Computer simulation of shock waves in the completely asymmetric simple exclusion process
The authors study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density {rho}{sub {minus}} ({rho}{sub +}) left (right) of the origin, {rho}{sup {minus}} {<=} {rho}{...
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Published in | Journal of statistical physics Vol. 55; no. 3-4; pp. 611 - 623 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Heidelberg
Springer
01.05.1989
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Subjects | |
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Abstract | The authors study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density {rho}{sub {minus}} ({rho}{sub +}) left (right) of the origin, {rho}{sup {minus}} {<=} {rho}{sub +}. The microscopic shock position is identified by introducing a second-class particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock position N(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover N(t) = V {times} t, with V = 1 {minus} {rho}{sub {minus}} {minus} {rho}{sub +}, as predicted, and the dispersion of N(t), {sigma}{sup 2}(t), behaves linearly, for not too small values of {rho}{sub +} {minus} {rho}{sup {minus}}, i.e., {sigma}{sup 2}(t) = S {times} t, where S is equal, up to a scaling factor, to the value S{sub WA} predicted in the weakly asymmetric case. For {rho}{sub +} = {rho}{sub {minus}} they find agreement with the conjecture {sigma}{sup 2}(t) = {anti S} {times} t{sup 4/3} |
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AbstractList | The authors study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density {rho}{sub {minus}} ({rho}{sub +}) left (right) of the origin, {rho}{sup {minus}} {<=} {rho}{sub +}. The microscopic shock position is identified by introducing a second-class particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock position N(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover N(t) = V {times} t, with V = 1 {minus} {rho}{sub {minus}} {minus} {rho}{sub +}, as predicted, and the dispersion of N(t), {sigma}{sup 2}(t), behaves linearly, for not too small values of {rho}{sub +} {minus} {rho}{sup {minus}}, i.e., {sigma}{sup 2}(t) = S {times} t, where S is equal, up to a scaling factor, to the value S{sub WA} predicted in the weakly asymmetric case. For {rho}{sub +} = {rho}{sub {minus}} they find agreement with the conjecture {sigma}{sup 2}(t) = {anti S} {times} t{sup 4/3} |
Author | FRIGIO, S GRASSO NUNES, M BOLDRIGHINI, C COSIMI, G |
Author_xml | – sequence: 1 givenname: C surname: BOLDRIGHINI fullname: BOLDRIGHINI, C organization: Univ. studi Camerino, Camerino, Italy – sequence: 2 givenname: G surname: COSIMI fullname: COSIMI, G organization: Univ. studi Camerino, Camerino, Italy – sequence: 3 givenname: S surname: FRIGIO fullname: FRIGIO, S organization: Univ. studi Camerino, Camerino, Italy – sequence: 4 givenname: M surname: GRASSO NUNES fullname: GRASSO NUNES, M organization: Univ. studi Camerino, Camerino, Italy |
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Issue | 3-4 |
Keywords | Scaling law Computer simulation Specific gravity One dimensional model Critical phenomenon Drift velocity Shock wave |
Language | English |
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References | E. D. Andjel (CR10) 1987; 47 CR2 H. Rost (CR1) 1981; 58 E. Andjel (CR11) 1982; 10 CR3 C. Kipnis (CR6) 1986; 14 CR5 P. A. Ferrari (CR4) 1986; 14 H. Beijeren van (CR12) 1985; 18 W. D. Wick (CR7) 1985; 38 B. M. Boghosian (CR8) 1987; 1 T. M. Ligget (CR9) 1985 |
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SubjectTerms | 656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-) 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics ASYMMETRY CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS COMPUTERIZED SIMULATION CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY DIFFERENTIAL EQUATIONS DIFFUSION EQUATIONS EQUILIBRIUM Exact sciences and technology Fluctuation phenomena, random processes, noise, and brownian motion INTERACTIONS MATHEMATICAL MODELS MECHANICS ONE-DIMENSIONAL CALCULATIONS PARTIAL DIFFERENTIAL EQUATIONS PARTICLE INTERACTIONS PARTICLE MODELS PAULI PRINCIPLE Physics QUANTUM MECHANICS SHOCK WAVES SIMULATION STABILITY STATISTICAL MECHANICS Statistical physics, thermodynamics, and nonlinear dynamical systems WAVE PROPAGATION ZERO-RANGE APPROXIMATION |
Title | Computer simulation of shock waves in the completely asymmetric simple exclusion process |
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