Current Search: Kopriva, David (x)
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 Title
 Numerical Simulation of Quench Propagation in Superconducting Magnets by Using High Order Methods.
 Creator

Mao, Shaolin, Luongo, Cesar A., Kopriva, David A., Shih, Chiang, Cartes, David A., Department of Mechanical Engineering, Florida State University
 Abstract/Description

In this study, two highorder numerical methods were applied to simulate quench propagation in cableinconduit superconductor (CICC) magnets. The main consideration in this dissertation is to seek some numerical methods with high accuracy (resolution) and efficiency. The first method was dispersionrelationpreserving (DRP) schemes to solve quench propagation in CICC at early phase to decrease dispersion errors. The second one was discontinuous Galerkin (DG) spectral element methods which...
Show moreIn this study, two highorder numerical methods were applied to simulate quench propagation in cableinconduit superconductor (CICC) magnets. The main consideration in this dissertation is to seek some numerical methods with high accuracy (resolution) and efficiency. The first method was dispersionrelationpreserving (DRP) schemes to solve quench propagation in CICC at early phase to decrease dispersion errors. The second one was discontinuous Galerkin (DG) spectral element methods which overcome numerical difficulties encountered by most classical methods. The numerical solution showed high accuracy and resolution in large gradient regions of quench propagation. Roe's approximate Riemann solver was solved for helium for the first time by using curve fitting to the Riemann integral. In the study, a simple physical model, the energy balance model, was proposed for the first time to track the superfluid helium and normal helium fronts in CICC magnets. This new model was used to analyze the thermal stability the NHMFL 45T hybrid magnets systems. This model resulted in high efficiency of numerical simulation of thermal stability analysis compared to complicated 1D quench propagation model. To improve numerical efficiency, adaptive mesh techniques were also introduced. This model can effectively speed up the simulation of helium boundary tracking problems while retaining high accuracy of simulation.
Show less  Date Issued
 2004
 Identifier
 FSU_migr_etd2748
 Format
 Thesis
 Title
 Discontinuous Galerkin Spectral Element Approximations on Moving Meshes for Wave Scattering from Reflective Moving Boundaries.
 Creator

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

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

Willyard, Matthew, Kopriva, David, Eugenio, Paul, Case, Bettye Anne, Gallivan, Kyle, Nolder, Craig, Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

We develop an adaptive spectral element method to price American options, whose solutions contain a moving singularity, automatically and to within prescribed errors. The adaptive algorithm uses an error estimator to determine where refinement or derefinement is needed and a work estimator to decide whether to change the element size or the polynomial order. We derive two local error estimators and a global error estimator. The local error estimators are derived from the Legendre...
Show moreWe develop an adaptive spectral element method to price American options, whose solutions contain a moving singularity, automatically and to within prescribed errors. The adaptive algorithm uses an error estimator to determine where refinement or derefinement is needed and a work estimator to decide whether to change the element size or the polynomial order. We derive two local error estimators and a global error estimator. The local error estimators are derived from the Legendre coefficients and the global error estimator is based on the adjoint problem. One local error estimator uses the rate of decay of the Legendre coefficients to estimate the error. The other local error estimator compares the solution to an estimated solution using fewer Legendre coefficients found by the Tau method. The global error estimator solves the adjoint problem to weight local error estimates to approximate a terminal error functional. Both types of error estimators produce meshes that match expectations by being fine near the early exercise boundary and strike price and coarse elsewhere. The produced meshes also adapt as expected by derefining near the strike price as the solution smooths and staying fine near the moving early exercise boundary. Both types of error estimators also give solutions whose error is within prescribed tolerances. The adjointbased error estimator is more flexible, but costs up to three times as much as using the local error estimate alone. The global error estimator has the advantages of tracking the accumulation of error in time and being able to discount large local errors that do not affect the chosen terminal error functional. The local error estimator is cheaper to compute because the global error estimator has the added cost of solving the adjoint problem.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0892
 Format
 Thesis
 Title
 Exotic Nuclei and Relativistic MeanField Theory.
 Creator

Rutel, Bonnie Gwen, Piekarewicz, Jorge, Capstick, Simon, Cottle, Paul, Reina, Laura, Kopriva, David A., Department of Physics, Florida State University
 Abstract/Description

A relativistic meanfield model is used to study the groundstate properties of neutronrich nuclei. Nonlinear isoscalarisovector terms, unconstrained by present day phenomenology, are added to the model Lagrangian in order to modify the poorly known density dependence of the symmetry energy. These new terms soften the symmetry energy and reshape the theoretical neutron drip line without compromising the agreement with existing groundstate information. A strong correlation between the...
Show moreA relativistic meanfield model is used to study the groundstate properties of neutronrich nuclei. Nonlinear isoscalarisovector terms, unconstrained by present day phenomenology, are added to the model Lagrangian in order to modify the poorly known density dependence of the symmetry energy. These new terms soften the symmetry energy and reshape the theoretical neutron drip line without compromising the agreement with existing groundstate information. A strong correlation between the neutron radius of Pb208 and the binding energy of valence orbitals is found: the smaller the neutron radius of Pb208, the weaker the binding energy of the last occupied neutron orbital. Thus, models with the softest symmetry energy are the first ones to drip neutrons. Further, in anticipation of the upcoming onepercent measurement of the neutron radius of Pb208 at the Thomas Jefferson Laboratory, a close relationship between the neutron radius of Pb208 and neutron radii of elements of relevance to atomic parityviolating experiments is established. On the basis of relativistic mean field calculations, we demonstrate that the spinorbit splitting of p3/2 and p1/2 neutron orbits depends sensitively on the magnitude of the proton density near the center of the nucleus, and in particular on the occupation of s1/2 proton orbits. We focus on two exotic nuclei, Ar46 and Hg206, in which the presence of a pair of s1/2 proton holes would cause the spinorbit splitting between the p3/2 and p1/2 neutron orbits near the Fermi surface to be much smaller than in the nearby doublymagic nuclei Ca48 and Pb208. We also explore how partial occupancy of the s1/2 proton orbits affects this quenching. We note that these two exotic nuclei depart from the longstanding paradigm of a central potential proportional to the ground state baryon density and a spinorbit potential proportional to the derivative of the central potential.
Show less  Date Issued
 2004
 Identifier
 FSU_migr_etd1956
 Format
 Thesis
 Title
 Singleand MultipleObjective Stochastic Programming Models with Applications to Aerodynamics.
 Creator

