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In this research, the totally asymmetric exclusion process without particle number conservation is discussed. Based on the mean field approximation and the Rankine-Hugoniot condition, the necessary and sufficient conditions of the existence of the domain wall have been obtained. Moreover, the properties of the domain wall, including the location and height, have been studied theoretically. All the theoretical results are demonstrated by the computer simulations.
We apply the bi-moment determinant method to compute a representation of the matrix product algebra -- a quadratic algebra satisfied by the operators $mathbf{d}$ and $mathbf{e}$ -- for the five parameter ($alpha$, $beta$, $gamma$, $delta$ and $q$) As
We revisit the totally asymmetric simple exclusion process with open boundaries (TASEP), focussing on the recent discovery by de Gier and Essler that the model has a dynamical transition along a nontrivial line in the phase diagram. This line coincid
We consider the one-dimensional totally asymmetric simple exclusion model (TASEP model) with open boundary conditions and present the analytical computations leading to the exact formula for distance clearance distribution, i.e. probability density f
As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a 1-dimensi
We consider the exclusion process on a ring with time-dependent defective bonds at which the hoping rate periodically switches between zero and one. This system models main roads in city traffics, intersecting with perpendicular streets. We explore b