The multiscale full-spectrum k-distribution (MSFSK) method has become a promising method for radiative heat transfer in inhomogeneous media. The scope of the MSFSK method has been limited to radiation calculations involving inhomogeneous gas mixtures only. The objective of this paper is to develop a MSFSK model that is accurate for inhomogeneous mixtures of both gases and nongray particles, suc...

By making decomposition of the Wigner function simultaneously in both the spinor and the isospin spaces we derive a set of kinetic equations for the quark distribution functions and the spin densities. A detailed analysis of the consequences imposed by the chiral invariance on the form of the transport equations is presented. 05.60.+w,11.30.Rd,12.39.-x Typeset using REVTEX 1

Visual appearance can be phenomenologically modeled through an integral equation, known as reflectance equation. It describes the surface radiance which depends on the interaction between incident light field and surface Bidirectional Reflectance Distribution Function (BRDF). Being defined on the Cartesian product of the incident and outgoing hemispheres, hemispherical basis is the natural way ...

here, we have considered the husimi and wigner distribution functions. we have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. the conclusion shows that the husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty pr...