequate approximation to the numerically calculated plume, except in areas near the advection front, where the model produces a plume whose shape differs noticeably from the numerical solution. Load calculations are carried out using a mass balance approach where the system is considered to be in the steady state. The steadystate condition allows for a load estimate by subtracting the mass removal rate due to denitrification from the input mass rate. The input mass rate is calculated by taking into account advection and dispersion while the mass removal rate due to denitrification is calculated from the definition of a first order reaction. Comparison with the synthetic scenarios of the transport model shows that for the test cases, when decay rates are low, the model agrees well with the load calculation from the numerical model. As decay rates increase and the plume becomes shorter, the input load is overestimated by about 9% in the test cases and the mass removed due to denitrification is underestimated by 30% in the worst case. These results are likely due to the underestimation of concentration values by the analytical solution of the transport model.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1851
 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
 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
 Analysis and Approximation of a TwoBand GinzburgLandau Model of Superconductivity.
 Creator

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

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

Larrea, Veronica G. Vergara, Gunzburger, Max, MeyerBaese, Anke, Peterson, Janet, Wilgenbusch, Jim, Department of Scientific Computing, Florida State University
 Abstract/Description

This thesis explores possible improvements in the construction of Delaunay Triangulations on the Sphere by designing and implementing a parallel alternative to the software package STRIPACK. First, it gives an introduction to Delaunay Triangulations on the plane and presents current methods available for their construction. Then, these concepts are mapped to the spherical case: Spherical Delaunay Triangulation (SDT). To provide a better understanding of the design choices, this document...
Show moreThis thesis explores possible improvements in the construction of Delaunay Triangulations on the Sphere by designing and implementing a parallel alternative to the software package STRIPACK. First, it gives an introduction to Delaunay Triangulations on the plane and presents current methods available for their construction. Then, these concepts are mapped to the spherical case: Spherical Delaunay Triangulation (SDT). To provide a better understanding of the design choices, this document includes a brief overview of parallel programming, that is followed by the details of the implementation of the SDT generation code. In addition, it provides examples of resulting SDTs as well as benchmarks to analyze its performance. This project was inspired by the concepts presented in Robert Renka's work and was implemented in C++ using MPI.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd4557
 Format
 Thesis
 Title
 Realtime Computing with the Parareal Algorithm.
 Creator

Christopherr.Harden, Peterson, Janet, Gunzburger, Max, Van Engelen, Robert, Department of Scientific Computing, Florida State University
 Abstract/Description

This thesis presents and evaluates a particular algorithm used for the real time computations of time dependent ordinary and partial differential equations which employs a parallelization strategy over the temporal domain. We also discuss the coupling of this method with another popular technique used for real time computations, model reduction, which will be shown to provide more gains than either method alone. In particular, we look at reduced order modeling based on proper orthogonal...
Show moreThis thesis presents and evaluates a particular algorithm used for the real time computations of time dependent ordinary and partial differential equations which employs a parallelization strategy over the temporal domain. We also discuss the coupling of this method with another popular technique used for real time computations, model reduction, which will be shown to provide more gains than either method alone. In particular, we look at reduced order modeling based on proper orthogonal decompositions. We present some applications in terms of solving time dependent nonlinear partial diÃ¯Â¬Â€erential equations and solving these equations with a coupled approach of combining model reduction and the parareal algorithm . The performance of this method, both numerically and computationally, is discussed in terms of the gains in speedup and efficiency, and in terms of the scalability of the parallelization of the temporal domain on a larger and larger set of compute nodes or processors.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd4272
 Format
 Thesis
 Title
 Reduced Order Modeling of Reactive Transport in a Column Using Proper Orthogonal Decomposition.
 Creator

McLaughlin, Benjamin R. S., Peterson, Janet, Ye, Ming, Shanbhag, Sachin, Department of Scientific Computing, Florida State University
 Abstract/Description

Estimating parameters for reactive contaminant transport models can be a very computationally intensive. Typically this involves solving a forward problem many times, with many degrees of freedom that must be computed each time. We show that reduced order modeling (ROM) by proper orthogonal decomposition (POD) can be used to approximate the solution to the forward model using many fewer degrees of freedom. We provide background on the finite element method and reduced order modeling in one...
Show moreEstimating parameters for reactive contaminant transport models can be a very computationally intensive. Typically this involves solving a forward problem many times, with many degrees of freedom that must be computed each time. We show that reduced order modeling (ROM) by proper orthogonal decomposition (POD) can be used to approximate the solution to the forward model using many fewer degrees of freedom. We provide background on the finite element method and reduced order modeling in one spatial dimension, and apply both methods to a system of linear uncoupled timedependent equations simulating reactive transport in a column. By comparing the reduced order and finite element approximations, we demonstrate that the reduced model, while having many fewer degrees of freedom to compute, gives a good approximation of the highdimensional (finite element) model. Our results indicate that one may substitute a reduced model in place of a highdimensional model to solve the forward problem in parameter estimation with many fewer degrees of freedom.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd5030
 Format
 Thesis
 Title
 A Study of Shock Formation and Propagation in the ColdIon Model.
 Creator

Cheung, James, Gunzburger, Max D., Peterson, Janet S., Shanbhag, Sachin, Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

The central purpose of this thesis is to explore the behavior of the numerical solution of the Cold Ion model with shock forming conditions in one and two dimensions. In the one dimensional case, a comparison between the numerical solution of the Vlasov equation is made. It is observed that the ColdIon model is no longer representative of the coldion limit of the VlasovPoisson equation when a spike forms in the solution. It was found that the lack of a spike in the solution of the Cold...
Show moreThe central purpose of this thesis is to explore the behavior of the numerical solution of the Cold Ion model with shock forming conditions in one and two dimensions. In the one dimensional case, a comparison between the numerical solution of the Vlasov equation is made. It is observed that the ColdIon model is no longer representative of the coldion limit of the VlasovPoisson equation when a spike forms in the solution. It was found that the lack of a spike in the solution of the ColdIon model does not necessarily mean that a bifurcation has not formed in the solution of the VlasovPoisson equation. It was also determined that the spike present in the solution of the one dimensional problem appears again in the two dimensional simulation. The findings presented in this thesis opens up the question of determining which initial and boundary conditions of the ColdIon model causes a shock to form in the solution.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd9158
 Format
 Thesis
 Title
 Adaptive Observations in a 4DVar Framework Applied to the Nonlinear Burgers Equation Model.
 Creator