Croicu, AnaMaria, Hussaini, M. Yousuﬀ, Srivastava, Anuj, Kopriva, David, Wang, Qi, Department of Mathematics, Florida State University
 Abstract/Description

Deterministic design assumes that there is no uncertainty in the modeling parameters, and as a consequence, there is no variability in the simulation outputs. Therefore, deterministic optimal designs that are obtained without taking into account uncertainty are usually unreliable. This is the case with transonic shape optimization, where the randomness in the cruise Mach number might have significant impact on the optimal geometric design. In this context, a stochastic search turns out to be...
Show moreDeterministic design assumes that there is no uncertainty in the modeling parameters, and as a consequence, there is no variability in the simulation outputs. Therefore, deterministic optimal designs that are obtained without taking into account uncertainty are usually unreliable. This is the case with transonic shape optimization, where the randomness in the cruise Mach number might have significant impact on the optimal geometric design. In this context, a stochastic search turns out to be more appropriate. Approaches to stochastic optimization have followed a variety of modeling philosophies, but little has been done to systematically compare different models. The goal of this thesis is to present a comparison between two stochastic optimization algorithms, with the emphasis on applications, especially on the airfoil shape optimization. Singleobjective and multiobjective optimization programs are analyzed as well. The relationship between the expected minimum value (EMV) criterion and the minimum expected value (MEV) criterion is explored, and it is shown that, under favorable conditions, a better optimal point could be obtained via the EMV approach. Unfortunately, the advantages of using the EMV approach are far outweighed by the prohibitive exorbitant computational cost.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd3027
 Format
 Thesis
 Title
 Partial Differential Equation Methods to Price Options in the Energy Market.
 Creator

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

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

Bosque, Ernesto, Van Sciver, Steven, Kopriva, David, Ordoñez, Juan, Clark, Jonathan, Department of Mechanical Engineering, Florida State University
 Abstract/Description

Rapid heat deposition is a natural consequence of an insulating vacuum jacket failure around a He IIcooled system. This loss of vacuum is often referred to as the worstcase scenario, as it seriously endangers its surroundings and the low temperature equipment cooled within. In the case of a vacuum break, air floods into the vacuum jacket, impinging on the inner vacuum wall. The air carries with it a significant amount of energy (~500 kJ/kg) that is ultimately transferred to the He II...
Show moreRapid heat deposition is a natural consequence of an insulating vacuum jacket failure around a He IIcooled system. This loss of vacuum is often referred to as the worstcase scenario, as it seriously endangers its surroundings and the low temperature equipment cooled within. In the case of a vacuum break, air floods into the vacuum jacket, impinging on the inner vacuum wall. The air carries with it a significant amount of energy (~500 kJ/kg) that is ultimately transferred to the He II coolant. Given large magnitudes, the heat flux results in rapid pressurization due to the expansion of the helium as it boils to its vapor phase. An experimental rig has been designed, built, and successfully operated to simulate such a sudden loss of insulating vacuum incident confined to onedimension in space. The rig consists of an evacuated tube that deadends to a He IIcooled disk, beneath which is a column of He II near 1.8 K, open to its bath. A wide range of mass flow rates are studied for warm gas flooding into the evacuated tube, causing the gas to cryodeposit and transfer its internal energy through the disk and to the He II. Thermometry in the disk and axially through the He II column is used to quantify the heat transport generated by the cryodeposition process. In general, it is found that the heat flux to the He II is indeed limited by peak heat flux theory. It is further confirmed that noisy film boiling, though mechanically violent, reduces the heat transfer to the He II. The cryodeposition behavior of warm gas onto a He IIcooled surface is also shown to be somewhat stochastic. In summary, an accurate conceptual model is developed to fundamentally describe and predict the coupled mass and heat transport phenomena that result after such a vacuum failure.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8734
 Format
 Thesis
 Title
 Uncertainty Quantification and Data Fusion Based on DempsterShafer Theory.
 Creator

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

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

Garreau, Pierre, Kercheval, Alec N., Marquis, Milton H., Beaumont, Paul M., Kopriva, David A., Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

