Torla Hassan

Transient radiative heat transfer through thin films using Laguerre–Galerkin method

Heat transfer through a semiconductor or dielectric thin film is investigated by using the single relaxation time approximation to the Boltzmann equation. The radiance is expanded in terms of the Laguerre polynomial with time as argument, and the ensuing time-independent equation is solved with the aid of the Galerkin technique. Films of different thicknesses, ranging from 0.01 to 10 mean free paths, have been considered. The results, calculated for different time, ranging from 0.01 to 10 relaxation times, are presented in the forms of the following quantities (in dimensionless units): the temperature (normalized dimensionless internal energy), the heat flux, and the irradiance. Differences between the results obtained by this approach and those found by solving partial differential equations of heat conduction (Fouriers Law and Cattaneos equation) are noted.

Time-dependent radiative transfer through thin films: Chapman–Enskog-maximum entropy method

Approximate solutions to the time-dependent radiative transfer equation, also called the phonon radiative transfer equation, for a plane-parallel system have been obtained by combining the flux-limited Chapman–Enskog approximation with the maximum entropy method. For problems involving heat transfer at small scales (short times and/or thin films), the results found by this combined approach are closer to the outcome of the more labour-intensive Laguerre–Galerkin technique (a moment method described recently by the authors) than the results obtained by using the diffusion equation (Fouriers law) or the telegraph equation (Cattaneos law). The results for heat flux and temperature are presented in graphical form for xL = 0.01, 0.1, 1 and 10, and at τ = 0.01, 0.1, 1.0 and 10, where xL is the film thickness in mean free paths, and τ is the value of time in mean free times.

Localized solutions of extended discrete nonlinear Schrödinger equation

We consider the extended discrete nonlinear SchrAodinger (EDNLSE) equation which includes the nearest neighbor nonlinear interaction in addition to the on-site cubic and quintic nonlinearities. This equation describes nonlinear excitations in dipolar Bose-Einstein condensate in a periodic optical lattice. We are particularly interested with the existence and stability conditions of localized nonlinear excitations of di®erent types. The problem is tackled numerically, by application of Newton methods and by solving the eigenvalue problem for linearized system near the exact solution. Also the modulational instability of plane wave solution is discussed.

Flat top solitons on linear gaussian potential

The study of Nonlinear Schrodinger Equation has been wide focus from many researchers especially analysing the result of collision as it describes the soliton propagation. This paper considers the soliton scattering of cubic-quintic Nonlinear Schrodinger Equation on localized Gaussian potential. By applying Super-Gaussian ansatz as the trial function for variational approximation (VA) method, the soliton interaction may acquire flat-top shape with appropriate parameters. The result of VA will be compared to numerical analysis to check the accuracy of analytical predictions.

Equiconvergence in Summation Associated with Elliptic Polynomial

In this paper we prove a precise equiconvergence relation between index of the Bochner-Riesz means of the expansions and power of the singularity of the distributions with compact support in summation associated with the elliptic operator.

Interaction of Two Pulses in Defocusing Nonlinear Schrodinger Equation

In this work we are using initial conditions in the form of two separated bright pulses with the rectangular shape to analyse the interaction of pulses in a defocusing Nonlinear Scrodinger Equation (NLSE). By exact solution of the direct scattering problem associated with the defocusing NLSE, we have obtained the expressions for long time behavior of the solution. Obtained results interpreted as a nonlinear interference of two pulses.