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—and derive new results for the jammi...

We analyze a finite volume scheme for nonlocal SIR model, which is a nonlocal reaction-diffusion system modeling an epidemic disease. We establish existence solutions to the finite volume scheme, and show that it converges to a weak solution. The convergence proof is based on deriving series of a priori estimates and using a general L compactness criterion.

where D is a certain function of the electric field. For derivation of such type of equation see [1, 2]. Recent theoretical and experimental results highlight a very interesting phenomenology, such as “accessible solitons”, collapse arrest, optical vortices (see e.g. [3−6] and references therein), associated with so-called nonlocal nonlinear media. Most of the models studied before are not inte...

Scientific facts are constituted as consensus about observable phenomena against the background of an accepted, or at least plausible, theory. Empirical data without a theoretical framework are at best curiosities and anomalies, at worst they are neglected. The problem of parapsychological research since its inception with the foundation of the Society of Psychical Research in 1882 was that no ...

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 ...

Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using spatial variation material properties to investigate free vibration response incorporating porosities and...

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...