Abstract Based on an analysis of the results original research performed in Laboratory Sorption Methods Vernadsky Institute Geochemistry and Analytical Chemistry Russian Academy Sciences within project “Mathematical Chromatograph,” review covers aim strategy imitation modeling high-performance chromatography; associated problems theory intermolecular interactions; classifications polar stationa...

Analytical spiral wave solutions for reaction-diffusion equations play an important role in studying spiral wave dynamics. In this paper, we focus on such analytical solutions in the case of highly excitable media. We present numerical evidence that, for rigidly rotating spiral waves in highly excitable media, the species values in the spiral core region do harmonic oscillations but not relaxat...

Some new nonlinear analytical solutions are found for axisymmetric horizontal flows dominated by strong heat sources. These flows are common in multiscale atmospheric and oceanic flows such as hurricane embryos and ocean gyres. The analytical solutions are illustrated with several examples. The proposed exact solutions provide analytical support for previous numerical observations and can be al...

the hybrid fuzzy differential equations have a wide range of applications in science and engineering. we consider the problem of nding their numerical solutions by using a novel hybrid method based on fuzzy neural network. here neural network is considered as a part of large eld called neural computing or soft computing. the proposed algorithm is illustrated by numerical examples and the resu...

In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid conversion and external film transport. In this part, the analytical solutions are extended to no...

In this paper, we present an original derivation process of a nonhydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by a minimal energy constraint instead of an asymptotic expansion. The model slightly differs from the well-known Green-Naghdi model and is confronted with statio...

on the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional linear and nonlinear schrödinger equations is presented. the analytical solution is shown in a series form in the reproducing kernel space and the approximate solution is constructed by truncating the series. the convergence of the approximate solution to the analytical solution is also proved. th...

in this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎fredholm-volterra integral equations (fvies) are smooth‎.

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In ...

Abstract This research article examines the correctness of two new analytical methods for solving internal solitary waves shallow seas. To get computational solutions to positive (2 + 1)-dimensional Gardner–Kadomtsev–Petviashvili model, extended simplest equation and modified Kudryashov are used. Numerous traveling wave in various forms developed order assess starting conditions required variat...