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 Title
 A Comparative Study between a Single Sorption Constant Model and a Humic Ion Binding Model.
 Creator

Pham, Serena Otsuka, Ye, Ming, Shanbhag, Sachin, Huang, Chen, Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

Software packages that model geochemical speciation and complexation are useful for predicting how different materials such as heavy metals and organic matter interact with the environment. The East Fork Poplar Creek (EFPC) in Oak Ridge, Tennessee suffers from extensive mercury pollution as a result of postWWII activities to develop thermonuclear weapons. A current model that predicts the speciation of mercury and methylmercury species treats dissolved organic matter (DOM) as a single entity...
Show moreSoftware packages that model geochemical speciation and complexation are useful for predicting how different materials such as heavy metals and organic matter interact with the environment. The East Fork Poplar Creek (EFPC) in Oak Ridge, Tennessee suffers from extensive mercury pollution as a result of postWWII activities to develop thermonuclear weapons. A current model that predicts the speciation of mercury and methylmercury species treats dissolved organic matter (DOM) as a single entity instead of a multidimensional and multisite molecule. The HumicIon Binding Model VII is a discrete multisite model implemented by default in the WHAM7 software that represents binding behavior between protons, metal cations, and humic substances. Implementing Model VII into the current EFPC model using the PHREEQC speciation program can predict site interactions of organic matter with mercury and methylmercury. Adding surface complexation to the model shows a substantial increase in the amount of methylmercury bound to DOM compared to the original model. Thus, when appropriate, employing a surface complexation model in geochemical simulations should be considered.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Pham_fsu_0071N_14265
 Format
 Thesis
 Title
 Computational Studies of Equilibrium and NonEquilibrium Phase Diagrams and Critical Properties of Two Physical and Chemical Model Systems with Both ShortRange and LongRange Interactions or Reactivities.
 Creator

Chan, ChorHoi, Rikvold, Per Arne, Shanbhag, Sachin, Brown, Gregory, Capstick, Simon, Xiong, Peng, Florida State University, College of Arts and Sciences, Department of Physics
 Abstract/Description

In this dissertation, we introduce longrange interactions into one equilibrium model (Ising model) and one nonequilibrium system (ZiffGulariBarshad model), and study their phase diagrams and critical properties. A new approach to do WangLandau simulation: macroscopically constrained WangLandau, is proposed in connection with the former system. Our macroscopically constrained WangLandau method breaks a multidimensional random walk process in phase space into many separate, one...
Show moreIn this dissertation, we introduce longrange interactions into one equilibrium model (Ising model) and one nonequilibrium system (ZiffGulariBarshad model), and study their phase diagrams and critical properties. A new approach to do WangLandau simulation: macroscopically constrained WangLandau, is proposed in connection with the former system. Our macroscopically constrained WangLandau method breaks a multidimensional random walk process in phase space into many separate, onedimensional random walk processes in the energy space. Each of these random walks is constrained to a different value of the macroscopic order parameters. By knowing the distribution of these constrained variables, we can deduce the multivariable density of states. When the multivariable density of states for one set of external parameters is obtained, the density of states at any point in the phase diagram can be obtained by simple transformations. After that, all thermodynamic quantities can be obtained. We apply this method to an antiferromagnetic Ising model with a ferromagnetic longrange interaction. The addition of the longrange interaction induces metastable regions in the phase diagram, and a meanfield class critical point emerges for sufficiently strong longrange interaction. We demonstrate how to use the multivariable density of states obtained to sketch out the complicated phase diagrams for different values of the longrange interaction. We also give freeenergy plots, and plots of the distributions of the order parameters of the system for different special points in these phase diagrams. The ZiffGulariBarshad (ZGB) model, a simplified description of the oxidation of carbon monoxide (CO) on a catalyst surface, is widely used to study properties of nonequilibrium phase transitions. Instead of restricting the CO and atomic oxygen (O) to react to form carbon dioxide (CO₂) only when they are adsorbed in close proximity, we consider a modified model that includes an adjustable probability for adsorbed CO and O atoms located far apart on the lattice to react. We employ largescale Monte Carlo simulations to study the critical properties of this system. We find that the nonequilibrium critical point changes from the twodimensional Ising universality class to the meanfield universality class upon introducing even a weak longrange reactivity mechanism.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Chan_fsu_0071E_13552
 Format
 Thesis
 Title
 ContactFree Simulations of Rigid Particle Suspensions Using Boundary Integral Equations.
 Creator

Bystricky, Lukas, Quaife, Bryan, Shanbhag, Sachin, Cogan, Nicholas G., Huang, Chen, Moore, Matthew Nicholas J., Florida State University, College of Arts and Sciences,...
Show moreBystricky, Lukas, Quaife, Bryan, Shanbhag, Sachin, Cogan, Nicholas G., Huang, Chen, Moore, Matthew Nicholas J., Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

