Abstract In this contribution, we present a novel approach on how to treat material interfaces in nonlocal models based peridynamics (PD) and particular continuum‐kinematics‐inspired (CPD), variationally consistent peridynamic formulation. Our method relies interface where the subdomains overlap. Within region, kinematic coupling of two constituents is enforced. The contact purely geometrical a...

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge. PACS numbers: 11.15.Ha, 11.30.Rd, 11.30.Fs It is well known that all fundame...

We develop a simple model for coupling the pseudo-Goldstone bosons of QCD Or's, K's, -q) to quark fields. This nonlocal model incorporates a momentum dependent dynamical quark mass ,~ (p) in a manner consistent with global chiral symmetry. Explicit current quark masses and gauge fields are also introduced. All low energy parameters of the chiral lagrangian are expressed in terms of ~(p). In par...

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge. PACS numbers: 11.15.Ha, 11.30.Rd, 11.30.Fs It is well known that all fundame...

The relationship between the variational principles for equations of continuum mechanics in Eulerian and Lagrangian descriptions is considered. It shown that, a system differential variables, corresponding description related to introducing nonlocal variables. connection obtained terms coverings. relation its symplectic structures discussed. if variables can be derived from principle, then ther...

A nonlocal continuum theory of solvation is applied using an oscillating dielectric function with spatial dispersion. It is found that a convergent solution cannot be calculated using a model of a fixed solute cavity inside the solvent continuum. This is attributed to the fact that the dielectric oscillations appear as a result of coupling between polarization and density fluctuations, contradi...