Browsing by Subject "ASEP"

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Open Access
Analysis of nonequilibrium steady-states
(2016-11) Yeşil, Ayşe Ferhan
Non-equilibrium is the state of the almost all systems in the universe. Unlike equilibrium systems, they interfere with their surroundings which results in never ceasing uxes. There is no unified theory to understand these systems, since their complexity have no bounds. However, there is a restricted subset of them, namely a steady state, in which system maintains constant uxes and its macroscopic observables are not changing in time. Majority of the non-equilibrium problems that the scientific community is interested in comprise systems at steady states or the way such systems relax to steady states, due to their relative ease of analysis. Steady states of Totally Asymmetric Simple Exclusion Processes (TASEPs) are the main focus of this dissertation. We analyze them through Monte Carlo (MC) simulations. The technique is basically a computational experiment done by utilizing random numbers. Performing a computational experiment is a natural way to study these systems since most of the time they are still too complex to have analytical solutions. We present MC simulation results of our studies on the response of TASEP steady states to sinusoidal boundary oscillations. Typically over-damped systems, such as TASEPs, give monotonous frequency response to sinusoidal driving. However, there are exceptions to these all which draw significant attention from the community, e.g., stochastic resonance. We report a novel resonance phenomena on over-damped systems. We present our results in two different but related works. In our first work, we study the motion of shock profiles of TASEP with single class of particles under oscillatory boundary conditions using MC analysis. We also model its dynamics as a Fokker-Planck (FP) system, which incorporates a retarded-oscillatory force with a static single well potential. We solve the FP system by numerical integration. We showed that amplitudes of statistical quantities in both of these systems, (e.g., average position), display resonant effects and their results are qualitatively very similar. In our second work, we showed that by periodically manipulating the boundary conditions of TASEP with two classes of particles, we can achieve otherwise unreachable states of the system by the same parameters. We also report the hysteresis behavior in the same system, existence of which leads to the identifi- cation of typical velocity of the system. All these phenomena are the results of resonant response of the particle number density of the system.
Open Access
Extended phase diagram of ASEP with two types of particles
(2010) Yeşil, Ayşe Ferhan
The ASEP (Asymmetric Simple Exclusion Process) model system with two types of particles is studied. The system is interesting because it exhibits spontaneous symmetry breaking when parameters controlling the dynamics of the two types of particles of the same system. By using Mean Field approximation its extended phase diagram was obtained for non-symmetric values of entering rates of the two types of particles. The system is understood to be the combination of two decoupled ASEP systems with one type of particle system for the values of equal hopping and exchange rates. (Evans et al.,PR E, 74 208, (1995)) It is understood that for the exchange rates different from the hopping rates the system can no longer be analyzed as combination of two decoupled one particle ASEP. The “tiny phase” first observed by Evans et al, is examined in more detail. It is found that this phase still exists when entering rates are not symmetric. Also, Monte Carlo simulations for certain values of parameters of the system were carried out to determine the particle density profiles. The phase diagram of the system displays unexpectedly rich structure for the relatively simple dynamics.