Hossen, Md. Jakir, Navon, Ionel Michael, Peterson, Janet, Erlebacher, Gordon, Department of Scientific Computing, Florida State University
 Abstract/Description

In 4DVar data assimilation for geophysical models, the goal is to reduce the lack of fit between model and observations (strong constraint approach assuming perfect model). In the last two decades four dimensional variational technique has been extensively used in the numerical weather prediction due to the fact that time distributed observations are assimilated to obtain a better initial condition thus leading to more accurate forecasts using the above 4DVar approach. The use of large...
Show moreIn 4DVar data assimilation for geophysical models, the goal is to reduce the lack of fit between model and observations (strong constraint approach assuming perfect model). In the last two decades four dimensional variational technique has been extensively used in the numerical weather prediction due to the fact that time distributed observations are assimilated to obtain a better initial condition thus leading to more accurate forecasts using the above 4DVar approach. The use of largescale unconstrained minimization routines to minimize a cost functional measuring lack of fit between observations and model forecast requires availability of the gradient of the cost functional with respect to the control variables. Nonlinear Burgers equation model is used as numerical forecast model. First order adjoint model can be used to find the gradient of the cost functional. The use of targeted observations supplementing routine observations contributes to the reduction of the forecast analysis error and can provide improved forecast of weather events of critical societal impact, for instance, hurricanes, tornadoes, sharp fronts etc. The optimal space and time locations of the adaptive observations can be determined by using a singular vector approach. In our work we use both adjoint sensitivity and sensitivity to observation approaches to identify the optimal space and time locations for targeted observations at future time aimed at providing an improved forecast. Both approaches are compared in this work and some conclusions are outlined.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd3765
 Format
 Thesis
 Title
 Level Set and Conservative Level Set Methods on Dynamic Quadrilateral Grids.
 Creator

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

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

Lyngaas, Isaac Ron, Peterson, Janet S., Gunzburger, Max D., Burkardt, John V., Florida State University, College of Arts and Sciences, Department of Mathematics
 Abstract/Description

Nonlocal models differ from traditional partial differential equation (PDE) models because they contain no spatial derivatives; instead an appropriate integral is used. Nonlocal models are especially useful in the case where there are issues calculating the spatial derivatives of a PDE model. In many applications (e.g., biological systems, flow through porous media) the observed rate of diffusion is not accurately modeled by the standard diffusion differential operator but rather exhibits so...
Show moreNonlocal models differ from traditional partial differential equation (PDE) models because they contain no spatial derivatives; instead an appropriate integral is used. Nonlocal models are especially useful in the case where there are issues calculating the spatial derivatives of a PDE model. In many applications (e.g., biological systems, flow through porous media) the observed rate of diffusion is not accurately modeled by the standard diffusion differential operator but rather exhibits socalled anomalous diffusion. Anomalous diffusion can be represented in a PDE model by using a fractional Laplacian operator in space whereas the nonlocal approach only needs to slightly modify its integral formulation to model anomalous diffusion. Anomalous diffusion is one such case where approximating the spatial derivative operator is a difficult problem. In this work, an approach for approximating standard and anomalous nonlocal diffusion problems using a new technique that utilizes radial basis functions (RBFs) is introduced and numerically tested. The typical approach for approximating nonlocal diffusion problems is to use a Galerkin formulation. However, the Galerkin formulation for nonlocal diffusion problems can often be difficult to compute efficiently and accurately especially for problems in multiple dimensions. Thus, we investigate the alternate approach of using quadrature rules generated by RBFs to approximate the nonlocal diffusion problem. This work will be split into three major parts. The first will introduce RBFs and give some examples of how they are used. This part will motivate our approach for using RBFs on the nonlocal diffusion problem. In the second part, we will derive RBFgenerated quadrature rules in one dimension and show they can be used to approximate nonlocal diffusion problems. The final part will address how the RBF quadrature approach can be extended to higher dimensional problems. Numerical test cases are shown for both the standard and anomalous nonlocal diffusion problems and compared with standard finite element approximations. Preliminary results show that the method introduced is viable for approximating nonlocal diffusion problems and that highly accurate approximations are possible using this approach.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Lyngaas_fsu_0071N_13512
 Format
 Thesis
 Title
 The Impact of DISCOVER for Adult Learners and SIGI PLUS on the Career Decision Making of Adults Technical Report Number 9.
 Creator

Sampson, James P, Reardon, Robert C, Lenz, Janet G, RyanJones, Rebecca E, Peterson, Gary W, Levy, Rick
 Abstract/Description

This study evaluated the effects of DISCOVER for Adult Learners and SIGI PLUS on career decidedness, vocational identity, and perceptions of computer use for 116 adults seeking services at a selfhelp oriented career center. Adults were randomly assigned to either DISCOVER for Adult Learners (DAL), SIGI PLUS, or a control condition that involved unstructured use of print and AV materials in a university career center. Use of DAL and SIGI PLUS by adults resulted in positive gains in vocational...
Show moreThis study evaluated the effects of DISCOVER for Adult Learners and SIGI PLUS on career decidedness, vocational identity, and perceptions of computer use for 116 adults seeking services at a selfhelp oriented career center. Adults were randomly assigned to either DISCOVER for Adult Learners (DAL), SIGI PLUS, or a control condition that involved unstructured use of print and AV materials in a university career center. Use of DAL and SIGI PLUS by adults resulted in positive gains in vocational identity. Subjects in the control condition and subjects using DISCOVER experienced a significant increase in career decidedness. Adults perceived both systems as having a positive impact on three dimensions of computer effectiveness, Analysis, Synthesis, and Computer Effect. The conclusion was that computerbased interventions are equivalent to more traditional career interventions. Implications of these results for practice and further research are discussed.
Show less  Date Issued
 19931001
 Identifier
 FSU_libsubv1_scholarship_submission_1525886209_752378bb, 10.17125/fsu.1525886209
 Format
 Citation
 Title
 The Impact of DISCOVER and SIGI on the Career Decision Making of College Students: Technical Report No. 5.
 Creator

Sampson, James P, Reardon, Robert C, Shahnasarian, Michael, Peterson, Gary W, RyanJones, Rebecca, Lenz, Janet G
 Abstract/Description

