A bi-isotropic magneto-electric metamaterials is modeled by two independent reservoirs. The reservoirs contain a continuum of three dimensional harmonic oscillators, which describe polarizability and magnetizability of the medium. The paper aimed to investigate the effect of electromagnetic field on bi-isotropic. Starting with a total Lagrangian and using Euler-Lagrange equation, researcher cou...

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

For a one-dimensional stationary system, we derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. We then integrate this equation in the constant potential case and calculate the time spent by a particle tunneling through a potential barrier .

The stability of shear flows of electrically conducting fluids, with respect to finite amplitude three-dimensional localized disturbances is considered. The time evolution of the fluid impulse integral, characterizing such disturbances, for the case of low magnetic Reynolds number is obtained by integrating analytically the vorticity equation. Analysis of the resulted equation reveals a new ins...

The one-dimensional matrix Schrr odinger equation is considered when the matrix potential is selfadjoint and satisses certain general restrictions. The small-energy asymptotics of the scattering solutions and scattering coeecients are derived. The continuity of the scattering coeecients is established. The unique solvability of the corresponding matrix Marchenko integral equations is proved. Sh...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

We report on a computer simulation and integral equation study of a simple model of patchy spheres, each of whose surfaces is decorated with two opposite attractive caps, as a function of the fraction chi of covered attractive surface. The simple model explored--the two-patch Kern-Frenkel model--interpolates between a square-well and a hard-sphere potential on changing the coverage chi. We show...

Using the fundamental solution of the heat equation, we give an expression of the solutions to two-dimensional initial-boundary value problems of the Navier-Stokes equations, where the vorticity is expressed in terms of a Poisson integral, a Newtonian potential, and a single layer potential. The density of the single layer potential is the solution to an integral equation of Volterra type along...

The recovery of the coe cient H(x) in the one-dimensional generalized Schrodinger equation d =dx + kH(x) = Q(x) ; where H(x) is a positive, piecewise continuous function with positive limits H as x ! 1; is studied. The large-k asymptotics of the wavefunctions and the scattering coe cients are analyzed. A factorization formula is given expressing the total scattering matrix as a product of simp...