In many composite materials, rigid fibers are distributed throughout the material to tune the mechanical, thermal, and electric properties of the composite. The orientation and distribution of the fibers play a critical role in the properties of the composite. Many composites are processed as a liquid molten suspension of fibers and then solidified, holding the fibers in place. Once the fiber orientations are known, theoretical models exist that can predict properties of the composite...
Show moreIn many composite materials, rigid fibers are distributed throughout the material to tune the mechanical, thermal, and electric properties of the composite. The orientation and distribution of the fibers play a critical role in the properties of the composite. Many composites are processed as a liquid molten suspension of fibers and then solidified, holding the fibers in place. Once the fiber orientations are known, theoretical models exist that can predict properties of the composite.Modeling the suspended fibers in the liquid state is important because their ultimate configuration depends strongly on the flow history during the molten processing. Continuum models, such as the FolgarTucker model, predict the evolution of the fibers’ orientation in a fluid. These models are limited in several ways. First, they require empirical constants and closure relations that must be determined a priori, either by experiments or detailed computer simulations. Second, they assume that all the fibers are slender bodies of uniform length. Lastly, these methods break down for concentrated suspensions. For these reasons, it is desirable in certain situations to model the movement of individual fibers explicitly. This dissertation builds upon recent advances in boundary integral equations to develop a robust, accurate, and stable method that simulates fibers of arbitrary shape in a planar flow. In any method that explicitly models the individual fiber motion, care must be taken to ensure numerical errors do not cause the fibers to overlap. To maintain fiber separation, a repulsion force and torque are added when required. This repulsion force is free of tuning parameters and is determined by solving a sequence of linear complementarity problems to ensure that the configuration does not have any overlap between fibers. Numerical experiments demonstrate the stability of the method for concentrated suspensions.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Bystricky_fsu_0071E_14725
 Format
 Thesis
 Title
 Detonability of Turbulent White Dwarf Plasma: Hydrodynamical Models at Low Densities.
 Creator

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

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

Pouranvari, Mohammad, Yang, Kun, Shanbhag, Sachin, Bonesteel, N. E., Balicas, Luis, Chiorescu, Irinel, Florida State University, College of Arts and Sciences, Department of Physics
 Abstract/Description

In this thesis, we study the entanglement properties of quantum systems to characterize quantum phases and phase transitions. We focus on the free fermion lattice systems and we use numerical calculation to verify our ideas. Behavior of the entanglement entropy is used to distinguish different phases, in addition the area law of the entanglement entropy is studied. We propose that beside the entanglement entropy, there is physical information in the entanglement Hamiltonian of the reduced...
Show moreIn this thesis, we study the entanglement properties of quantum systems to characterize quantum phases and phase transitions. We focus on the free fermion lattice systems and we use numerical calculation to verify our ideas. Behavior of the entanglement entropy is used to distinguish different phases, in addition the area law of the entanglement entropy is studied. We propose that beside the entanglement entropy, there is physical information in the entanglement Hamiltonian of the reduced density matrix of a chosen subsystem. We verify our ideas by studying different free fermion models. The verification is made by comparing the results we obtain from studying the behavior of the entanglement Hamiltonian with the known previous results. As starting point, to show that entanglement Hamiltonian eigenmodes have physical information, we employ the XX spin chain model. Real space renormalization group method predicts that the ground state is the product state of singlet states and thus those singlet that cross the boundary make the entanglement. We use the entanglement Hamiltonian to show that its single particle eigenmode shows the location of the entangled singlet spins. This is done in the case of ground state at T = 0. We also studied the entanglement properties of the highly excited eigenstate of the system. We use modified version of real space renormalization group for excited state and we show that in T ≠ 0 case where singlet and triplet state with total S[subscript Z] = 0 make entanglement, entanglement Hamiltonian eigenmode shows the location of the entangled spins. We distinguish one eigenmode of the entanglement Hamiltonian as the maximally entangled mode. This mode corresponds to the smallest entanglement energy and thus contributes the most to the entanglement entropy. In addition, we use two onedimensional free fermion models, namely the random dimer model and power law random banded model to show that for a localizeddelocalized phase transition, behavior of the maximally entangled mode is similar to the behavior of the eigenmode of the original Hamiltonian at the Fermi level. We quantify this by comparing their overlaps and the inverse participation ratio of eigenmodes. The behavior of the entanglement entropy as a wellknown quantity is studied in disordered free fermion models. In random dimer model and power law random banded model where the correlated disorder yields to the localizeddelocalized phase transition, we show that entanglement entropy saturates in localized phase and diverges in delocalized phase. In addition it violates the area law in delocalized phase. Entanglement entropy of Anderson model in one, two, and three dimensions is also studied and we observed that area law is correct even for the delocalized phase of the Anderson model in three dimensions, provided that system size is larger than the mean free path. The study of a single impurity, one nonzero onsite energy, in the Anderson model is also examined. We concluded that this single impurity changes only the subleading term of the entanglement entropy which is proportional to the inverse of the subsystem size. This subleading term has nonoscillation and oscillating part.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Pouranvari_fsu_0071E_13052
 Format
 Thesis
 Title
 Estimation of Nitrogen Load from Septic Systems to Surface Waterbodies in Indian River County, FL.
 Creator

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

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

Wei, Ling, Van Winkle, David H., Shanbhag, Sachin, Xiong, Peng, Rikvold, Per Arne, Wahl, Horst D., Florida State University, College of Arts and Sciences, Department of Physics
 Abstract/Description

