We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely ...

In isopycnal coordinate ocean models, diapycnal diffusion must be expressed as a nonlinear difference equation. This nonlinear equation is not amenable to traditional implicit methods of solution, but explicit methods typically have a time step limit of order (where is the time step, h is the isopycnal layer thickness, and κ is the diapycnal diffusivity), which cannot generally be satisfied sin...

In this paper we consider the convection-diffusion problem of a passive scalar in Lagrangian coordinates, i.e., in a coordinate system fixed on fluid particles. Both the convection-diffusion partial differential equation and the Langevin equation are expressed in Lagrangian coordinates and are shown to be equivalent for uniform, isotropic diffusion. The Lagrangian diffusivity is proportional to...

We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of the hydrodynamic fields are obtained from the microscopic dynamics. This analysis yields a fluctuating balance equation for the local energy density at the mes...

Electrophoretic separation of a mixture of chemical species is a fundamental technique of great usefulness in biology, health care, and forensics. In capillary electrophoresis, the sample migrates in a microcapillary in the presence of a background electrolyte. When the ionic concentration of the sample is sufficiently high, the signal is known to exhibit features reminiscent of nonlinear waves...

Successful organ cryopreservation will significantly benefit human health and biomedical research. One of the major challenges to this accomplishment is the need for optimization of cryoprotectant agent (CPA) perfusion procedures that involve highly complicated mass transfer processes in organs. The diffusivity of CPA is of critical importance for designing perfusion procedures to minimize the ...

This study investigates the effects of fitness changes on hippocampal microstructure and hippocampal volume. Fifty-two healthy participants aged 59-74years with a sedentary lifestyle were randomly assigned to either of two levels of exercise intensity. Training lasted for six months. Physical fitness, hippocampal volumes, and hippocampal microstructure were measured before and after training. H...

A new apparatus for measuring both the thermal conductivity and thermal diffusivity of fluids at temperatures from 220 to 775 K at pressures to 70 MPa is described. The instrument is based on the step-power-forced transient hot-wire technique. Two hot wires are arranged in different arms of a Wheatstone bridge such that the response of the shorter compensating wire is subtracted from the respon...

In order to understand the role of glucose limitations in controlling multicellular tumor spheroid growth, knowledge of the glucose diffusion coefficient is essential. The effective diffusivity of glucose in spheroids of rodent and human tumor cell lines has been determined by measuring the efflux of tritium labeled L-glucose from spheroids with time. When the rapid and irreversible binding of ...