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 ...

Quantum mechanical phenomena have a ected our lives in numerous ways. Their impact on modern technology ranges from everyday applications such as transistors, lasers and solar cells to ground breaking equipment such as Scanning-Tunneling electron microscopes. However, in spite all results in fundamental quantum theory research, various aspects of the theory are still not fully understood. This ...

In the quantized two-dimensional non-linear supersymmetric σ-model, the supercurrent supermultiplet, which contains the energy-momentum tensor, is transformed by the nonlocal symmetry of the model into the isospin current supermultiplet. This effect incorporates supersymmetry into the known infinite-dimensional Yangian deformation symmetry of plain σ-models, leads to precisely the same nontrivi...

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...

Abstract In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enjoys maximum principle, monotonicity-preserving and entropy condition on the continuum level. Moreover, it has a well-defined local limit given by a conventional local cons...

Abstract Partial wave theory of a three dmensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a “hard shere” like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermio...

The electromagnetic enhancement factor for surface enhanced Raman scattering is reexamined taking into account the nonlocal dielectric response of the substrate surface. Surface roughness is represented typically by a spherical island and nonlocal effect is introduced via a simple phenomenological model which makes possible a closer quantitative comparison with experiments. It is found that the...

We study the bound states of two-dimensional bright solitons in nonlocal nonlin-ear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady bound state of coherent nonrotating and rotating solitary structures (azimuthons) can exist above some threshold power. A dipolar nonrotating multisoliton occur...

The Born–Kirkwood–Onsager ~BKO! model of solvation, where a solute molecule is positioned inside a cavity cut into a solvent, which is considered as a dielectric continuum, is studied within the bounds of nonlocal electrostatics. The nonlocal cavity model is explicitly formulated and the corresponding nonlocal Poisson equation is reduced to an integral equation describing the behavior of the ch...

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...