This paper presents numerical analysis of electroosmotic flows (EOF) in charged anisotropic porous media using the lattice Poisson-Boltzmann method (LPBM), which combines two sets of lattice evolution methods solving the nonlinear Poisson equation for electric potential distribution and the Navier-Stokes equations for fluid flow respectively. Consistent boundary condition implementations are proposed for solving both the electrodynamics and the hydrodynamics on a same grid set. The anisotropic structure effects on EOF characteristics are therefore studied by modeling the electrically driven flows through ellipse arrays packed in a microchannel whose shape and orientation angle are used to control the anisotropy of porous media. The results show that flow rates increase with the axis length along the external electric field direction for a certain porosity and decrease with the angle between the semimajor axis and the bulk flow direction when the orientation angle is smaller than π/2. After introducing random factors into the microstructures of porous media, the statistical results of flow rate show that the anisotropy of microstructure decreases the permeability of EOFs in porous media.

An extension of the standard Shan-Chen model for non ideal-fluids, catering for mid-range, soft-core and hard-core repulsion, is investigated. It is shown that the inclusion of such mid-range interactions does not yield any visible enhancement of the density jump across the dense and light phases. Such an enhancement can however be obtained by tuning the exponents of the effective interaction. The results also indicate that the inclusion of soft-core repulsion can prevent the coalescence of neighborhood bubbles, thereby opening the possibility of tailoring the size of multi-droplet configurations, such as sprays and related phase-separating fluids. 

A model is developed to calculate emission spectrum from plasmas in non-local-thermodynamic-equilibrium (NLTE). The populations are obtained with a Collisional Radiative Model and the spectrum is calculated with the Unresolved-Transition-Array (UTA) approximation. The present model is applied to the calculation of emissivity from low-, medium- and high-Z plasmas. The integrated emissivity and the spectra are compared with those calculated by other theoretical models. In general speaking, the present results of the mean charge state and emissivity agree well with some theoretical ones while large differences are found when all the theoretical results are included.

An adaptive meshing technique and solution method is proposed in which a two-dimensional body-fitted multi-block mesh is locally adjusted to arbitrarily embedded boundaries that are not necessarily aligned with the mesh. Not only does this scheme allow for rapid and robust mesh generation involving complex embedded boundaries, it also enables the solution of unsteady flow problems involving bodies and interfaces moving relative to the flow domain. This scheme has been implemented within a block-based adaptive mesh refinement (AMR) numerical framework which can ease computational expense while maintaining a detailed representation of the embedded boundary and providing an accurate resolution of the spatial characteristics of the fluid flow. Rigid body motion and evolving motion due to physical processes are considered. A block-based AMR level set method is used to deal with evolving embedded boundaries. Numerical results for various test problems are presented to verify the validity of the scheme as well as demonstrate the capabilities of the approach for predicting complex two-dimensional inviscid and laminar fluid flows.

The velocity slip and temperature jump in micro-Couette flow are investigated with the lattice Boltzmann method (LBM). A new slip boundary condition with the non-equilibrium extrapolation scheme is used in a thermal lattice Boltzmann model (TLBM) where double distribution functions are used to simulate the velocity and the temperature fields in order to capture the velocity slip and the temperature jump of the wall boundary. The simulated velocity and temperature profiles are in good agreement with the analytic results, which shows the suitability of the present model and the new boundary treatment for describing thermal microflows with viscous heat dissipation.

This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems. The method proposed is a generalization of the "operator expansion method" developed by Recchioni and Zirilli [SIAM J. Sci. Comput., 25 (2003), 1158-1186]. The numerical method proposed reduces, via a perturbative approach, the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations. The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved. A computational method has been developed to solve these challenging problems with affordable computing resources. To this aim a new way of using the wavelet transform and new bases of wavelets are introduced, and a version of the operator expansion method is developed that constructs directly element by element in a fully parallelizable way. Several numerical experiments involving realistic obstacles and "small" wavelengths are proposed and high dimensional vector spaces are used in the numerical experiments. To evaluate the performance of the proposed algorithm on parallel computing facilities, appropriate speed up factors are introduced and evaluated.

A deterministic model of an age-structured population with genetics analogous to the discrete time Penna model [1,2] of genetic evolution is constructed on the basis of the Lotka-Volterra scheme. It is shown that if, as in the Penna model, genetic information is represented by the fraction of defective genes in the population, the population numbers for each specific individual's age are represented by exactly the same functions of age in both models. This gives us a new possibility to consider multi-species evolution without using detailed microscopic Penna model. We discuss a particular case of the predator-prey system representing an ecosystem consisting of a limited amount of energy resources consumed by the age-structured species living in this ecosystem. Then, the increase in number of the individuals in the population under consideration depends on the available energy resources, the shape of the distribution function of defective genes in the population and the fertility age. We show that these parameters determine the trend toward equilibrium of the whole ecosystem.

The annihilation of a hedgehog-antihedgehog pair in hydrodynamics of (elastically isotropic) nematic liquid crystal materials is modeled using the Erickson-Leslie theory which results in a nonlinear system for the flow velocity field and liquid crystal director field coupled through the transport of the directional order parameter and the induced elastic stress. An efficient and accurate numerical scheme is presented and implemented for this coupled nonlinear system in an axi-symmetric domain. Numerical simulations of annihilation of a hedgehog-antihedgehog pair with different types of transport are presented. In particular, it is shown that the stretching parameter in the transport equation contributes to the symmetry breaking of the pair's moving speed during the dynamics of annihilation.

We develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. We show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, we discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.

In this paper, the zero-temperature string method and the nudged elastic band method for computing the transition paths and transition rates between metastable states are investigated. The stability, accuracy as well as computational cost of the two methods are discussed. The results are verified by numerical experiments.