Gravity-induced sagging can amplify variations in goniometric measurements of the contact angles of sessile drops on super-liquid-repellent surfaces. The very large value of the effective contact angle leads to increased optical noise in the drop profile near the solid-liquid free surface and the progressive failure of simple geometric approximations. We demonstrate a systematic approach to det...

When the exact time-dependent solutions of a system of ordinary differential equations are chaotic, numerical solutions obtained by using particular schemes for approximating time derivatives by finite differences, with particular values of the time increment τ , are sometimes stably periodic. It is suggested that this phenomenon be called computational periodicity. A particular system of three...

In this manuscript, a qualitative analysis of the mathematical model novel coronavirus (COVID-19) involving anew devised fractal-fractional operator in Caputo sense having fractional-order q and fractal dimension p is considered. The concerned composed eight compartments: susceptible, exposed, infected, super-spreaders, asymptomatic, hospitalized, recovery fatality. When, choosing order one we ...

In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand dynamic behavior COVID-19. For study, new SEIAPHR fractional was purposed in which infectious individuals were divided into three sub-compartments. The purpose is construct more reliable and realistic for complete computational analysis design different control strategies proposed Caputo–Fabrizio...

We develop numerical methods for performing efficient Brownian dynamics of col-loidal suspensions confined to remain in the vicinity of a no-slip wall by gravity or active flows. We present a stochastic Adams-Bashforth integrator for the Brown-ian dynamic equations, which is second-order accurate deterministically and uses a random finite difference to capture the stochastic drift proportional ...

This paper analyzes a number of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, and elastic waves. The spatial operators analyzed include compact schemes, noncompact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-mar...

Many different numerical models exist for solving the parabolic wave equation. Hardin and Tappert[2] suggested a split-step algorithm in conjunction with the fast Fourier Transform (FFr) method. Lee and Papadakis[3] used a scheme which is based on the predictor-corrector technique of Adams-Bashforth; Lee, Botseas and Papadakis[4] introduced an implicit finitedifference scheme. Chan, Shen and Le...

A numerical model used to simulate global convection and magnetic field generation in stars is described. Nonlmear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical, fluid shell heated from below. The velocity, magnetic field, and thermodynamic perturbations are expanded in spherical harmonics to resol...

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to...

The bidomain model is a system of partial differential equations used to model the propagation of electrical potential waves in the myocardium. It is composed of coupled parabolic and elliptic partial differential equations, as well as at least one ordinary differential equation to model the ion activity through the cardiac cell membranes. The purpose of this paper is to propose and analyze sev...