Elimination For Systems Of Algebraic Differential Equations, 2017 The Graduate Center, City University of New York

#### Elimination For Systems Of Algebraic Differential Equations, Richard Gustavson

*All Graduate Works by Year: Dissertations, Theses, and Capstone Projects*

We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, if the given system of differential equations has a solution. We first look solely at the ``algebraic data" of ...

A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, 2017 West Chester University of Pennsylvania

#### A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou

*Andreas Aristotelous*

We develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate two-dimensional in space natural convective flows in a vertical cavity. The physical problem is modeled by a coupled nonlinear system of partial differential equations and admits various solutions including stable and unstable modes in the form of traveling and/or standing waves, depending on the governing parameters. These flows are characterized by steep boundary and internal layers which evolve with time and can be well-resolved by high-order methods that also are adept to adaptive meshing. The standard no-slip boundary conditions which apply on ...

Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, 2017 Dublin Institute of Technology

#### Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

*Articles*

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion ...

A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, 2017 University of Kentucky

#### A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

*Theses and Dissertations--Mechanical Engineering*

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model ...

Abstract Template Resrb 2017, 2016 Wroclaw University of Technology

#### Abstract Template Resrb 2017, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Order Form Resrb 2017, 2016 Wroclaw University of Technology

#### Order Form Resrb 2017, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

C.V., 2016 Wroclaw University of Technology

On The Propagation Of Atmospheric Gravity Waves In A Non-Uniform Wind Field: Introducing A Modified Acoustic-Gravity Wave Equation, 2016 Utah State University

#### On The Propagation Of Atmospheric Gravity Waves In A Non-Uniform Wind Field: Introducing A Modified Acoustic-Gravity Wave Equation, Ahmad Talaei

*All Graduate Plan B and other Reports*

Atmospheric gravity waves play fundamental roles in a broad-range of dynamical processes extending throughout the Earth’s neutral atmosphere and ionosphere. In this paper, we present a modified form for the acoustic-gravity wave equation and its dispersion relationships for a compressible and non-stationary atmosphere in hydrostatic balance. Importantly, the solutions have been achieved without the use of the well-known Boussinesq approximation which have been used extensively in previous studies.

We utilize the complete set of governing equations for a compressible atmosphere with non-uniform airflows to determine an equation for vertical velocity of possible atmospheric waves. This intricate wave equation is ...

Spreading Speeds Along Shifting Resource Gradients In Reaction-Diffusion Models And Lattice Differential Equations., 2016 University of Louisville

#### Spreading Speeds Along Shifting Resource Gradients In Reaction-Diffusion Models And Lattice Differential Equations., Jin Shang

*Electronic Theses and Dissertations*

A reaction-diffusion model and a lattice differential equation are introduced to describe the persistence and spread of a species along a shifting habitat gradient. The species is assumed to grow everywhere in space and its growth rate is assumed to be monotone and positive along the habitat region. We show that the persistence and spreading dynamics of a species are dependent on the speed of the shifting edge of the favorable habitat, c, as well as c^{*}(∞) and c^{*}(−∞), which are formulated in terms of the dispersal kernel and species growth rates in both directions. When the favorable habitat edge ...

Foundations Of Wave Phenomena: Complete Version, 2016 Department of Physics, Utah State University

#### Foundations Of Wave Phenomena: Complete Version, Charles G. Torre

*Foundations of Wave Phenomena*

This is the complete version of *Foundations of Wave Phenomena. Version 8.2.*

Please click here to explore the components of this work.

Microstructural Analysis Of Thermoelastic Response, Nonlinear Creep, And Pervasive Cracking In Heterogeneous Materials, 2016 University of Maine

#### Microstructural Analysis Of Thermoelastic Response, Nonlinear Creep, And Pervasive Cracking In Heterogeneous Materials, Alden C. Cook

*Electronic Theses and Dissertations*

This dissertation is concerned with the development of robust numerical solution procedures for the generalized micromechanical analysis of linear and nonlinear constitutive behavior in heterogeneous materials. Although the methods developed are applicable in many engineering, geological, and materials science fields, three main areas are explored in this work. First, a numerical methodology is presented for the thermomechanical analysis of heterogeneous materials with a special focus on real polycrystalline microstructures obtained using electron backscatter diffraction techniques. Asymptotic expansion homogenization and finite element analysis are employed for micromechanical analysis of polycrystalline materials. Effective thermoelastic properties of polycrystalline materials are determined and compared ...

