this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

The dynamical cluster approximation ~DCA! is modified to include disorder. The DCA incorporates nonlocal corrections to local approximations such as the coherent potential approximation ~CPA! by mapping the lattice problem with disorder, and in the thermodynamic limit, to a self-consistently embedded finite-sized cluster problem. It satisfies all of the characteristics of a successful cluster a...

The energy-dependent, nonlocal correlation potential known as the selfenergy that appears in the Dyson equation has a pole and residue structure that enables renormalizations of its low-order, perturbative contributions to be estimated. The partial third-order (P3) approximation has been extensively applied to the ionization energies of closed-shell, organic molecules and is the most successful...

The lowest-order nonlocal small slope approximation (NLSSA) reflection coefficient is derived, and numerical results are presented for one-dimensional (1-D) surfaces, satisfying the Dirichlet boundary condition. Reduction to the perturbation expression occurs in the small height limit, and the first term of the reflection coefficient gives the Kirchhoff approximation (KA) result. Numerical resu...

The dynamical cluster approximation (DCA) is a method which systematically incorporates nonlocal corrections to the dynamical mean-field approximation. Here we present a pedagogical discussion of the DCA by describing it as a ̊-derivable coarse-graining approximation in k-space, which maps an infinite lattice problem onto a periodic finite-sized cluster embedded in a self-consistently determine...

Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation. Nonlocal governing equation and boundary conditions for carbon nanotubes are obtained by using Hamilton’s minimum energy principle. Eringen’s nonlocal stress gr...

We explore the approximation of feedback control integro-differential equations containing a fractional Laplacian term. To obtain for state variable this nonlocal equation, we use Hamilton–Jacobi–Bellman equation. It is well known that approach suffers from curse dimensionality, and to mitigate problem couple semi-Lagrangian schemes discretization dynamic programming principle with Shepard appr...

We study the existence of a mild solution to nonlocal initial value problem for semilinear second-order differential inclusions in abstract spaces. The result is obtained by combining Kakutani fixed point theorem with approximation solvability method and weak topology. This combination enables getting without any requirements compactness right-hand side or cosine family generated linear operator.

This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish unknown coefficient. A finite difference scheme is constructed and a numerical approximation made. Examples experiments, such as man-made noise, provided show stability efficiency this method.

We present kinetic equations that describe the evolution of O(N)–symmetric real scalar quantum fields out of thermal equilibrium in a systematic nonperturbative approximation scheme. This description starts from the 1/N –expansion of the 2PI effective action to next–to–leading order, which includes scattering and memory effects. From this starting point one is lead to evolution equations for th...