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. Particles interact through the hard core exclusion rule, meaning that no more than one particle is allowed to occupy one lattice site. ?br: Here we extended standard one-dimensional ASEP model to two dimensions and considered four sub-models. First we study square lattice with particles that occupy one lattice site and move along the square diagonals. Second model was lattice with extended particles, i.e. particles that occupy more than one lattice site. Third system is the lattice with vertical particle drift, where 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. Also we explore the system with immovable obstacle (consisted of several fixed particles). Mean-field theory was developed for these models and its results were compared to the Monte-Carlo simulations.