Electrophoresis as an analytical technique has made considerable contributions to the separations and analysis of macromolecules in biologyrelated research. Pluronic gels, which are composed of orderly packed spherical micelles assembled by triblock copolymers, have been developed as novel sieving media to separate oligonucleotides, duplex DNA molecules and proteins, providing ease of manipulations due to their thermoreversibility and higher resolution in comparison with other polymer gels...
Show moreElectrophoresis as an analytical technique has made considerable contributions to the separations and analysis of macromolecules in biologyrelated research. Pluronic gels, which are composed of orderly packed spherical micelles assembled by triblock copolymers, have been developed as novel sieving media to separate oligonucleotides, duplex DNA molecules and proteins, providing ease of manipulations due to their thermoreversibility and higher resolution in comparison with other polymer gels. Electrophoretic mobility of short doublestranded DNA molecules in pluronic F127 is reported to have a nonmonotonic dependence on DNA length, which is not observed in other polymerbased sieving media or explained by any welldeveloped theories. In this dissertation, the unusual DNAlength dependence of electrophoretic mobility is experimentally investigated in several different pluronic gels, and the DNA dynamics in pluronic liquid crystals is systematically studied by coarsegrained Brownian dynamics simulations. The crystal structures and micelle dimensions of pluronics P105, P123 and F127 are characterized by atomic force microscopy, smallangle xray scattering, smallangle neutron scattering and dynamic light scattering. Twodimensional gel electrophoresis is performed and the electrophoretic mobility of DNA molecules in the size range of 20500 bp is measured in pluronics P105, P123 and F127. The unusual DNA lengthdependent mobility is consistently obtained in three pluronic gels, where the mobility of very short DNA molecules increases with increasing DNA length, and the mobility of long DNA molecules monotonically decreases with DNA length. Superposed on the rising and falling trends are the subtle oscillations of mobility with DNA length in the intermediate regime. Brownian dynamics simulations are implemented to numerically calculate the DNA mobility in pluronic lattices, by including the shortranged intramolecular hydrodynamic interactions, and modeling the interactions between DNA molecules and pluronic micelles via a repulsive force and entanglement effect. The rise, fall and oscillations of mobility with DNA length, as obtained in experimental measurements, are reproduced by the Brownian dynamics simulations, and essential physics that dominates the unusual features of mobility is extracted from the simulations. In addition, electric fielddependent mobility of DNA molecules in pluronic lattices is studied by Brownian dynamics simulations, and the conceptual connection between highfield simulations along specific field directions and lowfield experiments in bulk gels is established, and the Brownian dynamic simulations are proven to be an appropriate approach to interpret the DNA electrophoretic dynamics in pluronic matrices. Moreover, electrophoretic mobility of duplex DNA flanked by singlestranded overhangs is measured in pluronic gels, and it is shown that the mobility of DNA with overhangs is higher than the corresponding bluntended DNA molecules. Brownian dynamics simulations are carried out, and the enhancement of mobility for DNA with overhangs is captured by the simulations. By integrating numerical simulations with experimental measurements, the fundamental physical quantities and interactions that manipulate the DNA electrophoretic migration in pluronic liquid crystals are revealed. Understanding the unusual DNA lengthdependent mobility in pluronic gels potentially provides profound insights in designing and optimizing highperformance sieving matrices for sizebased separation purposes.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Wei_fsu_0071E_13585
 Format
 Thesis
 Title
 Ice versus Liquid Water Saturation in Regional Climate Simulations of the Indian Summer Monsoon.
 Creator

Glazer, Russell Henderson, Misra, Vasubandhu, Shanbhag, Sachin, Bourassa, Mark Allan, Hart, Robert E., Liu, Guosheng, Florida State University, College of Arts and Sciences,...
Show moreGlazer, Russell Henderson, Misra, Vasubandhu, Shanbhag, Sachin, Bourassa, Mark Allan, Hart, Robert E., Liu, Guosheng, Florida State University, College of Arts and Sciences, Department of Earth, Ocean and Atmospheric Science
Show less  Abstract/Description

At the same temperature, below 0oC, the saturation vapor pressure (SVP) over ice is slightly less than the SVP over liquid water. Numerical models use the ClausiusClapeyron relation to calculate the SVP and relative humidity, but there is not a consistent method for the treatment of saturation above the freezing level where ice and mixedphase clouds may be present. In the context of current challenges presented by cloud microphysics in climate models, we argue that a better understanding of...
Show moreAt the same temperature, below 0oC, the saturation vapor pressure (SVP) over ice is slightly less than the SVP over liquid water. Numerical models use the ClausiusClapeyron relation to calculate the SVP and relative humidity, but there is not a consistent method for the treatment of saturation above the freezing level where ice and mixedphase clouds may be present. In the context of current challenges presented by cloud microphysics in climate models, we argue that a better understanding of the impact that this treatment has on saturationrelated processes like cloud formation and precipitation, is needed. This study explores the importance of the SVP calculation through model simulations of the Indian Summer Monsoon (ISM) using atmosphereonly simulations with the Regional Spectral Model (RSM) and RSM coupled to the Regional Ocean Modeling System (RSMROMS). Atmosphereonly simulations are conducted with two saturation parameterizations. In one, the SVP over liquid water is prescribed through the entire atmospheric column (woIce), and in another the SVP over ice is used above the freezing level (wIce). When SVP over ice is prescribed, a thermodynamic drying of the middle and upper troposphere above the freezing level occurs due to increased condensation. In the wIce runs, the model responds to the slight decrease in the saturation condition by increasing, relative to the SVP over liquid water only run, gridscale condensation of water. Changes in the cloud layer amounts in the wIce simulation cause in increase in the net heat flux (NHF) at the surface of 23 W/m2 over the Arabian Sea (AS) and a decrease of similar magnitude over the eastern equatorial Indian Ocean (EEIO). Motivated by these NHF changes the wIce and woIce experiments were repeated in the coupled simulations. With coupling added, the ocean is allowed to respond to any NHF changes; however we find that the NHF difference between wIcewoIce over the AS is near zero. It is proposed that with the inclusion of airsea coupling the atmospheric and oceanic response to changes in the SVP is damped relative to the forced RSM integrations. The importance of airsea interaction for the northward propagation and evolution of the Indian monsoon intrareasonal oscillation (ISO) is examined through a comparison between the uncoupled and coupled simulations, and the observed ISO. It was found that the observed ISO contains a robust airsea interaction during its evolution which would suggest that coupling is required to simulate the observed relationship between the ocean and atmosphere during the ISO. However, the uncoupled simulations show the ability to simulate realistic amplitude ISOs without coupling to the ocean, suggesting that there is an internal atmospheric component that is important for simulating the observed ISO period and amplitude.
Show less  Date Issued
 2018
 Identifier
 2018_Sp_Glazer_fsu_0071E_14515
 Format
 Thesis
 Title
 Learning and Motion Planning for GaitBased Legged Robots.
 Creator