The purpose of this research was to compare two widely used computerassisted career guidance (CACG) systems, DISCOVER and SIGI. The goals were to: 1) assist practitioners in learning more about the benefits of using a CACG system as a component of total program services; 2) assist CACG system developers in revising software and support materials to more fully meet the needs of practitioners and users; and 3) assist researchers in planning further investigations concerning the optimal use of...
Show moreThe purpose of this research was to compare two widely used computerassisted career guidance (CACG) systems, DISCOVER and SIGI. The goals were to: 1) assist practitioners in learning more about the benefits of using a CACG system as a component of total program services; 2) assist CACG system developers in revising software and support materials to more fully meet the needs of practitioners and users; and 3) assist researchers in planning further investigations concerning the optimal use of this technology. This technical report includes three separate studies designed to answer three different research questions. A sample of undergraduate psychology students was used for all three studies.
Show less  Date Issued
 19870201
 Identifier
 FSU_libsubv1_scholarship_submission_1525881042_a9d2505a, 10.17125/fsu.1525881042
 Format
 Citation
 Title
 Expert and Novice Practitioner Use of the ComputerBased Test Interpretation for the SelfDirected Search: A Qualitative Analysis.
 Creator

Shy, Jonathan David, Sampson, James P., Lenz, Janet, Padavic, Irene, Peterson, Gary, Reardon, Robert, Department of Educational Psychology and Learning Systems, Florida State...
Show moreShy, Jonathan David, Sampson, James P., Lenz, Janet, Padavic, Irene, Peterson, Gary, Reardon, Robert, Department of Educational Psychology and Learning Systems, Florida State University
Show less  Abstract/Description

This qualitative research study explored the process by which expert and novice counseling practitioners use the computerbased test interpretation (CBTI) for the SelfDirected Search (SDS). Two groups of people were involved in the study: (a) research participants and (b) student assistants. Research participants were the focus of the study; student assistants were not measured or assessed in any way. Research participants were selected from a career center at a large southeastern university...
Show moreThis qualitative research study explored the process by which expert and novice counseling practitioners use the computerbased test interpretation (CBTI) for the SelfDirected Search (SDS). Two groups of people were involved in the study: (a) research participants and (b) student assistants. Research participants were the focus of the study; student assistants were not measured or assessed in any way. Research participants were selected from a career center at a large southeastern university. All received some training in the use of the CBTI for the SDS prior to their participation in the study. Student assistants were selected from an undergraduate course in career development. Students in the course take the SDS and receive an interpretation of their CBTI as part of normal classroom procedures. They were invited to have their interpretation audiorecorded for the current study and were offered extra credit as an incentive. Twelve students were selected; those who wanted to assist but were not selected were still presented with an opportunity to receive extra credit. Data collection occurred in two phases. Research participants first interpreted a CBTI for the SDS to two student assistants. These interpretations were audiorecorded. Following the interpretative events, the researcher interviewed research participants; interviews were also audiorecorded. During the interview, research participants were asked about the nature of the student participant's SDS scores and their reactions to the interpretive process. Following the data collection procedures a professional transcription agency transcribed audio recordings. The researcher reviewed transcribed audio recordings from interpretive events and interviews for one participant and identified a preliminary coding system based on themes present in the data. Nvivo qualitative software was used to assist with this effort. The preliminary coding system went through several iterations as data from additional participants was analyzed. The characteristics of expertise identified by Glaser and Chi (1988) were used as sensitizing concepts in order to link the data analysis to relevant literature. Raw data and the preliminary coding system were presented to an auditor with knowledge of qualitative research to provide an objective opinion of the data. Feedback was received and a final coding system was identified. The final coding system consisted of a thematic hierarchy of five major categories, 12 higher order themes, and 13 lower order themes. A second auditor reviewed the final coding system and raw data to ensure the appropriateness of the data analysis. Results revealed that experts and novices interpreted much of the same content presented in the CBTI for the SDS, but did so in different ways. Experts explained more content of the CBTI for the SDS, solicited background information, discussed resources and services, and incorporated elements from two career theories during interpretations. Experts also made decisions about: the relative importance of data, student's career problems, and how to adjust their performance and structure the interpretive process based on the unique needs of students. The results suggested that this study's experts possessed more complex domainspecific schema for the interpretation of the CBTI for the SDS. These schema appeared to enable experts to examine more data, which was used to form more complex conceptualizations of students' career functioning. The findings lent support to the characteristics of expertise identified by Glaser and Chi (1988), as well as for stage theories of the development of expertise identified by Dreyfus and Dreyfus (1986). The findings were used to develop a suggested interpretive process of the interpretation of the CBTI for the SDS.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0327
 Format
 Thesis
 Title
 Peridynamic Multiscale Models for the Mechanics of Materials: Constitutive Relations, Upscaling from Atomistic Systems, and Interface Problems.
 Creator

Seleson, Pablo D, Gunzburger, Max, Rikvold, Per Arne, ElAzab, Anter, Peterson, Janet, Shanbhag, Sachin, Lehoucq, Richard B., Parks, Michael L., Department of Scientific...
Show moreSeleson, Pablo D, Gunzburger, Max, Rikvold, Per Arne, ElAzab, Anter, Peterson, Janet, Shanbhag, Sachin, Lehoucq, Richard B., Parks, Michael L., Department of Scientific Computing, Florida State University
Show less  Abstract/Description

This dissertation focuses on the non local continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel capabilities. A more generalized role is defined for influence functions in the statebased peridynamic model which allows for the strength of non local interactions to be modulated. This enables the connection between different peridynamic constitutive models,...
Show moreThis dissertation focuses on the non local continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel capabilities. A more generalized role is defined for influence functions in the statebased peridynamic model which allows for the strength of non local interactions to be modulated. This enables the connection between different peridynamic constitutive models, establishing a hierarchy that reveals that some models are special cases of others. Furthermore, this allows for the modulation of the strength of non local interactions, even for a fixed radius of interactions between material points in the peridynamics model. The multiscale aspect of peridynamics is demonstrated through its connections to molecular dynamics. Using higherorder gradient models, it is shown that peridynamics can be viewed as an upscaling of molecular dynamics, preserving the relevant dynamics under appropriate choices of length scales. The statebased peridynamic model is shown to be appropriate for the description of multiscale and multimodel systems. A formulation for nonlocal interface problems involving scalar fields is presented, and derivations of non local transmission conditions are derived. Specializations that describe local, non local, and local/non local transmission conditions are considered. Moreover, the convergence of the non local transmission conditions to their classical local counterparts is shown. In all cases, results are illustrated by numerical experiments.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0273
 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
 Comparison of Different Noise Forcings, Regularization of Noise, and Optimal Control for the Stochastic NavierStokes Equations.
 Creator

