We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient...

in the present study, modelling and vibration analysis of carbon nanotubes/ fiber/ polymer composite microplates are investigated. the governing equations of the carbon nanotubes/ fiber/ polymer composite microplates are derived based on first order shear deformation plate theory, rather than other plate theories, due to accuracy and simplicity of polynomial functions. the modified couple stres...

The Enskog–Vlasov equation provides a consistent description of the microscopic molecular interactions for real fluids based on kinetic and mean-field theories. fluid flows in nano-channels are investigated by Bhatnagar–Gross–Krook (BGK) type model, which simplifies complicated collision operator enables large-scale engineering design simulations. density distributions found to exhibit inhomoge...

We give two hypotheses of the relativistic collision kernal and show the existence and uniqueness of the global mild solution to the relativistic Enskog equation with the initial data near the vacuum for a hard sphere gas.

There are several reasons to extend the presentation of Navier-Stokes equations multicomponent systems. Many technological applications based on physical phenomena that present neither in pure elements nor binary mixtures. Whereas Fourier's law must already be generalized binaries, it is only with more than two components Fick's breaks down its simple form. The emergence dissipative affects als...

Rosenau Phys. Rev. A, 40 (1989), pp. 7193-6] has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. In this paper we study the behavi...

A Legendre expansion of the (matrix) scattering kernel relevant to the (vectorvalued) linearized Boltzmann equation for a binary mixture of rigid spheres is used to define twelve solutions that are linear in the spatial variables {x, y, z}. The twelve (asymptotic) solutions are expressed in terms of three vector-valued functions A(c), A(c), and B(c). These functions are generalizations of the C...