Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStatistics of current activity fluctuations in asymmetric flow with exclusion
198
0
0.0
(
0
)
Added by
Sergio L. A. de Queiroz
Publication date
2012
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider steady-state current activity statistics for the one-dimensional totally asymmetric simple exclusion process (TASEP). With the help of the known operator algebra (for general open boundary conditions), as well as general probabilistic concepts (for the periodic case), we derive and evaluate closed-form expressions for the lowest three moments of the probability distribution function. These are confirmed, to excellent degree of accuracy, by numerical simulations. Further exact expressions and asymptotic approximations are provided for probability distributions and generating functions.
rate research
Read More
We consider fluctuations of steady-state current activity, and of its dynamic counterpart, the local current, for the one-dimensional totally asymmetric simple exclusion process. The cumulants of the integrated activity behave similarly to those of the local current, except that they do not capture the anomalous scaling behavior in the maximal-current phase and at its boundaries. This indicates that the systemwide sampling at equal times, characteristic of the instantaneous activity, overshadows the subtler effects which come about from non-equal time correlations, and are responsible for anomalous scaling. We show that apparently conflicting results concerning asymmetry (skewness) of the corresponding distributions can in fact be reconciled, and that (apart from a few well-understood exceptional cases) for both activity and local current one has positive skew deep within the low-current phase, and negative skew everywhere else.
We numerically study the large deviation function of the total current, which is the sum of local currents over all bonds, for the symmetric and asymmetric simple exclusion processes with open boundary conditions. We estimate the generating function by calculating the largest eigenvalue of the modified transition matrix and by population Monte Carlo simulation. As a result, we find a number of interesting behaviors not observed in the exactly solvable cases studied previously as follows. The even and odd parts of the generating function show different system-size dependences. Different definitions of the current lead to the same generating function in small systems. The use of the total current is important in the Monte Carlo estimation. Moreover, a cusp appears in the large deviation function for the asymmetric simple exclusion process. We also discuss the convergence property of the population Monte Carlo simulation and find that in a certain parameter region, the convergence is very slow and the gap between the largest and second largest eigenvalues of the modified transition matrix rapidly tends to vanish with the system size.
We investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. At the left boundary, particles are injected onto the lattice; from there, the particles hop to the right. Along the lattice, particles can adsorb or desorb, and the right boundary is defined by a wall particle. The confining wall particle has intrinsic forward and backward hopping, a net leftward drift, and cannot desorb. Performing Monte Carlo simulations and using a moving-frame finite segment approach coupled to mean field theory, we find the parameter regimes in which the wall acquires a steady state position. In other regimes, the wall will either drift to the left and fall off the lattice at the injection site, or drift indefinitely to the right. Our results are discussed in the context of non-equilibrium phases of the system, fluctuating boundary layers, and particle densities in the lab frame versus the frame of the fluctuating wall.
We study the nonequilibrium steady states in asymmetric exclusion processes (TASEP) with open boundary conditions having spatially inhomogeneous hopping rates. Assuming spatially smoothly varying hopping rates with a few (or no) discontinuities, we show that the steady states are in general classified by the steady state currents in direct analogy with open TASEPs having uniform hopping rates. We calculate the steady state density profiles, which are now space-dependent. We also obtain the phase diagrams in the plane of the control parameters, which though have phase boundaries that are in general curved lines, have the same topology as their counterparts for conventional open TASEPs, independent of the form of the hopping rate functions. This reveals a type of universality, not encountered in critical phenomena.
We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with an amplitude large compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking and exchange symmetry effect. The latter leads to a current equal to that of non-interacting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of non-equilibrium steady states to occur. Our results show that the particle size can be of crucial importance for non-equilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
