Lattice Boltzmann modeling with discontinuous collision components: Hydrodynamic and Advection-Diffusion Equations

Irrespective of the nature of the modeled conservation laws, we establish first the microscopic interface continuity conditions for Lattice Boltzmann (LB) multiple-relaxation time, link-wise collision operators with discontinuous components (equilibrium functions and/or relaxation parameters). Effective macroscopic continuity conditions are derived for a planar implicit interface between two immiscible fluids, described by the simple two phase hydrodynamic model, and for an implicit interface boundary between two heterogeneous and anisotropic, variably saturated soils, described by Richard’s equation. Comparing the effective macroscopic conditions to the physical ones, we show that the range of the accessible parameters is restricted, e.g. a variation of fluid densities or a heterogeneity of the anisotropic soil properties. When the interface is explicitly tracked, the interface collision components are derived from the leading order continuity conditions. Among particular interface solutions, a harmonic mean value is found to be an exact LB solution, both for the interface kinematic viscosity and for the interface vertical hydraulic conductivity function. We construct simple problems with the explicit and implicit interfaces, matched exactly by the LB hydrodynamic and/or advection-diffusion schemes with the aid of special solutions for free collision parameters.     

Electromagnetic scattering from perturbed surfaces

This paper studies the scattering of electromagnetic waves from a (local) perturbation of a fixed surface, the boundary of a given obstacle in ?³. The goal is to produce an algorithm for solving boundary value problems in the exterior of the perturbed domain solely based on the knowledge of the Green function for the original surface. This is done by solving a boundary integral equation which only involves the perturbed portion of the boundary. Copyright © 2006 John Wiley & Sons, Ltd.     

Asymptotics for the multiplicities in the cocharacters of some PI-algebras

We consider associative PI-algebras over a field of characteristic zero. We study the asymptotic behavior of the sequence of multiplicities of the cocharacters for some significant classes of algebras. We also give a characterization of finitely generated algebras for which this behavior is linear or quadratic.

     

A one-pot synthesis of 1-arylalka-1,3-diynes by sequential acetylene zipper and Sonogashira reactions

1,3-Diynes, formed in situ by base-induced acetylene zipper reactions, following anion quenching with water, undergo smooth Sonogashira-type couplings with functionalized aryl iodides, to give good overall yields of 1-arylalka-1,3-diynes.     

The Crystal Structure of [Cu(BTA)4(H2O)2](BF4)2 (BTA is Benzotriazole)

Russian Journal of Coordination Chemistry -     

Polarimetric optical fiber sensors: aspects of sensitivity and practical implementation

An analytical model for the pressure and strain sensitivity of highly-birefringent fibers is proposed which is in excellent agreement with numerical calculations. Results of polarimetry and coherence-multiplexing experiments are presented and a novel method for accurately splicing this kind of fibers is demonstrated.