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

Stochastic NavierStokes equations have been widely applied in various computational fluid dynamics (CFD) fields in recent years. It can be considered as another milestone in CFD. Our work focuses on exploring some theoretical and numerical properties of the stochastic NavierStokes equations and related optimal control problems. In particular, we consider: a numerical comparison of solutions of the stochastic NavierStokes equations perturbed by a large range of random noises in time and...
Show moreStochastic NavierStokes equations have been widely applied in various computational fluid dynamics (CFD) fields in recent years. It can be considered as another milestone in CFD. Our work focuses on exploring some theoretical and numerical properties of the stochastic NavierStokes equations and related optimal control problems. In particular, we consider: a numerical comparison of solutions of the stochastic NavierStokes equations perturbed by a large range of random noises in time and space; effective Martingale regularized methods for the stochastic NavierStokes equations with additive noises; and the stochastic NavierStokes equations constrained stochastic boundary optimal control problems. We systemically provide numerical simulation methods for the stochastic NavierStokes equations with different types of noises. The noises are classified as colored or white based on their autocovariance functions. For each type of noise, we construct a representation and a simulation method. Numerical examples are provided to illustrate our schemes. Comparisons of the influence of different noises on the solution of the NavierStokes system are presented. To improve the simulation accuracy, we impose a Martingale correction regularized method for the stochastic NavierStokes equations with additive noise. The original systems are split into two parts, a linear stochastic Stokes equations with Martingale solution and a stochastic modified NavierStokes equations with smoother noise. In addition, a negative fractional Laplace operator is introduced to regularize the noise term. Stability and convergence of the pathwise modified NavierStokes equations are proved. Numerical simulations are provided to illustrate our scheme. Comparisons of nonregularized and regularized noises for the NavierStokes system are presented to further demonstrate the efficiency of our numerical scheme. As a consequence of the above work, we consider a stochastic optimal control problem constrained by the NavierStokes equations with stochastic Dirichlet boundary conditions. Control is applied only on the boundary and is associated with reduced regularity, compared to interior controls. To ensure the existence of a solution and the efficiency of numerical simulations, the stochastic boundary conditions are required to belong almost surely to HÂ¹(âˆ‚D). To simulate the system, state solutions are approximated using the stochastic collocation finite element approach, and sparse grid techniques are applied to the boundary random field. Oneshot optimality systems are derived from Lagrangian functionals. Numerical simulations are then made, using a combination of Monte Carlo methods and sparse grid methods, which demonstrate the efficiency of the algorithm.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Zhao_fsu_0071E_14002
 Format
 Thesis
 Title
 Ensemble Proper Orthogonal Decomposition Algorithms for the Incompressible NavierStokes Equations.
 Creator

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

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

Cheung, James, Gunzburger, Max D., Steinbock, Oliver, Bochev, Pavel B., Perego, Mauro, Peterson, Janet S., Shanbhag, Sachin, Florida State University, College of Arts and...
Show moreCheung, James, Gunzburger, Max D., Steinbock, Oliver, Bochev, Pavel B., Perego, Mauro, Peterson, Janet S., Shanbhag, Sachin, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

In this dissertation, we present a new approach for approximating the solution of second order partial differential equations and interface problems. This approach is based on the classical finite element method, where instead of using geometric manipulations to fit the discrete domain to the curved domain given by the continuous problem, we use polynomial extensions to enforce that a suitably constructed extension of the numerical solution matches the boundary condition given by the...
Show moreIn this dissertation, we present a new approach for approximating the solution of second order partial differential equations and interface problems. This approach is based on the classical finite element method, where instead of using geometric manipulations to fit the discrete domain to the curved domain given by the continuous problem, we use polynomial extensions to enforce that a suitably constructed extension of the numerical solution matches the boundary condition given by the continuous problem in the weak sense. This method is thus aptly named the Polynomial Extension Finite Element Method (PEFEM). Using this approach, we may approximate the solution of elliptic interface problems by enforcing that the extension of the solution on their respective subdomains matches weakly the continuity conditions prescribed by the continuous problem on a curved interface. This method is then called the Method of Virtual Interfaces (MVI), since, while the continuous interface exists in the context of the continuous problem, it is virtual in the context of its numerical approximation. The key benefits of this polynomial extension approach is that it is simple to implement and that it is optimally convergent with respect to the best approximation results given by interpolation. Theoretical analysis and computational results are presented.
Show less  Date Issued
 2018
 Identifier
 2018_Sp_Cheung_fsu_0071E_14328
 Format
 Thesis
 Title
 Mass Conserving HamiltonianStructurePreserving Reduced Order Modeling for the Rotating Shallow Water Equations Discretized by a Mimetic Spatial Scheme.
 Creator

