Systems of equations of Vlasov-Fokker-Planck type are suggested for multilane traffic flow. The equations include nonlocal and time-delayed braking and acceleration terms with rates depending on the densities and relative speeds. The braking terms include lane-change probabilities. It is shown that simple natural assumptions on the structure of these probabilities lead to multivalued fundamental diagrams, consistent with traffic observations. Lane-changing behavior is the critical ingredient in such bifunctions.

The concept of harmonic (or wave) maps up to rearrangement is introduced. A relation is established with the smooth solutions of the isothermal irrotational inviscid gas dynamics equations.

In this paper we present an application of the recently developed control volume function approximation (CVFA) method to the modeling and simulation of 2D and 3D horizontal wells in petroleum reservoirs. The base grid for this method is based on a Voronoi grid. One of the features of the CVFA is that the flux at the interfaces of control volumes can be accurately computed via function approximations. Also, it reduces grid orientation effects and applies to any shape of elements. It is particularly suitable for hybrid grid reservoir simulations. Through extensive numerical experiments and comparisons with the finite difference method for benchmark flow problems, we show that this method can effciently and accurately handle complex horizontal wells in any direction.

Mathematical filtering using wavelet transform was applied to analyse hydropathy signals of membrane proteins. The accuracy of our localization of transmembrane approaches that of well-established methods. The analysis of hydrophobicity plots using wavelets presents advantages with respect to other "filtering" methods based on fixed windows or Fourier transforms and compared to "training" (neutral networks) techniques. Although the method embodies principles that have long been appreciated, its simplicity makes it a very useful tool for the evaluation of protein membrane-spanning segments. Generalization of use of wavelets should be encouraged in other aspects of bioinformatics.

Crown splashing, produced by high speed impact of a droplet on a rough or wet wall, is physically very complicated. It is impossible to determine the size of secoundary ejected droplets by literally solving the full set of nonlinear Navier-Stokes equations supplemented by complex initial and boundary conditions. In order to get useful impact laws and, most importantly, to propose a genearl concept of deriving useful results without going through the complex mathematical details, we propose a backward formalism in which we determine the size of the secoundary ejected droplets by tracking the past event whenever it is required and just what is required. This procedure allows us to discard those complex details of negligible importance. Such a formalism, conceptually very simple and possibly meaningful for other complex problems, leads to a reasonably correct formula for the most probable diameter of secondary ejected droplets, compared to know experimental data.

We show the the voricity distribution obtained by minimizing the induced drag on a wing, the so called Prandtl-Munk vortex sheet, is not a travelling-wave weak solution of the Euler equations, contrary to what has been claimed by a number of authors. Instead, it is a weak solution of a non-homogeneous Euler equation, where the forcing term represents a "tension" force applied to the tips. This is consistent with a heuristic arguement due to Saffman. Thus, the notion of weak solution captures the correct physical behavior in this case.

A set of hydrodynamic equations modeling strong ionization in semiconductors is formally derived from a kinetic framework. To that purpose, a system of Boltzmann transport equations governing the distribution functions of conduction electrons and holes is considered. Apart from impact ionization, the model accounts for phonon, lattice defects, and particle-particle scattering. Also degeneracy effects are included. The band diagram models are approximations close to the extrema of actual band diagrams. Ionization initiated by a charge carrier (and its reverse recombination) is the leading order collisional process. The resulting set of hydrodynamic equations for strong ionization differs from the usual hydrodynamic system for semiconductors, which corresponds to weak ionization. Indeed, it governs the total charge, the crystal momentum, and the energy, but the total mass is not a conservation variable. This system is supplemented by an entropy inequality and proved to be hyperbolic. The particular case of a parabolic band diagram is discussed.

The heterogenous multiscale method (HMM) is presented as a general methodology for the efficient numerical computation of problems with multiscales and multiphysics on multigrids. Both variational and dynamic problems are considered. The method relies on an efficent coupling between the macroscopic and microscopic models. In cases when the macroscopic model is not explicity available or invalid, the microscopic solver is used to supply the necessary data for the microscopic solver. Besides unifying several existing multiscale methods such as the ab initio molecular dynamics [13], quasicontinuum methods [73,69,68] and projective methods for systems with multiscales [34,35], HMM also provides a methodology for designing new methods for a large variety of multiscale problems. A framework is presented for the analysis of the stability and accuracy of HMM. Applications to problems such as homogenization, molecular dynamics, kinetic models and interfacial dynamics are discussed.

The three-dimensional baroclinic quasigeostrophic flow model has been widely used to study basic mechanisms in oceanic flows and climate dynamics. In this paper, we consider this flow model under random wind forcing and time-periodic fluctuations on fluid boundary (the air-sea surface). The time-periodic fluctuations are due to periodic rotatios of the earth and thus periodic exposure of the earth to the solar radiation. After overcoming the difficulty due to the low regualrity of an associated Ornstein-Uhlenbeck process, we establish the well-posedness of the baroclinic quasigeostrophic flow model in the state space. Then we demonstrate the existence of the random attractors, again in the state space. We also discuss the relevance of out result to climate modeling.

In this work, a detailed description for an efficent adaptive mesh redistribution algorithm based on the Godunov's scheme is presented. After each mesh iteration a second-order finite-volume flow solver is used to update the flow parameters at the new time level directly without using interpolation. Numerical experiments are perfomed to demonstrate the efficency and robustness of the proposed adaptive mesh algorithm in one and two dimensions.

A fast finite difference method is proposed to solve the incompressible Navier-Stokes equations defined on a general domain. The method is based on the voricity stream-function formulation and a fast Poisson solver defined on a general domain using the immersed interface method. The key to the new method is the fast Poisson solver for general domains and the interpolation scheme for the boundary condition of the stream function. Numerical examples thats show second order accuracy of the computed solution are also provided.

In previous work, the L-stability of constant states in a model of radiative gases, under a zero-mass initial disturbance, was often left open. Actually, it was proved only for the Burgers flux and odd inital data which were non-negative on R⁺. We now prove this stability in full generality. This result is used, as usual, to prove the L-stability of shock profiles.

A new approach for the accurate solution of the Fokker-Planck-Landau (FPL) equation has been presented recently in [1,2]. The method is based on a fast spectral solver for the efficent solution of the collision operator. The use of a suitable explicit Runge-Kutta solver for the time intergreation of the collision phase avoids excessive small time steps included by the stiffness of the diffusive collision operator. Here we present the details of a numerical simulation of the relaxation process in a three-dimensional Coulomb gas.