A mathematical model considering mass and momentum transfer was developed for simulation of ethanol dewatering via pervaporation process. The process involves removal of water from a water/ethanol liquid mixture using a dense polymeric membrane. The model domain was divided into two compartments including feed and membrane. For a description of water transport in ...

The Maxwell equations contain a dielectric permittivity e that describes the particular media. For homogeneous materials at low temperatures this coefficient is constant within a material. However, it jumps at the interface between different media. This discontinuity can significantly reduce the order of accuracy of the numerical scheme. We solve the Maxwell equations, with an interface between...

We present a numerical method to solve the Vlasov–Maxwell equations for spin-1/2 particles, in semiclassical approximation where orbital motion is treated classically while spin variable fully quantum. Unlike spinless case, phase-space distribution function $2\times 2$ matrix, which can also be represented, Pauli basis, as one scalar $f_0$ and three-component vector $\boldsymbol f$ . The relati...

In this report, after pedagogical mathematical insight into basic notions of numerical analysis for di erential equations, more speci c Discontinuous Galerkin (DG) method is introduced. Afterwards, the DG method is combined with a fourth-order staggered Leap-Frog (LF4) scheme to be applied to the solution of the Maxwell equations wavepropagation problem. Stability analysis of the resulting sche...

We study the electromagnetic field equations on an arbitrary quantum curved background in the semiclassical approximation of Loop QuantumGravity. The effective interaction hamiltonian for the Maxwell and gravitational fields is obtained and the corresponding field equations, which can be expressed as a modified wave equation for the Maxwell potential, are derived. We use these results to analyz...