Title:	Driven inelastic Maxwell gases
Authors:	Prasad, V.V. Sabhapandit, Sanjib Dhar, Abhishek
Issue Date:	19-Dec-2014
Publisher:	American Physical Society
Citation:	Physical Review E, 2014, Vol. 90, p 062130
Abstract:	We consider the inelastic Maxwell model, which consists of a collection of particles that are characterized by only their velocities and evolving through binary collisions and external driving. At any instant, a particle is equally likely to collide with any of the remaining particles. The system evolves in continuous time with mutual collisions and driving taken to be point processes with rates τ−1c and τ−1w, respectively. The mutual collisions conserve momentum and are inelastic, with a coefficient of restitution r. The velocity change of a particle with velocity v, due to driving, is taken to be Δv=−(1+rw)v+η, where rw∈[−1,1] and η is Gaussian white noise. For rw∈(0,1], this driving mechanism mimics the collision with a randomly moving wall, where rw is the coefficient of restitution. Another special limit of this driving is the so-called Ornstein-Uhlenbeck process given by dvdt=−Γv+η. We show that while the equations for the n-particle velocity distribution functions (n=1,2,...) do not close, the joint evolution equations of the variance and the two-particle velocity correlation functions close. With the exact formula for the variance we find that, for rw≠−1, the system goes to a steady state. Also we obtain the exact tail of the velocity distribution in the steady state. On the other hand, for rw=−1, the system does not have a steady state. Similarly, the system goes to a steady state for the Ornstein-Uhlenbeck driving with Γ≠0, whereas for the purely diffusive driving (Γ=0), the system does not have a steady state.
Description:	Open Access
URI:	http://hdl.handle.net/2289/6209
ISSN:	1539-3755 1550-2376(Online)
Alternative Location:	http://arxiv.org/abs/1408.3964 http://dx.doi.org/10.1103/PhysRevE.90.062130
Copyright:	2014 American Physical Society
Appears in Collections:	Research Papers (TP)

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