The problem of optical reciprocity in the long wavelength limit is considered in terms of the symmetry for the scalar Green’s function under the Neumann boundary conditions, for materials with nonlocal and anisotropic dielectric responses. This extends the previous works in the literature which were limited either to the Dirichlet conditions or to cases of perfect conductor and local dielectric...

The recent paper entitled by K. C. Lee et al. (2011) establishes nonlocal macroscopic quantum correlations, which they term "entanglement", under ambient conditions. Photon(s)-phonon entanglements are established within each interferometer arm. However, our analysis demonstrates, the phonon fields between arms become correlated as a result of single-photon wavepacket path indistinguishability, ...

We construct and analyse a locally one-dimensional method (finite-difference scheme) for a two-dimensional parabolic equation with nonlocal integral conditions. The main attention is paid to the stability of the method. We apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite-difference scheme and demonstrate th...

Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. In the present work, the posbuckling response of orthotropic single-layered graphene sheet (SLGS) is investigated in a closedform analytical manner using the nonlocal theory of Eringen. Two opposite edges of the plate are subjected to normal stresses. The nonlocali...

Based on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived bas...

In this study, the small scale effect on the linear free-field vibration of a nano-circular plate has been investigated using nonlocal elasticity theory. The formulation is based on the classical theory and the linear strain in cylindrical coordinates. To take into account the small scale and the linear geometric effects, the governing differential equation based on the nonlocal elasticity theo...

In this paper, a numerical solution procedure is presented for the free and forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of Timoshenko beam theory. The influences of surface piezoelectricity, surface elasticity and residual surface stress are taken into consideration. Using Hamilton’s principle, t...

Abstract In this paper, we investigate the blow-up properties of a quasilinear reaction-diffusion system with nonlocal nonlinear sources and weighted nonlocal Dirichlet boundary conditions. The critical exponent is determined under various situations of the weight functions. It is observed that the boundary weight functions play an important role in determining the blow-up conditions. In additi...

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the hydrodynamic limit. Basing on phenomenological arguments, two scattering kernels which model non–local interactions between the gas molecules and the wall boundary are proposed. They satisfy the global mass conservation and a generalized reciprocity relation. The a...

The cone theory andmonotone iterative technique are used to investigate theminimal nonnegative solution of nonlocal boundary value problems for second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times. All the existing results obtained in previous papers on nonlocal boundary value problems are under the case of the boundary condi...