Harper, Mario Yuuji, Erlebacher, Gordon, Collins, E., Beaumont, Paul M., Clark, Jonathan E., Shanbhag, Sachin, MeyerBäse, Anke, Florida State University, College of Arts and...
Show moreHarper, Mario Yuuji, Erlebacher, Gordon, Collins, E., Beaumont, Paul M., Clark, Jonathan E., Shanbhag, Sachin, MeyerBäse, Anke, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Animals have demonstrated the capacity to traverse many complex unstructured terrains at high speeds by utilizing effective locomotion regimes. Motion in difficult and uncertain environments have only seen partial success on traditional wheeled or trackbased robots and is limited to slow deliberative maneuvers on legged robots, which are focused on maintaining continuous stability through proper foothold selection. While legged robots have demonstrated successful navigation across many...
Show moreAnimals have demonstrated the capacity to traverse many complex unstructured terrains at high speeds by utilizing effective locomotion regimes. Motion in difficult and uncertain environments have only seen partial success on traditional wheeled or trackbased robots and is limited to slow deliberative maneuvers on legged robots, which are focused on maintaining continuous stability through proper foothold selection. While legged robots have demonstrated successful navigation across many complex surfaces, motion planning algorithms currently fail to consider the unique mobility characteristics that honor the natural selfstabilizing dynamics of gaitbased locomotion such as running and climbing. This dissertation outlines some of the specific motion planning challenges faced when attempting to plan for legged systems with dynamic gaits, with specific instances of these demonstrated by four robots, the dynamic running platforms: XRL, LLAMA, Minitaur and the dynamic climbing platform TAILS. Using a unique implementation of Sampling Based Model Predictive Optimization (SBMPO) designed expressly for dynamic legged robots, we demonstrate the ability to learn kinodynamic models, motion plan through obstacles on varied terrains and demonstrate navigation on vertical walls. This research has pioneered the technique which allows dynamic legged robots to navigate while honoring the natural dynamics of robot gait. Further, this document will describe to the reader the methods and algorithms that enabled Florida State University to be the first in the world to demonstrate motion planning on a dynamic climbing robot. This work is demonstrated in simulation and verified through hardware experiments on canonical motion planning scenarios, controlled laboratory settings and in unstructured terrains. Finally, this work has opened the field of dynamic legged robot intelligence for future researchers by enabling fundamental navigation and planning, efficient realtime algorithms for onboard computing, and the development of techniques to account for complex constrained motions unique to individual robots and terrains.
Show less  Date Issued
 2018
 Identifier
 2018_Fall_Harper_fsu_0071E_14735
 Format
 Thesis
 Title
 Making Material Simulation Faster: Coarse Graining, Bridging and Bootstrapping.
 Creator

Crysup, Benjamin Rosser, Shanbhag, Sachin, Rikvold, Per Arne, Huang, Chen, MendozaCortes, Jose L., Slice, Dennis E., Florida State University, College of Arts and Sciences,...
Show moreCrysup, Benjamin Rosser, Shanbhag, Sachin, Rikvold, Per Arne, Huang, Chen, MendozaCortes, Jose L., Slice, Dennis E., Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Nanoparticles with a solid, inorganic core surrounded by long chain organic ligands have many useful properties and applications. A feature of these materials is that their properties can be tuned to an application: this makes preliminary simulations appealing (to cut down on the possibility space before going into the lab). However, from a simulation perspective, nanoparticles are big and expensive to simulate at the atomic level. There exist a collection of methods to take gross structural...
Show moreNanoparticles with a solid, inorganic core surrounded by long chain organic ligands have many useful properties and applications. A feature of these materials is that their properties can be tuned to an application: this makes preliminary simulations appealing (to cut down on the possibility space before going into the lab). However, from a simulation perspective, nanoparticles are big and expensive to simulate at the atomic level. There exist a collection of methods to take gross structural information and produce a potential fit for simulations at the molecular level. In this work, five such methods (and a few alterations to those methods) were performed on a series of increasingly large molecules to see how they perform at the most aggressive level of coarse graining. The methods were compared based on how well they reproduced structural information about the molecules, and on how much they sped up the dynamics of those systems. In order to make meaningful comparisons between these results, the uncertainty in the results needs to be known. Since large simulations are involved, running multiple simulations is expensive. However, Shanbhag (Shanbhag, 2013) recently proposed a method to obtain the uncertainty in diffusion coefficients obtained from a molecular dynamics simulation (via bootstrapping the atomic trajectories to generate estimates). This method was originally tested only on a simple system, so its validity on more complicated systems needed to be verified. This work tested the validity of this method by running two hundred LennardJones simulations, performing bootstrapping on each, and finding the percentage of bootstrap results that failed to capture the overall mean. This was repeated under different conditions and potentials to determine exactly when and how poorly this method fails. After running the bootstrapping comparisons, it was found that simulations start out with a certain level of underestimation: the exact amount depends on how strongly the particles are interacting. If using unweighted least squares regression on the mean squared displacement, the amount of underestimation approaches a minimum once the simulation has run long enough for the particles to traverse the simulation box. Other methods that put emphasis on short time data do not recover gracefully from the initial effects of correlation. Armed with the ability to get a measure of the uncertainty, the effects of coarse graining were studied. It was found that Inverse Boltzmann best reproduced structural information, at the cost of added computation. Of the computationally cheap methods, Hypernetted chain tended to perform the best for reproducing structural information, while the potential of mean force and force averaging were typically among the worst. When it comes to transferability, for the pure methods force averaging was fairly transferable, Hypernetted chain less so, with Inverse Boltzmann suffering from overfitting (though this problem is improved by calculating a bridge function). While it was expected that coarse graining would speed up dynamics, it was hoped the speedup would be consistent: it was not.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Crysup_fsu_0071E_14203
 Format
 Thesis
 Title
 Modeling of Complex Behaviors of Submarine Debris Flows.
 Creator

