in this paper, a numerical solution procedure is presented for the forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of timoshenko beam theory. using hamilton’s principle, the nonlocal governing differential equations are derived. the governing equations and the related boundary conditions are discreti...

For the nonlocal T-periodic Gross–Pitaevsky operator, formal solutions of the Floquet problem asymptotic in small parameter , → 0, up to O(3/2) have been constructed. The quasi-energy spectral series found correspond to the closed phase trajectories of the Hamilton–Ehrenfest system which are stable in the linear approximation. The monodromy operator of this equation has been constructed to with...

Abstract. This article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in f...

A hybrid theory which combines the full nonlocal “exact” exchange interaction with the local spindensity approximation of density-functional theory is shown to lead to marked improvement in the description of antiferromagnetically coupled systems. Semiquantitative agreement with experiment is found for the magnitude of the coupling constant in La2CuO4, KNiF3, and K2NiF4. The magnitude of the un...

We study the propagation of wave packets for nonlinear nonlocal Schrödinger equations in the semi-classical limit. When the kernel is smooth, we construct approximate solutions for the wave functions in subcritical, critical and supercritical cases (in terms of the size of the initial data). The validity of the approximation is proved up to Ehrenfest time. For homogeneous kernels, we establish ...

The mexican hat function is used to model a compensated (in density) gravitational lens. First we discuss the need for compensation. Then we integrate photon orbits to construct wavefronts. One consequence of underdensities is an o -axis caustic. We report the structure of the critical curves and caustics using the thin lens approximation, both for the mexican hat and for a perturbed mexican ha...

We propose a novel numerical approach for linear nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and a class of backward stochastic differential equations (BSDEs) driven by Lèvy processes with jumps. The nonlocal diffusion problem under consideration is converted into a BSDE, for which numerical schemes are developed a...

This paper presents several numerical techniques to generate solitary-wave profiles of the Benjamin equation. The formulation and implementation of the methods focus on the approximation of the nonlocal term and the use of numerical continuation algorithms. For solving the attendant nonlinear systems, a comparative study of the performance of such algorithms is made. The paper also explores the...

A modified version of susceptible-infected-recovered-susceptible (SIRS) model for the outbreaks of foot-and-mouth disease (FMD) is introduced. The model is defined on small-world networks, and a ring vaccination programme is included. This model can be a theoretical explanation for the nonlocal interactions in epidemic spreading. Ring vaccination is capable of eradicating FMD provided that the ...

We study, by numerical simulations on a lattice, the behaviour of the gauge–invariant quark–antiquark nonlocal condensates in the QCD vacuum with dynamical fermions. A determination is also done in the quenched approximation and the results are compared with the full–QCD case. The fermionic correlation length is extracted and compared with the analogous gluonic quantity. (PACS code: 12.38.Gc) ∗...