Free vibration characteristics of polymer composite plates reinforced by graphene nanosheets employing the Eringen nonlocal elasticity theory were investigated. Theoretical formulations are derived based on Hamilton’s principle implementing linear orthotropic constitutive equations of lamina while the behavior of nanostructure points affected by all other nonlocal points is also taken into acco...

We develop a strong coupling approach for a general lattice problem. We argue that this strong coupling perspective represents the natural framework for a generalization of the dynamical mean field theory (DMFT). The main result of this analysis is twofold: (1) It provides the tools for a unified treatment of any nonlocal contribution to the Hamiltonian. Within our scheme, nonlocal terms such a...

We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media. We establish unpinning asymptotics using geometric singular perturbation theory in several examples. We also present numerical evidence for the dependence of unpinning asymptotics on regularity of the nonlocal convo...

The Fermi interaction is interpreted as a nonlocal interaction resulting from a double Yukawa-type interaction in which the intervening boson has a definite chirality. The theory is quantizable and renormalizable, and in the "local" limit, the results agree with the usual (V—A) theory of the direct Fermi interaction. The general framework of the theory not only gives a basis for the existence o...

A brief account of the present status of the recent nonlocal generalization of Einstein’s theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenböck’s torsion and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. ...

We show how a unified method, due to Webb and Infante, of tackling many nonlocal boundary value problems, can be applied to nonlocal versions of some recently studied higher order boundary value problems. In particular, we give some explicit examples and calculate the constants that are required by the theory.

In this paper, we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal cqnditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer’s fixed-point theorem. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Existence theorem, Delay integrodifferential eq...