Current Search: Kopriva, David A. (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
 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
 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
 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
 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 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
 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
 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
 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
 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
 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