This thesis presents a new structural framework for multidimensional default risk. The time of default is the first jump of the logreturns of the stock price of a firm below a stochastic default level. When the stock price is an exponential Levy process, this new formulation is equivalent to a default model with stochastic intensity where the intensity process is parametrized by a Levy measure. This framework calibrates well to various term structures of credit default swaps. Furthermore,...
Show moreThis thesis presents a new structural framework for multidimensional default risk. The time of default is the first jump of the logreturns of the stock price of a firm below a stochastic default level. When the stock price is an exponential Levy process, this new formulation is equivalent to a default model with stochastic intensity where the intensity process is parametrized by a Levy measure. This framework calibrates well to various term structures of credit default swaps. Furthermore, the dependence between the default times of firms within a basket of credit securities is the result of the jump dependence of their respective stock prices: this class of models makes the link between the Equity and Credit markets. As an application, we show the valuation of a firsttodefault swaps. To motivate this new framework, we compute the default probability in a traditional structural model of default where the firm value follows a general Levy processes. This is made possible via the resolution of a partial integrodifferential equation (PIDE). We solve this equation numerically using a spectral element method based on the approximation of the solution with high order polynomials described in (Garreau & Korpiva, 2013). This method is able to handle the sharp kernels in the integral term. It is faster than the competing numerical Laplace transform methods used for first passage time problems, and can be used to compute the price of exotic options with barriers. This PIDE approach does not however extend well in higher dimensions. To understand the joint default of our new framework, we investigate the dependence structures of Levy processes. We show that for two one dimensional Levy processes to form a two dimensional Levy process, their joint survival times need to satisfy a two dimensional version of the memoryless property. We make the link with bivariate exponential random variables and the MarshallOlkin copula. This result yields a necessary construction of dependent Levy processes, a characterization theorem for Poisson random measures and has important ramification for default models with jointly conditionally Poisson processes.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8555
 Format
 Thesis
 Title
 Pricing and Hedging Derivatives with Sharp Profiles Using Tuned High Resolution Finite Difference Schemes.
 Creator

Islim, Ahmed Derar, Kopriva, David A., Winn, Alice, Kercheval, Alec N., Ewald, Brian, Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

We price and hedge different financial derivatives with sharp profiles by solving the corresponding advectiondiffusionreaction partial differential equation using new high resolution finite difference schemes, which show superior numerical advantages over standard finite difference methods. High order finite difference methods, which are commonly used techniques in the computational finance literature, fail to handle the discontinuities in the payoff functions of derivatives with...
Show moreWe price and hedge different financial derivatives with sharp profiles by solving the corresponding advectiondiffusionreaction partial differential equation using new high resolution finite difference schemes, which show superior numerical advantages over standard finite difference methods. High order finite difference methods, which are commonly used techniques in the computational finance literature, fail to handle the discontinuities in the payoff functions of derivatives with discontinuous payoff functions, like digital options. Their numerical solutions produce spurious oscillations in the neighborhood of the discontinuities, which make the numerical derivatives prices and hedges impractical. Hence, we extend the linear finite difference methods to overcome these difficulties by developing high resolution nonlinear schemes that resolve these discontinuities and facilitate pricing and hedging these options with higher accuracy. These approximations detect the discontinuous profiles automatically using nonlinear functions, called limiters, and smooth discontinuities minimally and locally to produce nonoscillatory prices and Greeks with high resolution. These limiters are modified and more relaxed versions of standard limiting functions in fluid dynamics area to accommodate for the extra physical diffusion (volatility) in financial problems. We prove that this family of new schemes is total variation diminishing (TVD), which guarantees the non oscillatory solutions. Also, we deduce and illustrate the limiting functions ranges and characteristics that allow the TVD condition to hold. We test these methods to price and hedge financial derivatives with digitallike profiles under BlackScholesMerton (BSM), constant elasticity of variance (CEV) and HeathJarrowMorton (HJM) models. More specifically, we price and hedge digital options under BSM and CEV models, and we price bonds under HJM model. Finally, we price supershare and gap options under the BSM model. Using the new limiters we developed show higher accuracy profiles (solutions) for the option prices and hedges than standard finite difference schemes or standard limiters, and guaranteed nonoscillatory solutions.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8813
 Format
 Thesis
 Title
 Design and Development of the Multiple Parabolic Reflector Flat Panel Collector (MPFC) to Generate Medium Temperature Steam.
 Creator

Pandolfini, Jonathan, Krothapalli, Anjaneyulu, Kopriva, David, Shih, Chiang, Hollis, Patrick J., Ordonez, Juan Carlos, Department of Mechanical Engineering, Florida State...
Show morePandolfini, Jonathan, Krothapalli, Anjaneyulu, Kopriva, David, Shih, Chiang, Hollis, Patrick J., Ordonez, Juan Carlos, Department of Mechanical Engineering, Florida State University
Show less  Abstract/Description

