In this paper, we analyze a multiscale method developed under the heterogeneous multiscale method (HMM) framework for numerical approximation of multiscale wave propagation problems in periodic media. In particular, we are interested in the long time O(ε−2) wave propagation, where ε represents the size of the microscopic variations in the media. In large time scales, the solutions of multiscale...

In atmospheric dynamics, the governing equations are usually non-linear partial differential equations. Some knowledge of finite-difference approximations to ordinary differential equations (especially first order) is needed, however. In fact, if we linearize a governing partial differential equation and assume a wave form for the solution, the equation simply reduces to an ordinary differentia...

It is shown that the solutions of the pure initial-value problem for the KP and regularized KP equations are the same, within the order of accuracy attributable to either, on the time scale 0 ≤ t ≤ −3/2 , during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles. under the Creative Commons Attribution License, which permits unrest...

This paper provides a detailed redescription of the adult and the first morphological description of all juvenile stages of Scutovertex sculptus. Specimens from four European countries, Austria, Germany, France and Spain were investigated. The species specific characters are the broadened posterior notogastral setae (lp, h1–h3), the slightly broadened anterior notogastral seta (dm), the gastron...

The upscaling process of mass transport with chemical reaction in porous media is carried out using the method of volume averaging under diffusive and dispersive conditions. We study cases in which the (first-order) reaction takes place in the fluid phase that saturates the porous medium or when the reaction occurs at the solid-fluid interface. The upscaling effort leads to average transport eq...

A differential polynomial G is called a divisor of a differential polynomial F if any solution of the differential equation G = 0 is a solution of the equation F = 0. We design an algorithm which for a class of quasi-linear partial differential polynomials of order k + 1 finds its quasi-linear divisors of order k.