Sockwell, K. Chad (Kenneth Chad), Gunzburger, Max D., Wahl, Horst, Peterson, Janet S., Quaife, Bryan, Huang, Chen, Florida State University, College of Arts and Sciences,...
Show moreSockwell, K. Chad (Kenneth Chad), Gunzburger, Max D., Wahl, Horst, Peterson, Janet S., Quaife, Bryan, Huang, Chen, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Ocean modeling, in a climatemodeling context, requires long timehorizons over global scales, which when combined with accurate resolution in time and space makes simulations very timeconsuming. While highresolution oceanmodeling simulations are still feasible on large HPC machines, performing uncertainty quantification or other many query applications at these resolutions is no longer feasible. Developing a more efficient model would allow for efficient uncertainty quantification, data...
Show moreOcean modeling, in a climatemodeling context, requires long timehorizons over global scales, which when combined with accurate resolution in time and space makes simulations very timeconsuming. While highresolution oceanmodeling simulations are still feasible on large HPC machines, performing uncertainty quantification or other many query applications at these resolutions is no longer feasible. Developing a more efficient model would allow for efficient uncertainty quantification, data assimilation, and spinup initializations. For these techniques to be feasible in practice, a faster model must be designed which can still attain sufficient accuracy. Techniques such as reduced order modeling produce an efficient reduced model based on existing highresolution simulation data. Models produced by these techniques provide a tremendous speedup at the cost of reduced accuracy. To offset this tradeoff, novel strategies are developed to retain as much accuracy as possible while still achieving tremendous speedups. Some of these methods improve accuracy by incorporating physical properties into the reduced model, leading to better solution quality. In this dissertation, a novel reduced order modeling method, the Hamiltonianstructurepreserving reduced order modeling method, will be derived and analyzed. The Hamiltonian structure is possessed by many physical systems and is directly related to energy conservation. This method produces a reduced model which retains the Hamiltonian structure of noncanonical Hamiltonian systems, which are the category of systems that many ocean models fall into. Error estimates are proven for the new method. The model is also be made to preserve linear invariants in the reduced model which are Casimirs. Casimirs are a class of special conserved quantities in the Hamiltonian Framework. For oceanmodeling, the Casimirs we consider are mass and potential vorticity. The new reduced model is proven to conserve both of these quantities. The model is also implemented in a special inner product derived from the Hamiltonian Framework, the approximate energy inner product. This special inner product not only improves the accuracy of the new method but also improves the accuracy of the traditional reduced order modeling method and leads to favorable analytical properties for problems with quadratic Hamiltonian functionals. The new method will be applied to the rotating shallow water equations, which act as a proxy to real ocean models, and compared to the traditional reduced order modeling method. Both energy conserving and forced testcases are considered where energy conservation, accuracy, and stability are investigated. Special techniques are also implemented to ensure that the new method is as efficient as possible.
Show less  Date Issued
 2019
 Identifier
 2019_Summer_Sockwell_fsu_0071E_15277
 Format
 Thesis
 Title
 Sparse Grid Stochastic Collocation Techniques for the Numerical Solution of Partial Differential Equations with Random Input Data.
 Creator

Webster, Clayton G. (Clayton Garrett), Gunzburger, Max D., Gallivan, Kyle, Peterson, Janet, Tempone, Raul, Department of Mathematics, Florida State University
 Abstract/Description

The objective of this work is the development of novel, efficient and reliable sparse grid stochastic collocation methods for solving linear and nonlinear partial differential equations (PDEs) with random coefficients and forcing terms (input data of the model). These techniques consist of a Galerkin approximation in the physical domain and a collocation, in probability space, on sparse tensor product grids utilizing either ClenshawCurtis or Gaussian abscissas. Even in the presence of...
Show moreThe objective of this work is the development of novel, efficient and reliable sparse grid stochastic collocation methods for solving linear and nonlinear partial differential equations (PDEs) with random coefficients and forcing terms (input data of the model). These techniques consist of a Galerkin approximation in the physical domain and a collocation, in probability space, on sparse tensor product grids utilizing either ClenshawCurtis or Gaussian abscissas. Even in the presence of nonlinearities, the collocation approach leads to the solution of uncoupled deterministic problems, just as in the Monte Carlo method. The full tensor product spaces suffer from the curse of dimensionality since the dimension of the approximating space grows exponentially in the number of random variables. When this number is moderately large, we combine the advantages of isotropic sparse collocation with those of anisotropic full tensor product collocation: the first approach is effective for problems depending on random variables which weigh equally in the solution; the latter approach is ideal when solving highly anisotropic problems depending on a relatively small number of random variables. We also include a priori and a posteriori procedures to adapt the anisotropy of the sparse grids to each problem. These procedures are very effective for the problems under study. This work also provides a rigorous convergence analysis of the fully discrete problem and demonstrates: (sub)exponential convergence in the asymptotic regime and algebraic convergence in the preasymptotic regime, with respect to the total number of collocation points. Numerical examples illustrate the theoretical results and compare this approach with several others, including the standard Monte Carlo. For moderately large dimensional problems, the sparse grid approach with a properly chosen anisotropy is very efficient and superior to all examined methods. Due to the high cost of effecting each realization of the PDE this work also proposes the use of reducedorder models (ROMs) that assist in minimizing the cost of determining accurate statistical information about outputs from ensembles of realizations. We explore the use of ROMs, that greatly reduce the cost of determining approximate solutions, for determining outputs that depend on solutions of stochastic PDEs. One is then able to cheaply determine much larger ensembles, but this increase in sample size is countered by the lower fidelity of the ROM used to approximate the state. In the contexts of proper orthogonal decompositionbased ROMs, we explore these counteracting effects on the accuracy of statistical information about outputs determined from ensembles of solutions.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd1223
 Format
 Thesis
 Title
 The Effects of TheoryBased Techniques and Media Tools on InformationSeeking Behavior.
 Creator

Ruff, Elizabeth, Reardon, Robert, Lenz, Janet, Padavic, Irene, Peterson, Gary, Sampson, James, Department of Educational Psychology and Learning Systems, Florida State University
 Abstract/Description

The purpose of this study was to examine the effects of viewing a modelreinforced video on career informationseeking behavior (ISB). The treatment video was developed using historical principles of behaviorism and social learning theory with modern career development theories. The video portrayed an undergraduate student seeking career counseling services to assist in his career decision making. The counselor in the video used modeling, verbal and nonverbal reinforcement to encourage the...
Show moreThe purpose of this study was to examine the effects of viewing a modelreinforced video on career informationseeking behavior (ISB). The treatment video was developed using historical principles of behaviorism and social learning theory with modern career development theories. The video portrayed an undergraduate student seeking career counseling services to assist in his career decision making. The counselor in the video used modeling, verbal and nonverbal reinforcement to encourage the student to use a variety of types of career information resources (e.g., books, websites, informational interviews) through six methods of informationgathering strategies (e.g., reading, writing, listening, speaking, visiting, and observing). Participants were undergraduate students enrolled in a career development course at a large, southeastern university. The researcher hypothesized that the general effort, including amount of time spent engaged in career informationseeking activities (planned and actual), resources used (amount and variety), and informationseeking strategies employed would be significantly higher for participants who viewed the treatment video than for those who did not. The researcher also hypothesized that participants who viewed the treatment video would have fewer negative career thoughts related to career informationdeficit than participants who did not view the video. Data was analyzed using multivariate, univariate, and independent ttests, an analysis of covariance (ANCOVA) and chisquare analyses. Participants who viewed the video did not report putting more planned or general effort into engaging in career informationseeking behaviors. However, they did report spending significantly more time in the specific activities reinforced in the video, and used a significantly wider variety of informationseeking strategies and career resources. There was no significant difference in the number of negative career thoughts between groups. This study extended and supported the findings from previous studies that employed similar treatments and variables. The combination of replication, historical theoretical basis, and implications for modern technology and practice were unique to this study. Implications for future for research and practice based on the results of this study are discussed.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1931
 Format
 Thesis
 Title
 Goal Instability in Relation to Career Thoughts, Career Decision State, and Performance in a Career Development Course.
 Creator