The Multiple Parabolic Reflector Flat Panel Collector (MPFC) was designed to heat a working fluid to a temperature of 150oC using the sun. The use of stationary reflectors and a moving receiver tube allow for maximum energy collection with minimum amount of solar tracking. The reflectorreceiver combination is placed within an enclosure with multiple reflectors; the top of the enclosure allows solar radiation while stifling thermal losses from convection and radiation to the environment. A...
Show moreThe Multiple Parabolic Reflector Flat Panel Collector (MPFC) was designed to heat a working fluid to a temperature of 150oC using the sun. The use of stationary reflectors and a moving receiver tube allow for maximum energy collection with minimum amount of solar tracking. The reflectorreceiver combination is placed within an enclosure with multiple reflectors; the top of the enclosure allows solar radiation while stifling thermal losses from convection and radiation to the environment. A concentration ratio of 6 is used with respect to the aperture area of the reflector compared to the surface are of the receiver. The MPFC is a panel collector where the enclosure remains stationary and the receiver moves to track the sun. This is accomplished by combining aspects of flat panel (FP) collectors, compound parabolic concentrators (CPC), and parabolic trough collectors (PTC). The design is based on an analysis performed using ray tracing techniques to estimate the amount of radiation reaching the receiver. It was shown that the amount of possible energy collection is comparable to that of FP and CPC collectors. Computation Fluid Dynamics (CFD) was used to estimate convective heat transfer within the enclosure. Combining the ray tracing and CFD results with a thermodynamic model of the panel, the total performance of the MPFC can be estimated. Experiments were also performed to verify the method of the numerical model, the optical efficiency found from the ray tracing model, and the heat loss found from the CFD solution. It was found that the numerical model solves the system of equations appropriately, the ray tracing is an accurate description to the reflection of the radiation, and the CFD modeled the natural convection within a cavity with appropriate accuracy while remaining a conservative estimation. The final MPFC design is a compilation of the individual studies in a way that is simple while accomplishing its goals.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7959
 Format
 Thesis
 Title
 Uncertainty Quantification of Nonlinear Stochastic Phenomena.
 Creator

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

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

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

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

Yang, Sam, Kopriva, David A., Hruda, Simone P. (Simone Peterson), Van Sciver, Steven W., Florida State University, College of Engineering, Department of Mechanical Engineering
 Abstract/Description

The dissertation presents the mathematical formulation, experimental validation, and application of a volume element model (VEM) devised for modeling, simulation, and optimization of energy systems in their early design stages. The proposed model combines existing modeling techniques and experimental adjustment to formulate a reducedorder model, while retaining sufficient accuracy to serve as a practical systemlevel design analysis and optimization tool. In the VEM, the physical domain...
Show moreThe dissertation presents the mathematical formulation, experimental validation, and application of a volume element model (VEM) devised for modeling, simulation, and optimization of energy systems in their early design stages. The proposed model combines existing modeling techniques and experimental adjustment to formulate a reducedorder model, while retaining sufficient accuracy to serve as a practical systemlevel design analysis and optimization tool. In the VEM, the physical domain under consideration is discretized in space using lumped hexahedral elements (i.e., volume elements), and the governing equations for the variable of interest are applied to each element to quantify diverse types of flows that cross it. Subsequently, a system of algebraic and ordinary differential equations is solved with respect to time and scalar (e.g., temperature, relative humidity, etc.) fields are obtained in both spatial and temporal domains. The VEM is capable of capturing and predicting dynamic physical behaviors in the entire system domain (i.e., at system level), including mutual interactions among system constituents, as well as with their respective surroundings and cooling systems, if any. The VEM is also generalizable; that is, the model can be easily adapted to simulate and optimize diverse systems of different scales and complexity and attain numerical convergence with sufficient accuracy. Both the capability and generalizability of the VEM are demonstrated in the dissertation via thermal modeling and simulation of an OffGrid Zero Emissions Building, an allelectric ship, and a vapor compression refrigeration (VCR) system. Furthermore, the potential of the VEM as an optimization tool is presented through the integrative thermodynamic optimization of a VCR system, whose results are used to evaluate the tradeoffs between various objective functions, namely, coefficient of performance, second law efficiency, pulldown time, and refrigerated space temperature, in both transient and steadystate operations.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SU_Yang_fsu_0071E_13370
 Format
 Thesis
 Title
 A Spectral Element Method to Price Single and MultiAsset European Options.
 Creator

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

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

Shah, Manan, Okten, Giray, Goncharov, Yevgeny, Srinivasan, Ashok, Bellenot, Steve, Case, Bettye Anne, Kercheval, Alec, Kopriva, David, Nichols, Warren, Department of Mathematics...
Show moreShah, Manan, Okten, Giray, Goncharov, Yevgeny, Srinivasan, Ashok, Bellenot, Steve, Case, Bettye Anne, Kercheval, Alec, Kopriva, David, Nichols, Warren, Department of Mathematics, Florida State University
Show less  Abstract/Description

In this dissertation, we introduce a genetic algorithm approach to estimate the star discrepancy of a point set. This algorithm allows for the estimation of the star discrepancy in dimensions larger than seven, something that could not be done adequately by other existing methods. Then, we introduce a class of random digitpermutations for the Halton sequence and show that these permutations yield comparable or better results than their deterministic counterparts in any number of dimensions...
Show moreIn this dissertation, we introduce a genetic algorithm approach to estimate the star discrepancy of a point set. This algorithm allows for the estimation of the star discrepancy in dimensions larger than seven, something that could not be done adequately by other existing methods. Then, we introduce a class of random digitpermutations for the Halton sequence and show that these permutations yield comparable or better results than their deterministic counterparts in any number of dimensions for the test problems considered. Next, we use randomized quasiMonte Carlo methods to numerically solve a onefactor mortgage model expressed as a stochastic fixedpoint problem. Finally, we show that this mortgage model coincides with and is computationally faster than Citigroup's MOATS model, which is based on a binomial tree approach.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0297
 Format
 Thesis
 Title
 Dissipation of Mesoscale Energy by VortexTopography Interaction.
 Creator

