In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) whic...

An explanation is given for previous numerical results which suggest a certain bifurcation of ‘vector solitons’ from scalar (single-component) solitary waves in coupled nonlinear Schrödinger (NLS) systems. The bifurcation in question is nonlocal in the sense that the vector soliton does not have a small-amplitude component, but instead approaches a solitary wave of one component with two infini...

Nonlocal nonlinear Schrödinger equations are considered as models of liquid helium II. The models contain a nonlocal interaction potential that leads to a phonon–roton-like dispersion relation. Also, a higher-order term in the local density approximation for the correlation energy is introduced into the model to overcome nonphysical mass concentrations. These equations are solved for straight-l...

In this article, a new higher order shear deformation theory based on trigonometric shear deformation theory is developed. In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates. In the present theory, the transverse shear stresses satisfy the traction free...

Recent developments in modeling and analysis of nanostructures are illustrated discussed this paper. Starting with the early theories nonlocal elastic continua, a thorough investigation continuum nano-mechanics is provided. Two-phase local/nonlocal models shown as possible to recover consistency strain-driven purely integral theory, provided that mixture parameter not vanishing. Ground-breaking...

Recently increased interest in the study of self-trapped optical beams in nonlocal nonlinear media is explained by experimental observations of nonlocal spatial solitons in liquid crystals and lead glasses as well as a number of many interesting theoretical predictions, including stabilization of vortex solitons against symmetry breaking instability in the media with nonlocal optical response. ...

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive govern...

A two space dimensional active nonlinear nonlocal cochlear model is formulated in the time domain to capture nonlinear hearing effects such as compression, multitone suppression and difference tones. The micromechanics of the basilar membrane (BM) are incorporated to model active cochlear properties. An active gain parameter is constructed in the form of a nonlinear nonlocal functional of BM di...

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 ...

We propose a novel image decomposition method to decompose an image into its cartoon and texture components. To exploit the nonlocal selfsimilarity of cartoon-plus-texture images, we construct groups by stacking together similar image patches into 3-D arrays and consider group as the basic unit of decomposition. We decompose each group via a convex optimization model consisting of 3-D cartoon a...