Bertoch, Sara C., Lenz, Janet G., Reardon, Robert C., Reynolds, John R., Sampson, James P., Peterson, Gary W., Department of Educational Psychology and Learning Systems, Florida...
Show moreBertoch, Sara C., Lenz, Janet G., Reardon, Robert C., Reynolds, John R., Sampson, James P., Peterson, Gary W., Department of Educational Psychology and Learning Systems, Florida State University
Show less  Abstract/Description

The purpose of the present study was to examine the relationships among goal instability, career thoughts, career decision state, and performance in a career development course. Participants enrolled in an undergraduate career course at a large southeastern university completed measures of goal instability, career thoughts, career decision state, and performance in course activities. Bivariate correlations and multiple regression analyses were conducted. Results demonstrated that goal...
Show moreThe purpose of the present study was to examine the relationships among goal instability, career thoughts, career decision state, and performance in a career development course. Participants enrolled in an undergraduate career course at a large southeastern university completed measures of goal instability, career thoughts, career decision state, and performance in course activities. Bivariate correlations and multiple regression analyses were conducted. Results demonstrated that goal instability was significantly related to career thoughts, career satisfaction and tension, and performance in the course. The strongest relationship was demonstrated between goal instability and career thoughts, indicating that more goal instability is related to more negative career thoughts. Goal instability was not significantly related to career decidedness. Implications for practice and research based on the results of this study are discussed.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd1388
 Format
 Thesis
 Title
 An Optimal Control Problem for a TimeDependent GinzburgLandau Model of Superconductivity.
 Creator

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

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

Jacobsen, Douglas W. (Douglas William), Gunzburger, Max, Nof, Doron, Peterson, Janet, Erlebacher, Gordon, Navon, Michael, Burkardt, John, Ringler, Todd, Department of Scientific...
Show moreJacobsen, Douglas W. (Douglas William), Gunzburger, Max, Nof, Doron, Peterson, Janet, Erlebacher, Gordon, Navon, Michael, Burkardt, John, Ringler, Todd, Department of Scientific Computing, Florida State University
Show less  Abstract/Description

Spherical centroidal Voronoi tessellations (SCVT) are used in many applications in a variety of fields, one being climate modeling. They are a natural choice for spatial discretizations on the surface of the Earth. New modeling techniques have recently been developed that allow the simulation of ocean and atmosphere dynamics on arbitrarily unstructured meshes, including SCVTs. Creating ultrahigh resolution SCVTs can be computationally expensive. A newly developed algorithm couples current...
Show moreSpherical centroidal Voronoi tessellations (SCVT) are used in many applications in a variety of fields, one being climate modeling. They are a natural choice for spatial discretizations on the surface of the Earth. New modeling techniques have recently been developed that allow the simulation of ocean and atmosphere dynamics on arbitrarily unstructured meshes, including SCVTs. Creating ultrahigh resolution SCVTs can be computationally expensive. A newly developed algorithm couples current algorithms for the generation of SCVTs with existing computational geometry techniques to provide the parallel computation of SCVTs and spherical Delaunay triangulations. Using this new algorithm, computing spherical Delaunay triangulations shows a speed up on the order of 4000 over other well known algorithms, when using 42 processors. As mentioned previously, newly developed numerical models allow the simulation of ocean and atmosphere systems on arbitrary Voronoi meshes providing a multiresolution modeling framework. A multiresolution grid allows modelers to provide areas of interest with higher resolution with the hopes of increasing accuracy. However, one method of providing higher resolution lowers the resolution in other areas of the mesh which could potentially increase error. To determine the effect of multiresolution meshes on numerical simulations in the shallowwater context, a standard set of shallowwater test cases are explored using the Model for Prediction Across Scales (MPAS), a new modeling framework jointly developed by the Los Alamos National Laboratory and the National Center for Atmospheric Research. An alternative approach to multiresolution modeling is Adaptive Mesh Refinement (AMR). AMR typically uses information about the simulation to determine optimal locations for degrees of freedom, however standard AMR techniques are not well suited for SCVT meshes. In an effort to solve this issue, a framework is developed to allow AMR simulations on SCVT meshes within MPAS. The resulting research contained in this dissertation ties together a newly developed parallel SCVT generator with a numerical method for use on arbitrary Voronoi meshes. Simulations are performed within the shallowwater context. New algorithms and frameworks are described and benchmarked.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd3743
 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
 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
 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
 ReducedOrder Modeling of Reactive Solute Transport for AdvectionDominated Problems with Nonlinear Kinetic Reactions.
 Creator

