Linearized multipole solutions and their representation

Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 1: Linearized Approximations and Linearized Output Functionals

This paper analyzes the convergence of discrete approximations to the linearized equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. A simple modified Lax–Friedrichs discretization is used on a uniform grid, and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined. It ...

Axisymmetric stationary solutions with arbitrary multipole moments

In this paper, the problem of finding an axisymmetric stationary spacetime from a specified set of multipole moments, is studied. The condition on the multipole moments, for existence of a solution, is formulated as a convergence condition on a power series formed from the multipole moments. The methods in this paper can also be used to give approximate solutions to any order as well as estimat...

Representation: Problems and Solutions

The current orthodoxy in cognitive science, what I describe as a commitment to deep representationalism, faces intractable problems. If we take these objections seriously, and I will argue that we should, there are two possible responses: 1. We are mistaken that representation is the locus of our cognitive capacities — we manage to be the successful cognitive agents in some other, non-represent...

Multipole representation of the elastic field of dislocation ensembles

Modeling of Nanofiltration for ‎Concentrated Electrolyte Solutions using ‎Linearized Transport Pore Model

   In this study, linearized transport pore model (LTPM) is applied for modeling nanofiltration (NF) membrane separation process. This modeling approach is based on the modified extended Nernst-Planck equation enhanced by Debye-Huckel theory to take into account the variations of activity coefficient especially at high salt concentrations. Rejection of single-salt (NaCl) electrolyte is inve...