It is well known that transition rates in a canonical ensemble should respect the principle of detailed balance. What are the equivalent constraints that apply in non-equilibrium steady states, implied by maximization of information-entropy? The exact theorem for the non-equilibrium rates yields...

The hydrodynamic modes of a three-dimensional sheared granular flow are determined by solving the linearised Boltzmann equation. The steady state is determined using an expansion in the parameter ε=(1−e)1/2, and terms correct to O(ε4) are retained in the expansion. The distribution function...

A recently proposed Monte Carlo simulation method for the Enskog equation is applied to uniform shear flow. This state is characterized by uniform density n and temperature T and a linear velocity profile: u(r)=a·r, aαβ=aδαxδβy. In each unit time step Δt, the peculiar velocities {Vi} of...

A two-dimensional square lattice computer model was used to study the cluster growth process by irreversible aggregation on the boundary of a shear flowing colloidal solution. The trajectories of the aggregating particles are determined by both a diffusion component and the streamlines of the...

The velocity distribution for a homogeneous shear flow of smooth nearly elastic disks is determined using a perturbation solution of the linearised Boltzmann equation. An expansion in the parameter εI=(1−e)1/2 is used, where e is the coefficient of restitution. In the leading order...

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell–Boltzmann distribution and a Hermite polynomial expansion in the...

The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order parameter in a binary mixture is discussed. The basic...

In the crowd security research area a primary concern is to identify the macro state of crowd behaviors to prevent disasters and to supervise the crowd behaviors. The entropy is used to describe the macro state of a self-organization system in physics. The entropy change indicates the system...