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...

The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake simplicity, focus on an antiplane problem a half-space prescribed shear stress along surface. In addition, 1D exponential kernel depending vertical coordinate considered. First, surface loading form travelling harmonic wave studied. This pro...

Acceleration-induced nonlocality and the corresponding Lorentz-invariant nonlocal field equations of accelerated systems in Minkowski spacetime are discussed. Under physically reasonable conditions, the nonlocal equation of motion of the field can be derived from a varia-tional principle of stationary action involving a nonlocal Lagrangian that is simply obtained by composing the local inertial...

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...

Puff field theory (PFT) is a low energy decoupling regime of string theory that still retains the nonlocal attributes of the parent theory—while preserving isotropy for its nonlocal degrees of freedom. It realizes an extended holographic dictionary at strong coupling and dynamical nonlocal states akin to defects or the surface operators of local gauge theories. In this work, we probe the nonloc...

The standard relativistic theory of accelerated reference frames in Minkowski spacetime is described. The measurements of accelerated observers are considered and the limitations of the standard theory, based on the hypothesis of locality, are pointed out. The physical principles of the nonlocal theory of accelerated observers are presented. The implications of the nonlocal theory are briefly d...

This paper is concerned with the existence of mild solutions to a class of semilinear differential inclusions with nonlocal conditions. By using the fixed point theory for multivalued maps, we get some general results on nonlocal differential inclusions, which include some recent results on nonlocal problems as special cases. An example of partial differential equations is provided to illustrat...

We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective m...

Three-dimensional exact solutions for temperature and thermoelastic stresses in multilayered anisotropic plates are derived advanced boundary-value problems with general boundary conditions. The extended Stroh formalism is formulated to include the thermal coupling Eringen nonlocal elasticity theory that captures small scale effects. simply supported structures subjected time-harmonic distribut...

Quantum mechanics permits nonlocality—both nonlocal correlations and nonlocal equations of motion—while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality: “superquantum” correlations, and nonlocal “jamming” of correlations. These models are consistent with so...