We present an existence theory based on minimization of the nonlocal energies appearing in peridynamics, which is a nonlocal continuum model in solid mechanics that avoids the use of deformation gradients. We employ the direct method of the calculus of variations in order to find minimizers of the energy of a deformation. Lower semicontinuity is proved under a weaker condition than convexity, w...

The complete UV-divergent contribution to the one-loop 1PI four-point function of Yang-Mills theory in the light-cone gauge is computed in this paper. The formidable UV-divergent contributions arising from each fourpoint Feynman diagram yield a succinct final result which contains nonlocal terms as expected. These nonlocal contributions are consistent with gauge symmetry, and correspond to a no...

Weakly nonlocal thermodynamic theories are critically revisited. The irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current. Several classical equations are derived , including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter...

In this article, small scale effects on free vibration analysis of non-uniform nanobeams is discussed. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width among the beams length with constant thickness. Analytical solution is achieved for free vibration with different boundary conditions. It is shown th...

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

In this paper, based on the nonlocal Timoshenko beam theory, a nonlinear model is presented for the vibrational behavior of carbon nanotubes (CNTs) embedded in elastic medium in thermal environment. Using the Timoshenko beam theory and nonlocal elasticity of Eringen, the influences of rotary inertia, transverse shear deformation and small scale effect are taken into account. To model the intera...

Using differential quadrature method (DQM), this study investigated pull-in instability of beam-type nano-switches under the effects of small-scale and intermolecular forces including the van der Waals (vdW) and the Casimir forces. In these nano-switches, electrostatic forces served as the driving force, and von-Karman type nonlinear strain was used to examine nonlinear geometric effects. To de...

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function which can be derived from the maximally nonlocal Lagrangian. The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is la...

A generalized nonlocal effective medium theory is derived based on the transfer-matrix method to determine the nonlocal effective permittivity and permeability for the symmetric and periodic metal–dielectric multilayer metamaterials, with respect to both transverse-electric and transversemagnetic polarized light at arbitrary angle of incidence. The nonlocal effective permittivity and permeabili...