Fast Method Of Particular Solutions For Solving Partial Differential Equations, 2016 University of Southern Mississippi

#### Fast Method Of Particular Solutions For Solving Partial Differential Equations, Anup Raja Lamichhane

*Dissertations*

Method of particular solutions (MPS) has been implemented in many science and engineering problems but obtaining the closed-form particular solutions, the selection of the good shape parameter for various radial basis functions (RBFs) and simulation of the large-scale problems are some of the challenges which need to overcome. In this dissertation, we have used several techniques to overcome such challenges.

The closed-form particular solutions for the Matérn and Gaussian RBFs were not known yet. With the help of the symbolic computational tools, we have derived the closed-form particular solutions of the Matérn and Gaussian RBFs for the Laplace and biharmonic ...

How Steep Is Steep? Learning Curves In Training Undergraduates To Do Fluid-Structure Interaction Modeling, 2016 University of North Carolina at Chapel Hill

#### How Steep Is Steep? Learning Curves In Training Undergraduates To Do Fluid-Structure Interaction Modeling, Nicholas A. Battista

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Interplay Of Quantum Size Effect, Anisotropy And Surface Stress Shapes The Instability Of Thin Metal Films, 2016 Western Kentucky University

#### Interplay Of Quantum Size Effect, Anisotropy And Surface Stress Shapes The Instability Of Thin Metal Films, Mikhail Khenner

*Mikhail Khenner*

An Algorithm For The Machine Calculation Of Minimal Paths, 2016 East Tennessee State University

#### An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

*Electronic Theses and Dissertations*

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R^{3}, but also to the general case of finding minimal functionals on hypersurfaces in R^{n} associated with an arbitrary metric.

Krylov Subspace Spectral Method With Multigrid For A Time-Dependent, Variable-Coefficient Partial Differential Equation, 2016 The University of Southern Mississippi

#### Krylov Subspace Spectral Method With Multigrid For A Time-Dependent, Variable-Coefficient Partial Differential Equation, Haley Renee Dozier

*Master's Theses*

Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.

This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.

Mathematical Hybrid Models For Image Segmentation., 2016 University of Louisville

#### Mathematical Hybrid Models For Image Segmentation., Carlos M. Paniagua Mejia

*Electronic Theses and Dissertations*

Two hybrid image segmentation models that are able to process a wide variety of images are proposed. The models take advantage of global (region) and local (edge) data of the image to be segmented. The first one is a region-based PDE model that incorporates a combination of global and local statistics. The influence of each statistic is controlled using weights obtained via an asymptotically stable exponential function. Through incorporation of edge information, the second model extends the capabilities of a strictly region-based variational formulation, making it able to process more general images. Several examples are provided showing the improvements of ...

An Averaging Method For Advection-Diffusion Equations, 2016 Graduate Center, City University of New York

#### An Averaging Method For Advection-Diffusion Equations, Nicholas Spizzirri

*All Graduate Works by Year: Dissertations, Theses, and Capstone Projects*

Many models for physical systems have dynamics that happen over various different time scales. For example, contrast the everyday waves in the ocean with the larger, slowly moving global currents. The method of multiple scales is an approach for approximating the solutions of differential equations by separating out the dynamics at slower and faster time scales. In this work, we apply the method of multiple scales to generic advection-diffusion equations (both linear and non-linear, and in arbitrary spatial dimensions) and develop a method for 'averaging out' the faster scale phenomena, giving us an 'effective' solution for the slower scale dynamics ...

Mathematical Models Of Biofilm For Antimicrobial Persistence, 2016 University of North Carolina at Chapel Hill

#### Mathematical Models Of Biofilm For Antimicrobial Persistence, Jia Zhao

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Modelling The Polarization, Migration And Neuromast Deposition In The Zebrafish Posterior Lateral Line System, 2016 University of British Columbia

#### Modelling The Polarization, Migration And Neuromast Deposition In The Zebrafish Posterior Lateral Line System, Hildur Knutsdottir

*Biology and Medicine Through Mathematics Conference*

No abstract provided.