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Core-shell particles allow highly efficient and fast separation of complex samples. They provide advantages over fully porous particles, such as highly efficient separation with fast flow rate due to shorter diffusional path length in particle macropores. On the other hand, capacities are reduced due to the inert core. This work is focused on the numerical approximation of a nonlinear general rate model for fixed-beds packed with core-shell particles. The model equations consider axial dispersion, interfacial mass transfer, intraparticle diffusion, and multi-component Langmuir isotherm. A semi-discrete high resolution fluxlimiting finite volume scheme is proposed to accurately and efficiently solve the model equations. The scheme is second order accurate in axial and radial coordinates. The resulting system of ordinary differential equations (ODEs) are solved by using a second-order TVD Runge-Kutta method. For illustration, a few selected scenarios of single solute and multi-component elution bands are generated to study theoretically the effects of the core radius fractions on the course of elution curves. Typically applied performance criteria are

The general rate model (GRM) is considered to be a comprehensive and reliable mathematical model for describing the separation and mass transfer processes of solutes in chromatographic columns. However, the numerical solution of model equations is complicated and time consuming. This paper presents analytical solutions of the GRM for linear adsorption isotherms and different sets of boundary conditions at the column inlet and outlet. The analytical solutions are obtained by means of Laplace transformation. Numerical Laplace inversion is used to transform back the solution in the time domain because analytical inversion cannot be obtained. The first four temporal moments are derived analytically using the Laplace domain solutions. The moments of GRM are utilized to analyze the retention times, band broadenings, front asymmetries and kurtosis of the

This writing is an attempt to explain a reliable numerical treatment for stochastic computer virus model. We are comparing the solutions of stochastic and deterministic computer virus models. This paper reveals that a stochastic computer virus paradigm is pragmatic in contrast to the deterministic computer virus model. Outcomes of threshold number C * hold in stochastic computer virus model. If C * < 1 then in such a condition virus controlled in the computer population while C * > 1 shows virus persists in the computer population. Unfortunately, stochastic numerical methods fail to cope with large step sizes of time. The suggested structure of the stochastic non-standard finite difference scheme (SNSFD) maintains all diverse characteristics such as dynamical consistency, boundedness and positivity as defined by Mickens. The numerical treatment for the stochastic computer virus model manifested that increasing the antivirus ability ultimates small virus dominance in a computer community.