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

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

Boren, Seth B., Slice, Dennis E., Shanbhag, Sachin, Beerli, Peter, Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

The mandible can provide valuable information on both the life history and genetic makeup of Archaic human populations. If two genetically separated Homo sapiens populations practice differing dietary behaviors, one may expect to see significant variation in mandibular morphology. The following analysis tests two hypotheses: (1) that there are significant differences in morphology in mandibular shape between the sexes amongst Archaic North American H. sapiens and (2) that there is a...
Show moreThe mandible can provide valuable information on both the life history and genetic makeup of Archaic human populations. If two genetically separated Homo sapiens populations practice differing dietary behaviors, one may expect to see significant variation in mandibular morphology. The following analysis tests two hypotheses: (1) that there are significant differences in morphology in mandibular shape between the sexes amongst Archaic North American H. sapiens and (2) that there is a significant difference in variance in mandibular shape between Archaic Floridian and Alaskan H. sapiens. The Archaic Floridian H. sapiens are taken from the Windover burial site and the Alaskan H. sapiens are taken from the Point Hope burial site. A sample made from mandible specimens taken from both populations is subjected to Principal Component Analyses (PCA). The component scores from the PCAs are subjected to both a Multivariate Analysis of Covariance (MANCOVA) and general Multivariate Analysis of Variance (MANOVA) to determine whether significant differences in variance exist between the sexes and the populations. The MANCOVA found that there were no significant interactions between the PC scores between populations, sexes, or size. Significant differences in variance were found between males and females and between the Windover and Point Hope populations. Differences in variance observed between the populations are suspected to be due to differences in subsistence strategies. Differences in variance between the sexes are suspected to be genetic in origin.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Boren_fsu_0071N_14264
 Format
 Thesis
 Title
 Multiscale Simulation in Material Science and Engineering: Computational Heterogeneous Catalysis and Molecular Design.
 Creator

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

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

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

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

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

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

Soda, K. James (Kenneth James), Slice, Dennis E., Beaumont, Paul M., Beerli, Peter, MeyerBaese, Anke, Shanbhag, Sachin, Florida State University, College of Arts and Sciences,...
Show moreSoda, K. James (Kenneth James), Slice, Dennis E., Beaumont, Paul M., Beerli, Peter, MeyerBaese, Anke, Shanbhag, Sachin, Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Many phenomena in ecology, evolution, and organismal biology relate to how a system changes through time. Unfortunately, most of the statistical methods that are common in these fields represent samples as static scalars or vectors. Since variables in temporallydynamic systems do not have stable values this representation is unideal. Differential equation and basis function representations provide alternative systems for description, but they are also not without drawbacks of their own....
Show moreMany phenomena in ecology, evolution, and organismal biology relate to how a system changes through time. Unfortunately, most of the statistical methods that are common in these fields represent samples as static scalars or vectors. Since variables in temporallydynamic systems do not have stable values this representation is unideal. Differential equation and basis function representations provide alternative systems for description, but they are also not without drawbacks of their own. Differential equations are typically outside the scope of statistical inference, and basis function representations rely on functions that solely relate to the original data in regards to qualitative appearance, not in regards to any property of the original system. In this dissertation, I propose that vector autoregressivemoving average (VARMA) and vector autoregressive (VAR) processes can represent temporallydynamic systems. Under this strategy, each sample is a time series, instead of a scalar or vector. Unlike differential equations, these representations facilitate statistical description and inference, and, unlike basis function representations, these processes directly relate to an emergent property of dynamic systems, their crosscovariance structure. In the first chapter, I describe how VAR representations for biological systems lead to both a metric for the difference between systems, the Euclidean process distance, and to a statistical test to assess whether two time series may have originated from a single VAR process, the likelihood ratio test for a common process. Using simulated time series, I demonstrate that the likelihood ratio test for a common process has a true Type I error rate that is close to the prespecified nominal error rate, regardless of the number of subseries in the system or of the order of the processes. Further, using the Euclidean process distance as a measure of difference, I establish power curves for the test using logistic regression. The test has a high probability of rejecting a false null hypothesis, even for modest differences between series. In addition, I illustrate that if two competitors follow the LotkaVolterra equations for competition with some additional white noise, the system deviates from VAR assumptions. Yet, the test can still differentiate between a simulation based on these equations in which the constraints on the system change and a simulation where the constraints do not change. Although the Type I error rate is inflated in this scenario, the degree of inflation does not appear to be larger when the system deviates more noticeably from model assumptions. In the second chapter, I investigate the likelihood ratio test for a common process's performance with shape trajectory data. Shape trajectories are an extension of geometric morphometric data in which a sample is a set of temporallyordered shapes as opposed to a single static shape. Like all geometric morphometric data, each shape in a trajectory is inherently highdimensional. Since the number of parameters in a VAR representation grows quadratically with the number of subseries, shape trajectory data will often require dimension reduction before a VAR representation can be estimated, but the effects that this reduction will have on subsequent inferences remains unclear. In this study, I simulated shape trajectories based on the movements of roundworms. I then reduced the number of variables that described each shape using principle components analysis. Based on these lower dimensional representations, I estimated the likelihood ratio test's Type I error rate and power with the simulated trajectories. In addition, I also used the same workflow on an empirical dataset of women walking (originally from Morris13) but also tried varying amounts of preprocessing before applying the workflow as well. The likelihood ratio test's Type I error rate was mildly inflated with the simulated shape trajectories but had a high probability of rejecting false null hypotheses. Without preprocessing, the likelihood ratio test for a common process had a highly inflated Type I error rate with the empirical data, but when the sampling density is lowered and the number of cycles is standardized within a comparison the degree of inflation becomes comparable to that of the simulated shape trajectories. Yet, these preprocessing steps do not appear to negatively impact the test's power. Visualization is a crucial step in geometric morphometric studies, but there are currently few, if any, methods to visualize differences in shape trajectories. To address this absence, I propose an extension to the classic vectordisplacement diagram. In this new procedure, the VAR representations for two trajectories' processes generate two simulated trajectories that share the same shocks. Then, a vectordisplacement diagram compares the simulated shapes at each time step. The set of all diagrams then illustrates the difference between the trajectories' processes. I assessed the validity of this procedure using two simulated shape trajectories, one based on the movements of roundworms and the other on the movements of earthworms. The result provided mixed results. Some diagrams do show comparisons between shapes that are similar to those in the original trajectories but others do not. Of particular note, diagrams show a bias towards whichever trajectory's process was used to generate pseudorandom shocks. This implies that the shocks to the system are just as crucial a component to a trajectory's behavior as the VAR model itself. Finally, in the third chapter I discuss a new R library to study dynamic systems and represent them as VAR and VARMA processes, iPARMA. Since certain processes can have multiple VARMA representations, the routines in this library place an emphasis on the reverse echelon format. For every process, there is only one VARMA model in reverse echelon format. The routines in iPARMA cover a diverse set of topics, but they all generally fall into one of four categories: simulation and study, model estimation, hypothesis testing, and visualization methods for shape trajectories. Within the chapter, I discuss highlights and features of key routines' algorithms, as well as how they differ from analogous routines in the R package MTS \citep{mtsCite}. In many regards, this dissertation is foundational, so it provides a number of lines for future research. One major area for further work involves alternative ways to represent a system as a VAR or VARMA process. For example, the parameter estimates in a VAR or VARMA model could depict a process as a point in parameter space. Other potentially fruitful areas include the extension of representational applications to other families of time series models, such as cointegrated models, or altering the generalized Procrustes algorithm to better suit shape trajectories. Based on these extensions, it is my hope that statistical inference based on stochastic process representations will help to progress what systems biologists are able to study and what questions they are able to answer about them.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Soda_fsu_0071E_13917_P
 Format
 Set of related objects
 Title
 Quantum Chemical Methods and Algorithms for Ground and Excited Electronic States.
 Creator

