[en] Transport of particles in media whose cross sections are random functions of space and time is considered. The linear transport equation, in the presence of this spacetime noise, is viewed as a Boltzmann-Langevin equation, the solution of which generates a stochastic process, the angular flux, for different realizations of the cross section. A Gaussian model of fluctuations is adopted with a prescribed mean, variance and correlation function. For white noise in time, but with otherwise arbitrary spatial correlation, an exactly closed equation for the ensemble averaged angular flux is obtained and seen to be identical to the transport equation but with renormalised cross sections. Similar exact closures are demonstrated for the second moment and the two-point space-angle correlation of the angular flux. Standard methods may be adapted to solve these averaged transport equations which are valid in the small correlation time limit. (Author)

[en] The exact solution of the system of equations for the second-order kinetic moments (stresses) is investigated for a flow with two microscales when an unsteady shear flow is superimposed on a one-dimensional unsteady gas flow

[en] Boltzmann's equation is solved for the diffusion of nonabsorbing particles through a thick slab. The dimensionless thickness D=dμ_s, where d is the thickness and μ_s is the rate of scattering. Our solution neglects terms of order O(e^-D) and is exact in the limit that D much-gt 1. Simple expressions are obtained for the reflection and transmission coefficients, as well as for the angular distributions on the front and back sides of the slab. copyright 1995 American Institute of Physics

[en] The Uehling endash Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier endash Stokes system are proved. copyright 1997 American Institute of Physics

[en] Short communication

[en] A mathematical model is developed to study the combined influences of electromagnetohydrodynamic forces in controlling the fluid flow through parallel plate rectangular microchannels. The electric double layer (EDL) effects are modelled by employing the classical Poisson-Boltzmann equation. The governing fluid flow equations are subsequently solved, in an effort to obtain closed form expressions depicting the variations in the overall flow rate as a function of various influencing system parameters. It is revealed that, with the aid of a relatively low-magnitude magnetic field, a substantial augmentation in the volumetric flow rates can be achieved. However, with magnetic fields of higher strengths, strongly opposing volumetric forces might offset any further possibilities of flow rate augmentation. Certain critical non-dimensional parameters are also identified, which can play significant roles in the overall flow augmentation mechanism

[en] The thrust force created by a propeller depends on the incoming flow velocity and the rotational velocity of the propeller. The performance of the propeller can be described by dimensionless variables, advanced ratio, thrust coefficient, and power coefficient. This study included the application of the immersed boundary lattice Boltzmann method (IBLBM) with the stereo lithography (STL) file of the rotating object for performance analysis. The immersed boundary method included the addition of the external force term to the LB equation defined by the velocity difference between the lattice points of the propeller and the grid points in the domain. The flow by rotating a 4-blade propeller was simulated with various Reynolds numbers (Re) (including 100, 500 and 1000), with advanced ratios in the range of 0.2~1.4 to verify the suggested method. The typical tendency of the thrust efficiency of the propeller was obtained from the simulation results of different advanced ratios. It was also necessary to keep the maximum mesh size ratio of the propeller surface to a grid size below 3. Additionally, a sufficient length of the downstream region in the domain was maintained to ensure the numerical stability of the higher Re and advanced ratio flow.

[en] The paper reviews some recent advances pertaining to the criticality and time eigenvalues of the one-speed transport equation. We discuss the nature, real or complex of the k_eff, c and λ eigenvalues and their variation with size and other parameters. Our emphasis is on accurate numerical results that display some novel features. In some cases these are explained theoretically. We also discuss the recent findings about continuous spectrum of time eigenvalue problem as it consists of a set of discrete lines rather than a half plane. (Author)

[en] A response of a homogeneous assembly of ions in the parent gas to a step change in an external electric field is studied. The ion distribution function is obtained when solving the Boltzmann kinetic equation by means of an analytical approach as well as by using the propagator method and the macrokinetic method. The relaxation of the drift velocity and the mean energy of ions towards the steady state is proved to be non-monotonic and the nature of arising oscillations is discussed. (author)

[en] A thorough analysis of two dimensional lid driven cavity flow has been performed by using lattice Boltzmann method. Simulations have been performed for various values of Reynolds numbers and the results are reported after the achievement of complete steady state stream traces, pressure counters, velocity profiles and drag coefficients have been studied. The result have been found in good agreement of the results present in the literature. The result obtained are compared with the other numerical solution of cavity flow and from this it has been concluded that lattice Boltzmann method is a valid numerical scheme. (author)