Abstract. The presented explanations are provided for the one–dimensional diffusion process with constant drift by using forward Fokker–Planck technique. We are interested in the outflow probability in a finite interval, i. e. first passage time probability density distribution taking into account reflecting boundary on left hand side and absorbing border on right hand side. This quantity is ca...

A numerical method is developed for solving the two dimensional Helmholtz equation in a two layer region bounded by a flat top, a flat bottom and a curved interface. A local orthogonal transform is used to flatten the curved interface of the waveguide. The one-way re-formulation based on the Dirichlet-to-Neumann (DtN) map is then used to reduce the boundary value problem to an initial value pro...

Purpose In this paper a computationally efficient approach is suggested for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines, such as a single phase transformer (a benchmark example that is considered in this paper). The approach is based on the Karhunen-Loève expansion. The stochastic model is further used to stud...

Ab initio calculations are presented for total and partial recombination cross sections and rate coefficients for e1Fe V→Fe IV, employing a unified treatment that incorporates both the radiative and dielectronic recombinations ~RR and DR! in a self-consistent and accurate manner. The theoretical treatment is based on the close-coupling approximation using the R-matrix method. Recombination calc...

Abstract Usually, evanescent modes or non-propagating waves are produced when a propagating incident wave impinges on an interface between two media or materials such as curtainwall-pile breakwater (CPB) at a subcritical angle and decay with distance from interface. To achieve an effective prediction of hydrodynamic performance of CPB and overcome the problem of underestimation of energy loss, ...

The spectral problem (A+V (z))ψ = zψ is considered with A, a self-adjoint Hamiltonian of sufficiently arbitrary nature. The perturbation V (z) is assumed to depend on the energy z as resolvent of another self-adjoint operator A ′ : V (z) = −B(A ′ −z) −1 B *. It is supposed that operator B has a finite Hilbert-Schmidt norm and spectra of operators A and A ′ are separated. The conditions are form...

Over the last two years, we have been developing a library of Matlab subprograms integrated with on-line lecture notes in the form of WWW documents which are used in both undergraduate and graduate-level Chemical Engineering Applied Mathematics classes. The goal has been to make as transparent as possible the relationships between model development, solution, and analysis of systems described b...

Propagation of electromagnetic waves in forest environments is examined in which both the transmitting and receiving points are located in the trunk layer of a four-layered anisotropic forest model. This propagation model considers the forest as a horizontally stratified, anisotropic media of canopy and trunk, bounded by ground below and air above. The electromagnetic fields are obtained using ...

For many wave propagation problems, it is often necessary to solve the variable coeecient Helmholtz equation in a very large domain. The one-way re-formulation based on the Dirichlet-to-Neumann (DtN) map can be used to nd the solutions of the Helmholtz equation over a large range distance. It is particularly useful for waveguide problems, since it leads to a numerical algorithm that marches in ...

We consider the diffusion of a material in a one-dimensional medium consisting of a large number of cells separated from the extracellular space by permeable membranes. The extracellular space is completely connected and allows unrestricted diffusion of the material. Furthermore, the material can diffuse within a given cell, i.e., the intracellular space; however, direct diffusion from one cell...