Bishnu, Siddhartha, Dewar, William K., Chassignet, Eric P., Clarke, Allan J., Kopriva, David A., Florida State University, College of Arts and Sciences, Department of Earth,...
Show moreBishnu, Siddhartha, Dewar, William K., Chassignet, Eric P., Clarke, Allan J., Kopriva, David A., Florida State University, College of Arts and Sciences, Department of Earth, Ocean, and Atmospheric Science
Show less  Abstract/Description

Energy is introduced into the oceans primarily at large scales by means of wind, tides and surface buoyancy forcing. This energy is transferred to the smaller mesoscale eld through the geostrophic instability processes. The mesoscale eld appears not to have accelerated appreciably over the last several decades, so we can assume that the mesoscale loses energy at roughly the same rate it receives energy. Interestingly, how the mesoscale loses energy is not quite clear. We have been exploring...
Show moreEnergy is introduced into the oceans primarily at large scales by means of wind, tides and surface buoyancy forcing. This energy is transferred to the smaller mesoscale eld through the geostrophic instability processes. The mesoscale eld appears not to have accelerated appreciably over the last several decades, so we can assume that the mesoscale loses energy at roughly the same rate it receives energy. Interestingly, how the mesoscale loses energy is not quite clear. We have been exploring topographic interaction as a pathway by which the mesoscale may lose energy to unbalanced forward cascading flows. To demonstrate this phenomenon, an approximate model theory is developed which consists of solving a reduced set of the momentum equations in density coordinates for any topographic conguration. The equations are solved using a high order spectral element technique and the results are similar to already published MITgcm simulations.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Bishnu_fsu_0071N_14263
 Format
 Thesis
 Title
 Relativistic Mean Field Models for Finite Nuclei and Neutron Stars.
 Creator

Chen, WeiChia, Piekarewicz, Jorge, Kopriva, David A., Volya, Alexander, Credé, Volker, Bonesteel, N. E., Florida State University, College of Arts and Sciences, Department of...
Show moreChen, WeiChia, Piekarewicz, Jorge, Kopriva, David A., Volya, Alexander, Credé, Volker, Bonesteel, N. E., Florida State University, College of Arts and Sciences, Department of Physics
Show less  Abstract/Description

In this dissertation we have created theoretical models for finite nuclei, nuclear matter, and neutron stars within the framework of relativistic mean field (RMF) theory, and we have used these models to investigate the elusive isovector sector and related physics, in particular, the neutronskin thickness of heavy nuclei, the nuclear symmetry energy, and the properties of neutron stars. To build RMF models that incorporate collective excitations in finite nuclei in addition to their ground...
Show moreIn this dissertation we have created theoretical models for finite nuclei, nuclear matter, and neutron stars within the framework of relativistic mean field (RMF) theory, and we have used these models to investigate the elusive isovector sector and related physics, in particular, the neutronskin thickness of heavy nuclei, the nuclear symmetry energy, and the properties of neutron stars. To build RMF models that incorporate collective excitations in finite nuclei in addition to their groundstate properties, we have extended the nonrelativistic sum rule approach to the relativistic domain. This allows an efficient estimate of giant monopole energies. Moreover, we have combined an exact shellmodellike approach with the meanfield calculation to describe pairing correlations in openshell nuclei. All the ingredients were then put together to establish the calibration scheme. We have also extended the transformation between model parameters and pseudo data of nuclear matter within the RMF context. Performing calibration in this pseudo data space can not only facilitate the searching algorithm but also make the pseudo data genuine model predictions. This calibration scheme is also supplemented by a covariance analysis enabling us to extract the information content of a model, including theoretical uncertainties and correlation coefficients. A series of RMF models subject to the same isoscalar constraints but one differing isovector assumption were then created using this calibration scheme. By comparing their predictions of the nuclear matter equation of state to both experimental and theoretical constraints, we found that a small neutron skin of about 0.16 fm in Pb208 is favored, indicating that the symmetry energy should be soft. To obtain stronger evidence, we proceeded to examine the evolution of the isotopic chains in both oxygen and calcium. Again, it was found that the model with such small neutron skin and soft symmetry energy can best describe both isotopic chains, and the resultant values of the neutronskin thickness and the symmetry energy are consistent with most current constraints. Finally, we addressed the recent tension between dense matter theory and the observation of neutron stars with rather small stellar radii. By employing Lindblom's algorithm, we were able to derive the underlying equation of state for assumed massradius relations having the "common radius" feature followed by recent analyses. We found that, in order to support twosolarmass neutron stars, the typical stellar radii must be greater than 10.7 km—barely compatible with recent analyses—to prevent the underlying equation of state from violating causality.
Show less  Date Issued
 2015
 Identifier
 FSU_2015fall_Chen_fsu_0071E_12869
 Format
 Thesis
 Title
 Clustering in Light Nuclei with Configuration Interaction Approaches.
 Creator

Kravvaris, Konstantinos, Volya, Alexander, Kopriva, David A., Weidenhoever, Ingo Ludwing M., Capstick, Simon, Reina, Laura, Florida State University, College of Arts and...
Show moreKravvaris, Konstantinos, Volya, Alexander, Kopriva, David A., Weidenhoever, Ingo Ludwing M., Capstick, Simon, Reina, Laura, Florida State University, College of Arts and Sciences, Department of Physics
Show less  Abstract/Description

