38 research outputs found

    Particle-hopping Models of Vehicular Traffic: Distributions of Distance Headways and Distance Between Jams

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    We calculate the distribution of the distance headways (i.e., the instantaneous gap between successive vehicles) as well as the distribution of instantaneous distance between successive jams in the Nagel-Schreckenberg (NS) model of vehicular traffic. When the maximum allowed speed, VmaxV_{max}, of the vehicles is larger than unity, over an intermediate range of densities of vehicles, our Monte Carlo (MC) data for the distance headway distribution exhibit two peaks, which indicate the coexistence of "free-flowing" traffic and traffic jams. Our analytical arguments clearly rule out the possibility of occurrence of more than one peak in the distribution of distance headways in the NS model when Vmax=1V_{max} = 1 as well as in the asymmetric simple exclusion process. Modifying and extending an earlier analytical approach for the NS model with Vmax=1V_{max} = 1, and introducing a novel transfer matrix technique, we also calculate the exact analytical expression for the distribution of distance between the jams in this model; the corresponding distributions for Vmax>1V_{max} > 1 have been computed numerically through MC simulation.Comment: To appear in Physica

    Exact time-dependent correlation functions for the symmetric exclusion process with open boundary

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    As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant density ρ\rho^\ast and which initially is in an non-equilibrium state with bulk density ρ0\rho_0. We calculate the exact time-dependent two-point density correlation function Ck,l(t)C_{k,l}(t)\equiv - and the mean and variance of the integrated average net flux of particles N(t)N(0)N(t)-N(0) that have entered (or left) the system up to time tt. We find that the boundary region of the semi-infinite relaxing system is in a state similar to the bulk state of a finite stationary system driven by a boundary gradient. The symmetric exclusion model provides a rare example where such behavior can be proved rigorously on the level of equal-time two-point correlation functions. Some implications for the relaxational dynamics of entangled polymers and for single-file diffusion in colloidal systems are discussed.Comment: 11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference 17 adde

    A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model

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    This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the probability α\alpha that a particle will flow into the chain to the leftmost site, the probability β\beta that a particle will flow out from the rightmost site, and the probability pp that a particle will jump to the right if the site to the right is empty. The renormalization-group procedure is conducted within the space of these transition probabilities, which are relevant to the system's dynamics. The method yields a critical point at αc=βc=1/2\alpha_c=\beta_c=1/2,in agreement with the exact values, and the critical exponent ν=2.71\nu=2.71, as compared with the exact value ν=2.00\nu=2.00.Comment: 14 pages, 4 figure

    Fluctuation Cumulant Behavior for the Field-Pulse Induced Magnetisation-Reversal Transition in Ising Models

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    The universality class of the dynamic magnetisation-reversal transition, induced by a competing field pulse, in an Ising model on a square lattice, below its static ordering temperature, is studied here using Monte Carlo simulations. Fourth order cumulant of the order parameter distribution is studied for different system sizes around the phase boundary region. The crossing point of the cumulant (for different system sizes) gives the transition point and the value of the cumulant at the transition point indicates the universality class of the transition. The cumulant value at the crossing point for low temperature and pulse width range is observed to be significantly less than that for the static transition in the same two-dimensional Ising model. The finite size scaling behaviour in this range also indicates a higher correlation length exponent value. For higher temperature and pulse width range, the transition seems to fall in a mean-field like universality class.Comment: 5 pages, 8 eps figures, thoroughly revised manuscript with new figures, accepted in Phys. Rev. E (2003

    First- and second-order phase transitions in a driven lattice gas with nearest-neighbor exclusion

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    A lattice gas with infinite repulsion between particles separated by 1\leq 1 lattice spacing, and nearest-neighbor hopping dynamics, is subject to a drive favoring movement along one axis of the square lattice. The equilibrium (zero drive) transition to a phase with sublattice ordering, known to be continuous, shifts to lower density, and becomes discontinuous for large bias. In the ordered nonequilibrium steady state, both the particle and order-parameter densities are nonuniform, with a large fraction of the particles occupying a jammed strip oriented along the drive. The relaxation exhibits features reminiscent of models of granular and glassy materials.Comment: 8 pages, 5 figures; results due to bad random number generator corrected; significantly revised conclusion

    Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

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    The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of quantum phi^4 model is established. A scaling analysis is performed for the ground-state properties. The influence of the external longitudinal magnetic field on the ground-state properties is investigated, and the corresponding magnetic susceptibility is calculated. Finite-temperature properties are considered with the use of the scaling analysis for the effective classical model proposed by Sachdev. Analytical results for the ordering temperature and temperature dependences of the magnetization and energy gap are obtained in the case of a small ground-state moment. The forms of dependences of observable quantities on the bare splitting (or magnetic field) and renormalized splitting turn out to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure

    Interfaces with a single growth inhomogeneity and anchored boundaries

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    The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an equilibrium stationary regime which allows for an exact calculation of roughening exponents. The stochastic evolution is related to a spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of late stages. For vanishing gaps the interface can exhibit a slow morphological transition followed by a change of scaling regimes which are studied numerically. Instead, a faceting dynamics arises for gapful situations.Comment: REVTeX, 11 pages, 9 Postscript figure

    Collective Diffusion and a Random Energy Landscape

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    Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different equations in case of an arbitrary occupation number per lattice site or in a system under exclusion. Based on scaling arguments it will be demonstrated that both systems belong below the critical dimension dcd_c to the same universality class leading to anomalous diffusion in the long time limit. The dynamical exponent zz can be calculated by an ϵ=dcd\epsilon = d_c-d expansion. Above the critical dimension we discuss the differences in the diffusion constant for sufficient high temperatures. For a random potential we find a higher mobility for systems with exclusion.Comment: 15 pages, no figure

    Universality Class of Thermally Diluted Ising Systems at Criticality

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    The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is investigated by finite size scaling techniques using the Monte Carlo method. We find that the critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. Our results agree fairly well with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.Comment: 7 pages, 6 figures, RevTe