McLaughlin, Benjamin R. S., Peterson, Janet S., Ye, Ming, Duke, D. W. (Dennis W.), Gunzburger, Max D., Shanbhag, Sachin, Florida State University, College of Arts and Sciences,...
Show moreMcLaughlin, Benjamin R. S., Peterson, Janet S., Ye, Ming, Duke, D. W. (Dennis W.), Gunzburger, Max D., Shanbhag, Sachin, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Groundwater is a vital natural resource, and our ability to protect and manage this resource efficiently and effectively relies heavily on our ability to perform reliable and accurate computer modeling and simulation of subsurface systems. This frequently raises research questions involving parameter estimation and uncertainty quantification, which are often prohibitively expensive to answer using standard highdimensional computational models. We have previously demonstrated the ability to...
Show moreGroundwater is a vital natural resource, and our ability to protect and manage this resource efficiently and effectively relies heavily on our ability to perform reliable and accurate computer modeling and simulation of subsurface systems. This frequently raises research questions involving parameter estimation and uncertainty quantification, which are often prohibitively expensive to answer using standard highdimensional computational models. We have previously demonstrated the ability to replace the highdimensional models used to solve linear, uncoupled, diffusiondominated multispecies reactive transport systems with lowdimension approximations using reduced order modeling (ROM) based on proper orthogonal decomposition (POD). In this work, we seek to apply ROM to more general reactive transport systems, where the reaction terms may be nonlinear, mathematical models may be coupled, and the transport may be advectiondominated. We discuss the use of operator splitting, which is prevalent in the reactive transport field, to simplify the computation of complex systems of reactions in the transport model. We also discuss the use of some stabilization methods which have been developed in the computational science community to treat advectiondominated transport problems. We present a method by which we are able to incorporate stabilization and operator splitting together in the finite element setting. We go on to develop methods for implementing both operator splitting and stabilization in the ROM setting, as well as for incorporating both of them together within the ROM framework. We present numerical results which establish the ability of this new approach to produce accurate approximations with a significant reduction in computational cost, and we demonstrate the application of this method to a more realistic reactive transport problem involving bioremediation.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9649
 Format
 Thesis
 Title
 MultiGPU Solutions of Geophysical PDEs with Radial Basis FunctionGenerated Finite Differences.
 Creator

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

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

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

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

Sockwell, K. Chadwick (Kenneth Chadwick), Gunzburger, Max D., Peterson, Janet S., Burkardt, John V., Florida State University, College of Arts and Sciences, Department of...
Show moreSockwell, K. Chadwick (Kenneth Chadwick), Gunzburger, Max D., Peterson, Janet S., Burkardt, John V., Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Superconductivity is a phenomenon characterized by two hallmark properties, zero electrical resistance and the Meissner effect. These properties give great promise to a new generation of resistance free electronics and powerful superconducting magnets. However this possibility is limited by the extremely low critical temperature the superconductors must operate under, typically close to 0K. The recent discovery of high temperature superconductors has brought the critical temperature closer to...
Show moreSuperconductivity is a phenomenon characterized by two hallmark properties, zero electrical resistance and the Meissner effect. These properties give great promise to a new generation of resistance free electronics and powerful superconducting magnets. However this possibility is limited by the extremely low critical temperature the superconductors must operate under, typically close to 0K. The recent discovery of high temperature superconductors has brought the critical temperature closer to room temperature than ever before, making the realization of room temperature superconductivity a possibility. Simulations of superconducting technology and materials will be necessary to usher in the new wave of superconducting electronics. Unfortunately these new materials come with new properties such as effects from multiple electron bands, as is the case for magnesium diboride. Moreover, we must consider that all high temperature superconductors are of a Type II variety, which possess magnetic tubes of flux, known as vortices. These vortices interact with transport currents, creating an electrical resistance through a process known as flux flow. Thankfully this process can be prevented by placing impurities in the superconductor, pinning the vortices, making vortex pinning a necessary aspect of our model. At this time there are no other models or simulations that are aimed at modeling vortex pinning, using impurities, in twoband materials. In this work we modify an existing GinzburgLandau model for twoband superconductors and add the ability to model normal inclusions (impurities) with a new approach which is unique to the twoband model. Simulations in an attempt to model the material magnesium diboride are also presented. In particular simulations of vortex pinning and transport currents are shown using the modified model. The qualitative properties of magnesium diboride are used to validate the model and its simulations. One main goal from the computational end of the simulations is to enlarge the domain size to produce more realistic simulations that avoid boundary pinning effects. In this work we also implement the numerical software library Trilinos in order to parallelize the simulation to enlarge the domain size. Decoupling methods are also investigated with a goal of enlarging the domain size as well. The OneBand GinzburgLandau model serves as a prototypical problem in this endeavor and the methods shown that enlarge the domain size can be easily implemented in the twoband model.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Sockwell_fsu_0071N_13577
 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
 Improvement of a Tracer Correlation Problem with a NonIterative Limiter.
 Creator

Lopez, Nicolas A., Gunzburger, Max D., Burkardt, John V., Peterson, Janet C., Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

A functional relation between two chemical species puts observational constraints on attempts to model the atmosphere. For example, adequate representation of these relations is important when modeling the depletion of stratospheric ozone by nitrous oxide. Previous work has shown a case where a linear functional relation is not preserved in the tracer transport scheme of the Higher Order Methods Modeling Environment (HOMME), which is the spectral element dynamics core used by the Community...
Show moreA functional relation between two chemical species puts observational constraints on attempts to model the atmosphere. For example, adequate representation of these relations is important when modeling the depletion of stratospheric ozone by nitrous oxide. Previous work has shown a case where a linear functional relation is not preserved in the tracer transport scheme of the Higher Order Methods Modeling Environment (HOMME), which is the spectral element dynamics core used by the Community Atmosphere Model (CAM). Application of a certain simple tracer chemistry reaction before each model time step can test whether the scheme actually preserves linear tracer correlations (LCs) to machine precision. Using this method, we confirm previous results that, the implementation of the default shapepreserving filter of HOMME used in the transport scheme does not preserve LCs. However, since we prove that this limiter along with a few other limiter algorithms do in fact preserve LCs in exact arithmetic, we suggest that these limiter algorithms exacerbate the growth of roundoff error in elements where tracers have very different magnitudes. Nevertheless, we manage to put forth a limiting scheme that improves the tracer correlation problem. We also derive another new limiter that relies on multiplicative rescaling of nodal values within a given element. This algorithm does not rely on iterations for convergence and thus has the advantage of being more computationally efficient than the current default CAMSE limiter. Results also show that the default limiter does not always introduce the lowest amount of Lâ‚‚ error, which contradicts its purpose, since it was derived to minimize error in the Lâ‚‚ norm.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SU_Lopez_fsu_0071N_13470
 Format
 Thesis
 Title
 Reduced Order Modeling for a Nonlocal Approach to Anomalous Diffusion Problems.
 Creator

Witman, David, Gunzburger, Max D., Peterson, Janet C., Stagg, Scott, Shanbhag, Sachin, Burkardt, John V., Florida State University, College of Arts and Sciences, Department of...
Show moreWitman, David, Gunzburger, Max D., Peterson, Janet C., Stagg, Scott, Shanbhag, Sachin, Burkardt, John V., Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