The formation of substructures within an atomic nucleus, appropriately termed nuclear clustering, is one of the core questions of nuclear manybody physics. In this thesis, we put forward a new method for the study of nuclear clustering relying on the completely microscopic Configuration Interaction approach. We construct reaction cluster channels in a Harmonic Oscillator manybody basis that respect the symmetries of the Hamiltonian, are fully antisymmetrized, and carry a separable and...
Show moreThe formation of substructures within an atomic nucleus, appropriately termed nuclear clustering, is one of the core questions of nuclear manybody physics. In this thesis, we put forward a new method for the study of nuclear clustering relying on the completely microscopic Configuration Interaction approach. We construct reaction cluster channels in a Harmonic Oscillator manybody basis that respect the symmetries of the Hamiltonian, are fully antisymmetrized, and carry a separable and controlled Center of Mass component. Such channels are then used to explore cluster signatures in Configuration Interaction manybody wavefunctions. The Resonating Group Method is then applied, utilizing the reaction channels as a basis to capture the essential cluster characteristics of the system. We investigate the emergence of nuclear clustering in 2α, 2α+n, 2α+2n and 3α systems using a No Core Shell Model approach from first principles, and traditional Shell Model studies of clustering in heavier nuclei.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Kravvaris_fsu_0071E_14611
 Format
 Thesis
 Title
 Sensitivity Analysis of Options under Lévy Processes via Malliavin Calculus.
 Creator

Bayazit, Dervis, Nolder, Craig A., Huﬀer, Fred, Case, Bettye Anne, Kopriva, David, Okten, Giray, Quine, Jack, Department of Mathematics, Florida State University
 Abstract/Description

The sensitivity analysis of options is as important as pricing in option theory since it is used for hedging strategies, hence for risk management purposes. This dissertation presents new sensitivities for options when the underlying follows an exponential Lévy process, specifically Variance Gamma and Normal Inverse Gaussian processes. The calculation of these sensitivities is based on a finite dimensional Malliavin calculus and the centered finite difference method via MonteCarlo...
Show moreThe sensitivity analysis of options is as important as pricing in option theory since it is used for hedging strategies, hence for risk management purposes. This dissertation presents new sensitivities for options when the underlying follows an exponential Lévy process, specifically Variance Gamma and Normal Inverse Gaussian processes. The calculation of these sensitivities is based on a finite dimensional Malliavin calculus and the centered finite difference method via MonteCarlo simulations. We give explicit formulas that are used directly in MonteCarlo simulations. By using simulations, we show that a localized version of the Malliavin estimator outperforms others including the centered finite difference estimator for the call and digital options under Variance Gamma and Normal Inverse Gaussian processes driven option pricing models. In order to compare the performance of these methods we use an inverse Fourier transform method to calculate the exact values of the sensitivities of European call and digital options written on S&P 500 index. Our results show that a variation of localized Malliavin calculus approach gives a robust estimator while the convergence of centered finite difference method in MonteCarlo simulations varies with different Greeks and new sensitivities that we introduce. We also discuss an approximation method for the Variance Gamma process. We introduce new random number generators for the path wise simulations of the approximating process. We improve convergence results for a type of sensitivity by using a mixed Malliavin calculus on the increments of the approximating process.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1157
 Format
 Thesis
 Title
 Asset Pricing in a Lucas Framework with Boundedly Rational, Heterogeneous Agents.
 Creator

Culham, Andrew J. (Andrew James), Beaumont, Paul M., Kercheval, Alec N., Schlagenhauf, Don, Goncharov, Yevgeny, Kopriva, David, Department of Mathematics, Florida State University
 Abstract/Description

The standard dynamic general equilibrium model of financial markets does a poor job of explaining the empirical facts observed in real market data. The common assumptions of homogeneous investors and rational expectations equilibrium are thought to be major factors leading to this poor performance. In an attempt to relax these assumptions, the literature has seen the emergence of agentbased computational models where artificial economies are populated with agents who trade in stylized asset...
Show moreThe standard dynamic general equilibrium model of financial markets does a poor job of explaining the empirical facts observed in real market data. The common assumptions of homogeneous investors and rational expectations equilibrium are thought to be major factors leading to this poor performance. In an attempt to relax these assumptions, the literature has seen the emergence of agentbased computational models where artificial economies are populated with agents who trade in stylized asset markets. Although they offer a great deal of flexibility, the theoretical community has often criticized these agentbased models because the agents are too limited in their analytical abilities. In this work, we create an artificial market with a single risky asset and populate it with fully optimizing, forward looking, infinitely lived, heterogeneous agents. We restrict the state space of our agents by not allowing them to observe the aggregate distribution of wealth so they are required to compute their conditional demand functions while simultaneously learning the equations of motion for the aggregate state variables. We develop an efficient and flexible model code that can be used to explore a wide number of asset pricing questions while remaining consistent with conventional asset pricing theory. We validate our model and code against known analytical solutions as well as against a new analytical result for agents with differing discount rates. Our simulation results for general cases without known analytical solutions show that, in general, agents' asset holdings converge to a steadystate distribution and the agents are able to learn the equilibrium prices despite the restricted state space. Further work will be necessary to determine whether the exceptional cases have some fundamental theoretical explanation or can be attributed to numerical issues. We conjecture that convergence to the equilibrium is global and that the marketclearing price acts to guide the agents' forecasts toward that equilibrium.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd2948
 Format
 Thesis
 Title
 Probabilistic Uncertainty Analysis and Its Applications in Option Models.
 Creator

