The conventional Lorenz-Mie formalism is extended to the case for a coated sphere embedded in an absorbing medium. The apparent and inherent scattering cross sections of a particle, derived from the far field and near field, respectively, are different if the host medium is absorptive. The effect of absorption within the host medium on the phase-matrix elements associated with polarization depe...

Numerical simulations of charged particle beams require an approximation to the particle distribution being simulated. We present a mathematical formalism for approximating two-dimensional (2D) particle distribution using a basis composed of scaled and translated Gauss-Hermite (STGH) functions. It is computationally efficient, because it only requires the values of the particle distribution at ...

Recent studies have shown the fluid of hard right triangles to possess fourfold and quasi-eightfold (octatic) orientational symmetries. However, standard density-functional theory for two-dimensional anisotropic fluids, based on two-body correlations, an extension incorporate three-body fail describe these To explain origin octatic symmetry we postulate strong particle clustering as a crucial i...

Self{scaled barrier functions on self{scaled cones were introduced through a set of axioms in 1994 by Y. E. Nesterov and M. J. Todd as a tool for the construction of long{step interior point algorithms. This paper provides rm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains of deenition, and subsequently their de...

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplit...

Poroelasticity theory predicts wave velocities in a saturated porous medium through coupling between the bulk deformation of solid skeleton and fluid flow. The challenge emerges below characteristic wavelengths at which hydrodynamic interactions grains pore become important. We investigate pressure volume fraction dependence compressional- shear-wave fluid-saturated, random, isotropic, friction...

The changes of hadron properties in dense and/or hot matter are discussed in terms of effective chiral Lagrangians with the parameters of the theory scaled in a simple way. The phenomenologically successful Walecka model is identified as a mean field chiral Lagrangian with the scaled parameters. Kaon condensation and chiral restoration transitions can be described within the same mean field fra...

Any central simple algebra over a field of characteristic not two has a well-defined non-singular quadratic form called the trace form attached to it. This quadratic form was studied in [6] from the viewpoint of the algebraic theory of quadratic forms. In this article we examine a generalization of trace forms to “scaled trace forms” which are defined via the reduced trace map together with sca...