The two-dimensional steady-state Boltzmann equation for hard-disk molecules in the presence of a temperature gradient has been solved explicitly to second order in density and the temperature gradient. The two-dimensional equation of state and some physical quantities are calculated from it and compared with those for the two-dimensional steady-state Bhatnagar-Gross-Krook equation and informati...

We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding Hamiltonian is convex with respect to the momentum variable as a by-product of the large deviation theory. This property ensures its superiority in the rare e...

Abstract. The periodic Lorentz gas describes an ensemble of non-interacting point particles in a periodic array of spherical scatterers. We have recently shown that, in the limit of small scatterer density (Boltzmann-Grad limit), the macroscopic dynamics converges to a stochastic process, whose kinetic transport equation is not the linear Boltzmann equation—in contrast to the Lorentz gas with a...

Possible phase transformation kinetic pathways from the high temperature b phase to the low temperature (a+ b) two-phase Ti alloys were analyzed using the graphical thermodynamic method and the assumption that diffusionless and displacive transformations take place much faster than phase separation which requires long-range diffusion. It is shown that depending on the composition of a b-stabili...

Mathematical models that describe the retention reactions of contaminants in the soil system are presented. Single and multireaction-type models for simultaneous retention and transport in the soil profile are discussed. Single retention models are classified into two types: equilibrium and kinetic models. Emphasis is given to the nonlinearity and kinetic behavior of solute retention processes ...