With the recent advances in using nonlocal approaches to approximate traditional partial differential equations(PDEs), a number of new research avenues have been opened that warrant further study. One such path, that has yet to be explored, is using reduced order techniques to solve nonlocal problems. Due to the interactions between the discretized nodes or particles inherent to a nonlocal model, the system sparsity is often significantly less than its PDE counterpart. Coupling a reduced...
Show moreWith the recent advances in using nonlocal approaches to approximate traditional partial differential equations(PDEs), a number of new research avenues have been opened that warrant further study. One such path, that has yet to be explored, is using reduced order techniques to solve nonlocal problems. Due to the interactions between the discretized nodes or particles inherent to a nonlocal model, the system sparsity is often significantly less than its PDE counterpart. Coupling a reduced order approach to a nonlocal problem would ideally reduce the computational cost without sacrificing accuracy. This would allow for the use of a nonlocal approach in large parameter studies or uncertainty quantification. Additionally, because nonlocal problems inherently have no spatial derivatives, solutions with jump discontinuities are permitted. This work seeks to apply reduced order nonlocal concepts to a variety of problem situations including anomalous diffusion, advection, the advectiondiffusion equation and solutions with spatial discontinuities. The goal is to show that one can use an accurate reduced order approximation to formulate a solution at a fraction of the cost of traditional techniques.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Witman_fsu_0071E_13130
 Format
 Thesis
 Title
 Using Deal.II to Solve Problems in Computational Fluid Dynamics.
 Creator

Bystricky, Lukas, Peterson, Janet C., Shanbhag, Sachin, Burkardt, John V., Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

Finite element methods are a common tool to solve problems in computational fluid dynamics (CFD). This thesis explores the finite element package deal.ii and specific applications to incompressible CFD. Some notation and results from finite element theory are summarised, and a brief overview of some of the features of deal.ii is given. Following this, several CFD applications are presented, including the Stokes equations, the NavierStokes equations and the equations for Darcy flow in porous...
Show moreFinite element methods are a common tool to solve problems in computational fluid dynamics (CFD). This thesis explores the finite element package deal.ii and specific applications to incompressible CFD. Some notation and results from finite element theory are summarised, and a brief overview of some of the features of deal.ii is given. Following this, several CFD applications are presented, including the Stokes equations, the NavierStokes equations and the equations for Darcy flow in porous media. Comparison with benchmark problems are provided for the Stokes and NavierStokes equations and a case study looking at foam deformation is provided for Darcy flow. Code is provided where applicable.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Bystricky_fsu_0071N_13237
 Format
 Thesis
 Title
 Using RBFGenerated Quadrature Rules to Solve Nonlocal Continuum Models.
 Creator

Lyngaas, Isaac R., Peterson, Janet S., Musslimani, Ziad H., Gunzburger, Max D., Quaife, Bryan, Shanbhag, Sachin, Florida State University, College of Arts and Sciences,...
Show moreLyngaas, Isaac R., Peterson, Janet S., Musslimani, Ziad H., Gunzburger, Max D., Quaife, Bryan, Shanbhag, Sachin, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Recently nonlocal continuum models have gained interest as alternatives to traditional PDE models due to their capability of handling solutions with discontinuities and their ease of modeling anomalous diffusion. The typical approach used for approximating timedependent nonlocal integrodifferential models is to use finite element or discontinuous Galerkin methods; however, these approaches can be quite computationally intensive especially when solving problems in more than one dimension due...
Show moreRecently nonlocal continuum models have gained interest as alternatives to traditional PDE models due to their capability of handling solutions with discontinuities and their ease of modeling anomalous diffusion. The typical approach used for approximating timedependent nonlocal integrodifferential models is to use finite element or discontinuous Galerkin methods; however, these approaches can be quite computationally intensive especially when solving problems in more than one dimension due to the approximation of the nonlocal integral. In this work, we propose a novel method based on using radial basis functions to generate accurate quadrature rules for the nonlocal integral appearing in the model and then coupling this with a finite difference approximation to the timedependent terms. The viability of our method is demonstrated through various numerical tests on time dependent nonlocal diffusion, nonlocal anomalous diffusion, and nonlocal advection problems in one and two dimensions. In addition to nonlocal problems with continuous solutions, we modify our approach to handle problems with discontinuous solutions. We compare some numerical results with analogous finite element results and demonstrate that for an equivalent amount of computational work we obtain much higher rates of convergence.
Show less  Date Issued
 2018
 Identifier
 2018_Fall_Lyngaas_fsu_0071E_14886
 Format
 Thesis
 Title
 An Introduction to CIP Theory, Research, and Practice.
 Creator

Sampson, James P, Osborn, Debra S, BullockYowell, Emily, Lenz, Janet G, Peterson, Gary W, Dozier, V Casey, Leierer, Stephen J, Hayden, Seth C W, Saunders, Denise E
 Abstract/Description

The primary purpose of this paper is to introduce essential elements of cognitive information processing (CIP) theory, research, and practice as they existed at the time of this writing. The introduction that follows describes the nature of career choices and career interventions, and the integration of theory, research, and practice. After the introduction, the paper continues with three main sections that include CIP theory related to vocational behavior, research related to vocational...
Show moreThe primary purpose of this paper is to introduce essential elements of cognitive information processing (CIP) theory, research, and practice as they existed at the time of this writing. The introduction that follows describes the nature of career choices and career interventions, and the integration of theory, research, and practice. After the introduction, the paper continues with three main sections that include CIP theory related to vocational behavior, research related to vocational behavior and career intervention, and CIP theory related to career interventions. The first main section describes CIP theory, including the evolution of CIP theory, the nature of career problems, theoretical assumptions, the pyramid of information processing domains, the CASVE Cycle, and the use of the pyramid and CASVE cycle. The second main section describes CIP theorybased research in examining vocational behavior and establishing evidencebased practice for CIP theorybased career interventions. The third main section describes CIP theory related to career intervention practice, including theoretical assumptions, readiness for career decision making, readiness for career intervention, the differentiated service delivery model, and critical ingredients of career interventions. The paper concludes with regularly updated sources of information on CIP theory.
Show less  Date Issued
 20200625
 Identifier
 FSU_libsubv1_scholarship_submission_1593091156_c171f50a
 Format
 Citation