in this paper, the stability characteristics of single-walled carbon nanotubes (swcnts) under the action of axial load are investigated. to this end, a nonlocal flügge shell model is developed to accommodate the small length scale effects. the analytical rayleigh-ritz method with beam functions is applied to the variational statement derived from the flügge-type buckling equations. molecular dy...

This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the mo...

We develop the continuous matrix-product states approach for description of inhomogeneous one-dimensional quantum systems with long-range interactions. The method is applied to exactly solvable Calogero-Moser model. show high accuracy reproducing ground-state properties many-body system and discuss potential errors that can originate from approximation nonlocal interaction potentials singularit...

We use an approximation scheme together with a variation of the fixed point theorem to show existence positive solution nonlocal boundary value problem. This problem has smooth bounded domain in R<sup>N</sup>, singular term, and combined nonlinearities. also study symmetric, monotonicity, asymptotic behavior solutions respect parameter involved

We study Galerkin approximation of pullback attractors for a nonautonomous nonlocal parabolic equation. show that the $ n $th system has attractor in $-dimensional subspace Lebesgue space. then prove sequence is uniformly backward bounded and solutions converges on any set. Using these results, we establish upper semi-convergence towards original infinite-dimensional system.

The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker-Planck equations that involve two small parameters and are driven by a timedependent constraint. In this paper we consider the fast reaction regime related to Kramers-type phase transitions and prove that the dynamics in the small-parameter limit can be described by a rate-independent ...