We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we...

A method used recently to obtain a discrete formalism for classical fields with nonlocal actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens’ principle with free discrete propagators that recover their continuum forms in certain limit.

In this paper, using energy method, small scale effects on the buckling analysis of a double-walled carbon nanotube (DWCNT) under external radial pressure is studied. The constitutive equations derived for a DWCNT using the nonlocal theory of elasticity which Eringen are presented for the first time. By minimizing the second variation of the total energy for a DWCNT, hence, the value of the non...

The present work mainly studies the free vibration of circular magneto-electro-elastic (MEE) nano-plates based on the Kirchhoff’s plate theory within the framework of nonlocal elasticity theory to account for the small scale effect. The MEE nano-plate studied here is considered to be fully clamped and subjected to the external magnetic and electric potentials. Using nonlocal constitutive relati...

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 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...

Parameters of Gasser Leutwyler chiral Lagrangian are proved saturated by dynamical quark self energy Σ(k2) in a gauge invariant, nonlocal, dynamical quark model. Much of low-energy QCD can be encoded into a series parameters appearing in a chiral Lagrangian, expanded to some finite order of low energy expansion. Attempts have been made to understand these parameters: it is shown that low lying ...

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...

this paper is concerned with the surface and small scale effects on transverse vibration of a viscoelastic single-layered graphene sheet (slgs) subjected to an in-plane magnetic field. the slgs is surrounded by an elastic medium which is simulated as visco-pasternak foundation. in order to investigate the small scale effects, the nonlocal elasticity theory is employed due to its simplicity and ...

The local theory of symmetries of differential equations has been well-established since the days of Sophus Lie. Generalized, or higher order symmetries can be traced back to the original paper of Noether, [32], but were not exploited until the discovery that they play a critical role in integrable (soliton) partial differential equations, cf. [30, 33, 35]. While the local theory is very well d...