Namihira, Motoi J., Kopriva, David A., Srivastava, Anuj, Ewald, Brian, Hussaini, M. Yousuﬀ, Nichols, Warren, Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

In this work we quantify the effect of uncertainty in volatility in the prices and Deltas of an American and European put using probabilistic uncertainty analysis. We review the current methods of uncertainty analysis including worst case or scenario analysis, Monte Carlo, and provide an in depth review of Polynomial Chaos in both one and multiple dimensions. We develop a numerically stable method of generating orthogonal polynomials that is used in the practical construction of the...
Show moreIn this work we quantify the effect of uncertainty in volatility in the prices and Deltas of an American and European put using probabilistic uncertainty analysis. We review the current methods of uncertainty analysis including worst case or scenario analysis, Monte Carlo, and provide an in depth review of Polynomial Chaos in both one and multiple dimensions. We develop a numerically stable method of generating orthogonal polynomials that is used in the practical construction of the Polynomial Chaos basis functions. We also develop a semi analytic density transform method that is 200 times faster and 1000 times more accurate than the Monte Carlo based kernel density method. Finally, we analyze the European and American put option models assuming a distribution for the volatility that is historically observed. We find that the sensitivity to uncertainty in volatility is greatest for the price of ATM puts, and tapers as one moves away from the strike. The Delta, however, exhibits the least sensitivity when ATM and is most sensitive when moderately ITM. The price uncertainty for ITM American puts is less than the price uncertainty of equivalent European puts. For OTM options, the price uncertainty is similar between American and European puts. The uncertainty in the Delta of ITM American puts is greater than the uncertainty of equivalent European puts. For OTM puts, the uncertainty in Delta is similar between American and European puts. For the American put, uncertainty in volatility introduces uncertainty in the location of the optimal exercise boundary, thereby making optimal exercise decisions more difficult.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7525
 Format
 Thesis
 Title
 Diffuse Interface Method for TwoPhase Incompressible Flows.
 Creator

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

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

Lingle, Mark, Volya, Alexander, Kopriva, David A., Capstick, Simon, Wiedenhöver, Ingo, Manousakis, Efstratios, Florida State University, College of Arts and Sciences, Department...
Show moreLingle, Mark, Volya, Alexander, Kopriva, David A., Capstick, Simon, Wiedenhöver, Ingo, Manousakis, Efstratios, Florida State University, College of Arts and Sciences, Department of Physics
Show less  Abstract/Description

Nuclear pairing correlations using Quantum Monte Carlo are studied in this dissertation. We start by defining the nuclear pairing problem and discussing several historical methods developed to solve this problem, paying special attention to the applicability of such methods. A numerical example discussing pairing correlations in several calcium isotopes using the BCS and Exact Pairing solutions are presented. The ground state energies, correlation energies, and occupation numbers are compared...
Show moreNuclear pairing correlations using Quantum Monte Carlo are studied in this dissertation. We start by defining the nuclear pairing problem and discussing several historical methods developed to solve this problem, paying special attention to the applicability of such methods. A numerical example discussing pairing correlations in several calcium isotopes using the BCS and Exact Pairing solutions are presented. The ground state energies, correlation energies, and occupation numbers are compared to determine the applicability of each approach to realistic cases. Next we discuss some generalities related to the theory of Markov Chains and Quantum Monte Carlo in regards to nuclear structure. Finally we present our configuration space Monte Carlo algorithm starting from a discussion of a path integral approach by the authors [2, 3]. Some general features of the Pairing Hamiltonian that boost the effectiveness of a configuration space Monte Carlo approach are mentioned. The full details of our method are presented and special attention is paid to convergence and error control. We present a series of examples illustrating the effectiveness of our approach. These include situations with nonconstant pairing strengths, limits when pairing correlations are weak, the computation of excited states, and problems when the relevant configuration space is large. We conclude with a chapter examining some of the effects of continuum states in 24O.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9383
 Format
 Thesis
 Title
 Discontinuous Galerkin Spectral Element Approximations for the Reflection and Transmission of Waves from Moving Material Interfaces.
 Creator

Winters, Andrew R., Kopriva, David, Piekarewicz, Jorge, Hussaini, M. Yousuff, Gallivan, Kyle, Cogan, Nick, Case, Bettye Anne, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation develops and evaluates a computationally efficient and highorder numerical method to compute wave reflection and transmission from moving material boundaries. We use a discontinuous Galerkin spectral element approximation with an arbitrary LagrangianEulerian mapping and derive the exact upwind numerical fluxes to model the physics of wave reflection and transmission at jumps in material properties. Spectral accuracy is obtained by placing moving material interfaces at...
Show moreThis dissertation develops and evaluates a computationally efficient and highorder numerical method to compute wave reflection and transmission from moving material boundaries. We use a discontinuous Galerkin spectral element approximation with an arbitrary LagrangianEulerian mapping and derive the exact upwind numerical fluxes to model the physics of wave reflection and transmission at jumps in material properties. Spectral accuracy is obtained by placing moving material interfaces at element boundaries and solving the appropriate Riemann problem. We also derive and evaluate an explicit local time stepping (LTS) integration for the DGSEM on moving meshes. The LTS procedure is derived from AdamsBashforth multirate time integration methods. We present speedup and memory estimates, which show that the explicit LTS integration scales well with problem size. The LTS time integrator is also highly parallelizable. The manuscript also gathers, derives and analyzes several analytical solutions for the problem of wave reflection and transmission from a plane moving material interface. We present timestep refinement studies and numerical examples to show the approximations for wave reflection and transmission at dielectric and acoustic interfaces are spectrally accurate in space and have design temporal accuracy. The numerical tests also validate theoretical estimates that the LTS procedure can reduce computational cost by as much as an order of magnitude for time accurate problems. Finally, we investigate the parallel speedup of the LTS integrator and compare it to a standard, lowstorage RungeKutta method.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8916
 Format
 Thesis
 Title
 Gulf Stream Separation Dynamics.
 Creator