Nascimento, Daniel R. (Daniel Ricardo), DePrince, A. Eugene (Albert Eugene), Shanbhag, Sachin, Dalal, Naresh S., Steinbock, Oliver, Florida State University, College of Arts and...
Show moreNascimento, Daniel R. (Daniel Ricardo), DePrince, A. Eugene (Albert Eugene), Shanbhag, Sachin, Dalal, Naresh S., Steinbock, Oliver, Florida State University, College of Arts and Sciences, Department of Chemistry and Biochemistry
Show less  Abstract/Description

In this dissertation, we address some of the needs faced in the development of modern ab initio quantum chemical methods to compute highaccuracy ground and excited electronic states. Chapters 1 and 2 should be seen as introductory Chapters, where the mathematical foundations of modern electronic structure theory necessary to understand this work are laid down. Chapters 3 and 4 covers the development of methods and algorithms relevant to ground state computations. We propose a semidefinite...
Show moreIn this dissertation, we address some of the needs faced in the development of modern ab initio quantum chemical methods to compute highaccuracy ground and excited electronic states. Chapters 1 and 2 should be seen as introductory Chapters, where the mathematical foundations of modern electronic structure theory necessary to understand this work are laid down. Chapters 3 and 4 covers the development of methods and algorithms relevant to ground state computations. We propose a semidefinitebased algorithm to compute groundstate HartreeFock energies and wave functions, that can be easily extended to KohnSham density functional theory. We also propose a parametrized coupledpair functional to compute accurate noncovalent molecular interaction energies. Chapters 3 through 7 cover methods relevant to excited state computations. We propose an explicitly timedependent coupledcluster framework rooted on the equationofmotion formalism to compute linear absorption spectra of molecular systems. The method is further expanded by recasting a linear absorption line shape function in terms of Pad ́e approximants. The expanded method is shown to be an efficient tool for the simulation of nearedge Xray absorption fine structure. Finally, we propose a timedependent HartreeFock method within the framework of cavity quantumelectrodynamics that allows us to simulate the interaction of molecular systems with quantized radiation fields, such as those found on plasmonic nanoparticles and nano cavities.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Nascimento_fsu_0071E_14251
 Format
 Thesis
 Title
 Reduced Order Modeling for a Nonlocal Approach to Anomalous Diffusion Problems.
 Creator

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

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

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

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

Bhingare, Apurva Chandrashekhar, Sinha, Debajyoti, Shanbhag, Sachin, Linero, Antonio Ricardo, Bradley, Jonathan R., Pati, Debdeep, Lipsitz, Stuart, Florida State University,...
Show moreBhingare, Apurva Chandrashekhar, Sinha, Debajyoti, Shanbhag, Sachin, Linero, Antonio Ricardo, Bradley, Jonathan R., Pati, Debdeep, Lipsitz, Stuart, Florida State University, College of Arts and Sciences, Department of Statistics
Show less  Abstract/Description

