Wei Wu

Type

Text

Type

Dissertation

Advisor

Allen, Philip | Wang, Jin | Allison, Thomas | Li, Huilin.

Date

2014-05-01

Keywords

Physics | global stability, non-equilibrium systems, non-equilibrium thermodynamics, potential landscape, spatially inhomogeneous systems

Department

Department of Physics.

Language

en_US

Source

This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.

Identifier

http://hdl.handle.net/11401/77832

Publisher

The Graduate School, Stony Brook University: Stony Brook, NY.

Format

application/pdf

Abstract

In this dissertation we establish a potential and flux field landscape theory for studying the global stability and dynamics as well as the non-equilibrium thermodynamics of spatially inhomogeneous non-equilibrium dynamical systems. The potential and flux landscape theory developed previously for spatially homogeneous non-equilibrium stochastic systems described by Langevin and Fokker-Planck equations is refined and further extended to spatially inhomogeneous non-equilibrium stochastic systems described by functional Langevin and Fokker-Planck equations. The probability flux field is found to be crucial in breaking detailed balance and characterizing non-equilibrium effects of spatially inhomogeneous systems. It also plays a pivotal role in governing the global dynamics and formulating a set of non-equilibrium thermodynamic equations for a generic class of spatially inhomogeneous stochastic systems. The general formalism is illustrated by studying more specific systems and processes, such as the reaction diffusion system, the Ornstein-Uhlenbeck process, the Brusselator reaction diffusion model, and the spatial stochastic neuronal model. The theory can be applied to a variety of physical, chemical and biological spatially inhomogeneous non-equilibrium systems abundant in nature. | 220 pages

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