Schoonover, Joseph Arthur, Dewar, William K., Kopriva, David A., Chassignet, Eric P., Speer, Kevin G. (Kevin George), Florida State University, College of Arts and Sciences,...
Show moreSchoonover, Joseph Arthur, Dewar, William K., Kopriva, David A., Chassignet, Eric P., Speer, Kevin G. (Kevin George), Florida State University, College of Arts and Sciences, Program in Geophysical Fluid Dynamics
Show less  Abstract/Description

Climate models currently struggle with the more traditional, coarse ( O(100 km) ) representation of the ocean. In these coarse ocean simulations, western boundary currents are notoriously difficult to model accurately. The modeled Gulf Stream is typically seen exhibiting a mean pathway that is north of observations, and is linked to a warm seasurface temperature bias in the MidAtlantic Bight. Although increased resolution ( O(10 km) ) improves the modeled Gulf Stream position, there is no...
Show moreClimate models currently struggle with the more traditional, coarse ( O(100 km) ) representation of the ocean. In these coarse ocean simulations, western boundary currents are notoriously difficult to model accurately. The modeled Gulf Stream is typically seen exhibiting a mean pathway that is north of observations, and is linked to a warm seasurface temperature bias in the MidAtlantic Bight. Although increased resolution ( O(10 km) ) improves the modeled Gulf Stream position, there is no clean recipe for obtaining the proper pathway. The 70 year history of literature on the Gulf Stream separation suggests that we have not reached a resolution on the dynamics that control the current's pathway just south of the MidAtlantic Bight. Without a concrete knowledge on the separation dynamics, we cannot provide a clean recipe for accurately modeling the Gulf Stream at increased resolutions. Further, any reliable parameterization that yields a realistic Gulf Stream path must express the proper physics of separation. The goal of this dissertation is to determine what controls the Gulf Stream separation. To do so, we examine the results of a model intercomparison study and a set of numerical regional terraforming experiments. It is argued that the separation is governed by local dynamics that are most sensitive to the steepening of the continental shelf, consistent with the topographic wave arrest hypothesis of Stern (1998). A linear extension of Stern's theory is provided, which illustrates that wave arrest is possible for a continuously stratified fluid.
Show less  Date Issued
 2015
 Identifier
 FSU_2016SP_Schoonover_fsu_0071E_12967
 Format
 Thesis
 Title
 Gas Propagation in a Liquid Helium Cooled Vacuum Tube Following a Sudden Vacuum Loss.
 Creator

Dhuley, Ram, Van Sciver, Steven W., Kopriva, David A., Hellstrom, Eric, Guo, Wei, Taira, Kunihiko, Florida State University, College of Engineering, Department of Mechanical...
Show moreDhuley, Ram, Van Sciver, Steven W., Kopriva, David A., Hellstrom, Eric, Guo, Wei, Taira, Kunihiko, Florida State University, College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

This dissertation describes the propagation of near atmospheric nitrogen gas that rushes into a liquid helium cooled vacuum tube after the tube suddenly loses vacuum. The lossofvacuum scenario resembles accidental venting of atmospheric air to the beamline of a superconducting radio frequency particle accelerator and is investigated to understand how in the presence of condensation, the inflowing air will propagate in such geometry. In a series of controlled experiments, room temperature...
Show moreThis dissertation describes the propagation of near atmospheric nitrogen gas that rushes into a liquid helium cooled vacuum tube after the tube suddenly loses vacuum. The lossofvacuum scenario resembles accidental venting of atmospheric air to the beamline of a superconducting radio frequency particle accelerator and is investigated to understand how in the presence of condensation, the inflowing air will propagate in such geometry. In a series of controlled experiments, room temperature nitrogen gas (a substitute for air) at a variety of mass flow rates was vented to a high vacuum tube immersed in a bath of liquid helium. Pressure probes and thermometers installed on the tube along its length measured respectively the tube pressure and tube wall temperature rise due to gas flooding and condensation. At high mass inflow rates a gas front propagated down the vacuum tube but with a continuously decreasing speed. Regression analysis of the measured front arrival times indicates that the speed decreases nearly exponentially with the travel length. At low enough mass inflow rates, no front propagated in the vacuum tube. Instead, the inflowing gas steadily condensed over a short section of the tube near its entrance and the front appeared to `freezeout'. An analytical expression is derived for gas front propagation speed in a vacuum tube in the presence of condensation. The analytical model qualitatively explains the front deceleration and flow freezeout. The model is then simplified and supplemented with condensation heat/mass transfer data to again find the front to decelerate exponentially while going away from the tube entrance. Within the experimental and procedural uncertainty, the exponential decay lengthscales obtained from the front arrival time regression and from the simplified model agree.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Dhuley_fsu_0071E_13054
 Format
 Thesis