It is common to encounter skewed response data in medicine, epidemiology and health care studies. Methodology needs to be devised to overcome the natural difficulties that occur in analyzing such data particularly when it is multivariate. Existing Bayesian statistical methods to deal with skewed data are mostly fully parametric. We propose novel semiparametric Bayesian methods to model an analyze such data. These methods make minimal assumptions about the true form of the distribution and...
Show moreIt is common to encounter skewed response data in medicine, epidemiology and health care studies. Methodology needs to be devised to overcome the natural difficulties that occur in analyzing such data particularly when it is multivariate. Existing Bayesian statistical methods to deal with skewed data are mostly fully parametric. We propose novel semiparametric Bayesian methods to model an analyze such data. These methods make minimal assumptions about the true form of the distribution and structure of the observed data. Through examples from real life studies, we demonstrate practical advantages of our semiparametric Bayesian methods over the existing methods. For many reallife studies with skewed multivariate responses, the level of skewness and association structure assumptions are essential for evaluating the covariate effects on the response and its predictive distribution. First, we present a novel semiparametric multivariate model class leading to a theoretically justifiable semiparametric Bayesian analysis of multivariate skewed responses. Like the multivariate Gaussian densities, this multivariate model is closed under marginalization, allows a wide class of multivariate associations, and has meaningful physical interpretations of skewness levels and covariate effects on the marginal density. Compared to existing models, our model enjoys several desirable practical properties, including Bayesian computing via available software, and assurance of consistent Bayesian estimates of parameters and the nonparametric error density under a set of plausible prior assumptions. We introduce a particular parametric version of the model as an alternative to various parametric skewsymmetric models available in the literature. We illustrate the practical advantages of our methods over existing parametric alternatives via application to a clinical study to assess periodontal disease and through a simulation study. Unlike most of the models existing in literature, this class of models advocates a latent variable approach making implementation under the Bayesian paradigm via standard software for MCMC computation like WinBUGS/JAGS straightforward. Although, JAGS and WinBUGS are flexible MCMC engines, for complex model structures they tend to be rather slow. We offer an alternative tool to implement the aforementioned parametric version of the models using PROC MCMC in SAS. Our goal is to facilitate and encourage more extensive implementation of these models. To achieve this goal, we illustrate the implementation using PROC MCMC in SAS via examples from real life and provide a full annotated SAS code. In large scale national surveys, we often come across skewed data as well as semicontinuous data, that is, data characterized by point mass at zero (degenerate) and right skewed continuous distribution on positive support. For example, in the Medical Expenditure Panel Survey (MEPS), the variable total health care expenditure (i.e., the response) for nonusers of the health care services is zero, whereas for the users it is has continuous distribution typically skewed towards the right. We provide an overview of the existing models and methods to analyze such data.
Show less  Date Issued
 2018
 Identifier
 2018_Sp_Bhingare_fsu_0071E_14468
 Format
 Thesis
 Title
 Simulating the Impacts and Sensitivity of the Southeastern United States Climatology to Irrigation.
 Creator

Selman, Christopher Manuel, Misra, Vasubandhu, Shanbhag, Sachin, Bourassa, Mark Allan, Liu, Guosheng, Wu, Zhaohua, Florida State University, College of Arts and Sciences,...
Show moreSelman, Christopher Manuel, Misra, Vasubandhu, Shanbhag, Sachin, Bourassa, Mark Allan, Liu, Guosheng, Wu, Zhaohua, Florida State University, College of Arts and Sciences, Department of Earth, Ocean, and Atmospheric Science
Show less  Abstract/Description

