Driven inelastic Maxwell gas in one dimension

V. V. Prasad, Sanjib Sabhapandit, Abhishek Dhar, and Onuttom Narayan
Phys. Rev. E 95, 022115 – Published 14 February 2017

Abstract

A lattice version of the driven inelastic Maxwell gas is studied in one dimension with periodic boundary conditions. Each site i of the lattice is assigned with a scalar “velocity,” vi. Nearest neighbors on the lattice interact, with a rate τc1, according to an inelastic collision rule. External driving, occurring with a rate τw1, sustains a steady state in the system. A set of closed coupled equations for the evolution of the variance and the two-point correlation is found. Steady-state values of the variance, as well as spatial correlation functions, are calculated. It is shown exactly that the correlation function decays exponentially with distance, and the correlation length for a large system is determined. Furthermore, the spatiotemporal correlation C(x,t)=vi(0)vi+x(t) can also be obtained. We find that there is an interior region x*<x<x*, where C(x,t) has a time-dependent form, whereas in the exterior region |x|>x*, the correlation function remains the same as the initial form. C(x,t) exhibits second-order discontinuity at the transition points x=±x*, and these transition points move away from the x=0 with a constant speed.

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  • Received 22 July 2016
  • Revised 6 November 2016

DOI:https://doi.org/10.1103/PhysRevE.95.022115

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPolymers & Soft Matter

Authors & Affiliations

V. V. Prasad1, Sanjib Sabhapandit2, Abhishek Dhar3, and Onuttom Narayan4

  • 1The Institute of Mathematical Sciences, Taramani, Chennai - 600113, India
  • 2Raman Research Institute, Bangalore - 560080, India
  • 3International Centre for Theoretical Sciences, TIFR, Bangalore - 560012, India
  • 4University of California, Santa Cruz, California 95064, USA

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Issue

Vol. 95, Iss. 2 — February 2017

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