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Full-Text Articles in Physical Sciences and Mathematics
A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang
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 is …
Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren
Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren
Theses and Dissertations--Mathematics
For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.
For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.
Global Well-Posedness For The Derivative Nonlinear Schrödinger Equation Through Inverse Scattering, Jiaqi Liu
Global Well-Posedness For The Derivative Nonlinear Schrödinger Equation Through Inverse Scattering, Jiaqi Liu
Theses and Dissertations--Mathematics
We study the Cauchy problem of the derivative nonlinear Schrodinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schrodinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.