The diurnal variations from a highresolution regional climate model (Regional Spectral Model; RSM) are analyzed from 6 independent decade long integrations using lateral boundary forcing data separately from the National Centers for Environmental Prediction Reanalysis 2 (NCEPR2), and European Center for MediumRange Weather Forecasts (ECMWF) 40year Reanalysis (ERA40) and the 20th Century Reanalysis (20CR). With each of these lateral boundary forcing data, the RSM is integrated separately...
Show moreThe diurnal variations from a highresolution regional climate model (Regional Spectral Model; RSM) are analyzed from 6 independent decade long integrations using lateral boundary forcing data separately from the National Centers for Environmental Prediction Reanalysis 2 (NCEPR2), and European Center for MediumRange Weather Forecasts (ECMWF) 40year Reanalysis (ERA40) and the 20th Century Reanalysis (20CR). With each of these lateral boundary forcing data, the RSM is integrated separately using two convection schemes: the Relaxed ArakawaSchubert (RAS) and KainFritsch (KF) schemes. The results show that RSM integrations forced with 20CR have the least fidelity in depicting the seasonal cycle and diurnal variability of precipitation and surface temperature over the Southeastern United States (SEUS). The remaining four model simulations show comparable skills. The differences in the diurnal amplitude of rainfall during the summer months of the 20CR forced integration from the corresponding NCEPR2 forced integration, for example, is found to be largely from the transient component of the moisture flux convergence. The root mean square error (RMSE) of the seasonal cycle of precipitation and surface temperature of the other four simulations (not forced by 20CR) were comparable to each other and highest in the summer months. But the RMSE of the diurnal amplitude of precipitation and the timing of its diurnal zenith were largest during winter months and least during summer and fall months in the four model simulations (not forced by 20CR). The diurnal amplitude of surface temperature in comparison showed far less fidelity in all models. The phase of the diurnal maximum of surface temperature however showed significantly better validation with corresponding observations in all of the 6 model simulations The impacts of irrigation on SEUS diurnal climate are then investigated. An extreme case is assumed, wherein irrigation is set to 100% of field capacity over the growing season of May through October (IRR100). Irrigation is applied to the root zone layers of 1040cm and 40100cm soil layers only. It is found that in this regime there is a pronounced decrease in monthly averaged temperatures in irrigated regions across all months. In nonirrigated areas a slight warming is simulated. Diurnal maximum temperatures in irrigated areas warm, while diurnal minimum temperatures cool. The daytime warming is attributed to an increase in shortwave flux at the surface owing to diminished low cloud cover. Nighttime cooling results as a consequence of higher net downward ground heat flux. Both diurnal and monthly average precipitations are reduced over irrigated areas at a magnitude and spatial pattern similar to one another. Due to the excess moisture availability, evaporation is seen to increase, but this is balanced by a corresponding reduction in sensible heat flux. Concomitant with additional moisture availability is an increase in both transient and stationary moisture flux convergences. However, despite the increase, there is a largescale stabilization of the atmosphere stemming from a cold surface and a warmed vertical column. Three additional regional climate model runs centered on the SEUS assume a crop growing season of May through October and are irrigated at 25%, 50%, 75% (IRR25, IRR50, IRR75, respectively) of the root zone field capacity to assess the sensitivity of the SEUS climate to irrigation. A fifth run, assuming no irrigation (CTL), is used as the basis for comparison. Across all IRR runs, it is found that there is a general reduction in monthly mean precipitation over the irrigated cells relative to CTL, with much of the change occurring in the subdiurnal scales. This manifests as an increase dry days and reduction in > 1 mm/day rainfall events. IRR25 is seen to have the lowest change in both, while IRR100 is seen to have the greatest change. Areaaveraged precipitation over the irrigated cells reveals a strong reduction in precipitation in IRR100 (on the order of 0.4 mm/hr) with a much weaker reduction in IRR25. Vertically integrated moisture convergence is seen to have the most pronounced sensitivity pattern across all runs. Monthly averaged temperatures are reduced over irrigated areas, with the intensity of the reduction increasing as irrigation vigor increases. This is attributed to a systematic change in ground heat flux that transports heat into the subsurface soil layers in the irrigated cells. The precipitation ahead of the transient cold fronts is reduced by irrigation as it passes over the irrigated cells. The intensity of the net precipitation reduction becomes more intense as irrigation vigor increases. Lastly, heat waves in the SEUS are reduced in intensity just over the irrigated cells, though likely increasing in frequency due to lowered temperature thresholds for heat wave definition.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9679
 Format
 Thesis
 Title
 Stochastic Modeling of Epidemic Diseases Considering Dynamic Contact Networks and Genealogy Information.
 Creator

Ashki, Haleh, Beerli, Peter, Coutts, Christopher, Shanbhag, Sachin, Slice, Dennis E., Lemmon, Alan R., Florida State University, College of Arts and Sciences, Department of...
Show moreAshki, Haleh, Beerli, Peter, Coutts, Christopher, Shanbhag, Sachin, Slice, Dennis E., Lemmon, Alan R., Florida State University, College of Arts and Sciences, Department of Scientific Computing
Show less  Abstract/Description

Human life and diseases are inseparable. For millions of years, humans and their ancestors suffered from diseases, caused by infectious pathogens (e.g., bacteria, viruses, parasites) and caused by our own bodies as they age and degenerate. Within the last century, with the advent of public health measures, improved nutrition and medicine, such as antibiotics, some of the infectious diseases have been controlled. However, infectious diseases still lead to most of the nonage related deaths in...
Show moreHuman life and diseases are inseparable. For millions of years, humans and their ancestors suffered from diseases, caused by infectious pathogens (e.g., bacteria, viruses, parasites) and caused by our own bodies as they age and degenerate. Within the last century, with the advent of public health measures, improved nutrition and medicine, such as antibiotics, some of the infectious diseases have been controlled. However, infectious diseases still lead to most of the nonage related deaths in the world, especially in nations with insufficient health support. My research has taken the complex and dynamic contact networks as well as heterogeneity in disease transmission and recovery into account. Real social networks among individuals were used to generate an adjacency matrix in my formulas. Both, transition and recovery rates have been used as unique variables for each individual. I have used the forward Kolmogorov equation to solve the system. To control and prevent the infectious diseases such as influenza, sexually transmitted diseases, we have to model the dynamics of a particular disease, estimate the parameters, and forecast the behavior of the disease over time. The estimated parameters help us to design and implement interventions, such as vaccination, closure of public places, to limit the spread of diseases. R0, the reproduction number is an important parameter in epidemiology. R0 is the average number of secondary infections produced by a primary infection. If R0 is larger than one an epidemic will most likely happen, an R0 smaller than one suggests that the disease outbreak is local and will die out. In this study I have shown that R0 estimators that only use the the number of contacts and some network features such as covariance of coefficient are not enough to estimate the epidemic threshold. I have formulated R0 to consider both node degree distribution as well as the spectral gap in the eigenvalue of a weighted adjacency matrix of contact network. Only recently, researchers have developed theoretical approaches that can take into account dynamic networks and, independently, that can use genomic data of the pathogen, sampled from infected persons, to reconstruct the path of an epidemic. By considering the location and time of the sampled pathogen sequence data we can combine the sampled infection network and the mutational history of the pathogen to reconstruct a more accurate contact network. We can reconstruct this dynamic contact network using genetic data and epidemic parameters via a Hidden Markov Model. Sampled genome sequenced data of the pathogen are the observation and a set of dynamic networks are the hidden states in our HMM framework. The system switches between the set of dynamic contact networks to fit the best pattern to observation data. The outcome of such an analysis is the accurate dynamic network among samples of the pathogen. These set of dynamic networks capture the dynamics of the social contact network of the infected people. My model will most likely enable earlier detection of infectious disease spread in dynamic social networks than currently available methods.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9542
 Format
 Thesis
 Title
 A Study of Shock Formation and Propagation in the ColdIon Model.
 Creator

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

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

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

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

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

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