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Full-Text Articles in Numerical Analysis and Computation
Thermodynamic Laws Of Billiards-Like Microscopic Heat Conduction Models, Ling-Chen Bu
Thermodynamic Laws Of Billiards-Like Microscopic Heat Conduction Models, Ling-Chen Bu
Doctoral Dissertations
In this thesis, we study the mathematical model of one-dimensional microscopic heat conduction of gas particles, applying both both analytical and numerical approaches. The macroscopic law of heat conduction is the renowned Fourier’s law J = −k∇T, where J is the local heat flux density, T(x, t) is the temperature gradient, and k is the thermal conductivity coefficient that characterizes the material’s ability to conduct heat. Though Fouriers’s law has been discovered since 1822, the thorough understanding of its microscopic mechanisms remains challenging [3] (2000). We assume that the microscopic model of heat conduction is a hard ball system. The …
Analysis Of Nonequilibrium Langevin Dynamics For Steady Homogeneous Flows, Abdel Kader A. Geraldo
Analysis Of Nonequilibrium Langevin Dynamics For Steady Homogeneous Flows, Abdel Kader A. Geraldo
Doctoral Dissertations
First, we propose using rotating periodic boundary conditions (PBCs) [13] to simulate nonequilibrium molecular dynamics (NEMD) in uniaxial or biaxial stretching flow. These specialized PBCs are required because the simulation box deforms with the flow. The method extends previous models with one or two lattice remappings and is simpler to implement than PBCs proposed by Dobson [10] and Hunt [24]. Then, using automorphism remapping PBC techniques such as Lees-Edwards for shear flow and Kraynik-Reinelt for planar elongational flow, we demonstrate expo-nential convergence to a steady-state limit cycle of incompressible two-dimensional
NELD. To demonstrate convergence [12], we use a technique similar …
Reducing Communication In The Solution Of Linear Systems, Neil S. Lindquist
Reducing Communication In The Solution Of Linear Systems, Neil S. Lindquist
Doctoral Dissertations
There is a growing performance gap between computation and communication on modern computers, making it crucial to develop algorithms with lower latency and bandwidth requirements. Because systems of linear equations are important for numerous scientific and engineering applications, I have studied several approaches for reducing communication in those problems. First, I developed optimizations to dense LU with partial pivoting, which downstream applications can adopt with little to no effort. Second, I consider two techniques to completely replace pivoting in dense LU, which can provide significantly higher speedups, albeit without the same numerical guarantees as partial pivoting. One technique uses randomized …
Space-Angle Discontinuous Galerkin Finite Element Method For Radiative Transfer Equation, Hang Wang
Space-Angle Discontinuous Galerkin Finite Element Method For Radiative Transfer Equation, Hang Wang
Doctoral Dissertations
Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and others. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables, which are 3 dimensions in space and 2 dimensions in the angular direction. This high dimensionality and the presence of the integral term present serious challenges when solving the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation (RTE) have been introduced. These include, but are certainly not limited to, Monte Carlo …
Data-Driven Computational Methods For Quasi-Stationary Distribution And Sensitivity Analysis, Yaping Yuan
Data-Driven Computational Methods For Quasi-Stationary Distribution And Sensitivity Analysis, Yaping Yuan
Doctoral Dissertations
The goal of the dissertation is to develop the computational methods for quasi-stationary- distributions(QSDs) and the sensitivity analysis of a QSD against the modification of the boundary conditions and against the diffusion approximation.
Many models in various applications are described by Markov chains with absorbing states. For example, any models with mass-action kinetics, such as ecological models, epidemic models, and chemical reaction models, are subject to the population-level randomness called the demographic stochasticity, which may lead to extinction in finite time. There are also many dynamical systems that have interesting short term dynamics but trivial long term dynamics, such as …
Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias
Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias
Doctoral Dissertations
In recent years, there has been an explosion of interest in media bearing quartic
dispersion. After the experimental realization of so-called pure-quartic solitons, a
significant number of studies followed both for bright and for dark solitonic struc-
tures exploring the properties of not only quartic, but also setic, octic, decic etc.
dispersion, but also examining the competition between, e.g., quadratic and quartic
dispersion among others.
In the first chapter of this Thesis, we consider the interaction of solitary waves in
a model involving the well-known φ4 Klein-Gordon theory, bearing both Laplacian and biharmonic terms with different prefactors. As a …