#### Year of Publication

2007

#### Document Type

Dissertation

#### College

Arts and Sciences

#### Department

Physics and Astronomy

#### First Advisor

Joseph Straley

#### Abstract

Asymmetric simple exclusion process (ASEP) is a driven stochastic lattice model of particles that move preferentially in one direction. If particles move only in one direction, the model is known as totally asymmetric process. Conventionally, preferred direction of motion is chosen to be to the right. Particles interact through the hard core exclusion rule, meaning that no more than one particle is allowed to occupy one lattice site. In this work following ASEP models are presented. First we study square diagonal lattice with particles that occupy one lattice site and move along the square diagonals. Mean-field theory was developed for this model. The results that were obtained are the dependency of the current on density of the particles, spatial density distribution along the horizontal direction and the phase diagram of the system. Mean-field theory results were compared to simulations. Next model was lattice with extended particles, i.e. particles that occupy more than one lattice site. Unlike the first model, in this system the particle-hole symmetry is broken. Results for current flow, density distribution and phase diagrams were obtained both by mean-field theory and Monte-Carlo (MC) simulations. Another system was the lattice with vertical particle drift. Now particles that occupy one lattice site jump not only in one preferred horizontal directions but there is also one preferred vertical direction for particle flow. Both mean-field theory and simulations were studied for this system and results were compared. Also we explore the system with immovable obstacle. Obstacle is one or several particles located at fixed positions. In this model we observe increase in particle density in front of the obstacle and "shadow" behind it. It is expected that the shape and size of those formations are symmetrical in transverse direction.

#### Recommended Citation

Goykolov, Dmytro, "ASYMMETRIC SIMPLE EXCLUSION PROCESS IN TWO DIMENSIONS" (2007). *University of Kentucky Doctoral Dissertations*. 496.

https://uknowledge.uky.edu/gradschool_diss/496