Foliation of an Asymptotically Flat End by Critical Capacitors

We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate spheres, and they admit solutions of a certain over-determined boundary value problem involving the Laplace–Beltrami operator. In a key step we must invert the Dirichlet-to-Neumann operator, highlighting the nonlocal nature of our problem.

Random fiber network loaded by a point force

This article presents the displacement field produced by a point force acting on an athermal random fiber network (the Green function for the network). The problem is defined within the limits of linear elasticity and the field is obtained numerically for nonaffine networks characterized by various parameter sets. The classical Green function solution applies at distances from the point force larger than a threshold which is independent of the network parameters in the range studied. At smaller distances, the nonlocal nature of fiber interactions modifies the solution.

Cross correlation mediated by Majorana island with finite charging energy

Based on the many-particle-number-state treatment for transport through a pair of Majorana zero modes (MZMs) which are coupled to the leads via two quantum dots, we identify that the reason for zero cross correlation of currents at uncoupling limit between the MZMs is from a degeneracy of the teleportation and the Andreev process channels. We then propose a scheme to eliminate the degeneracy by introducing finite charging energy on the Majorana island which allows for coexistence of the two channels. We find nonzero cross correlation established even in the Majorana uncoupling limit (and also in the small charging energy limit), which demonstrates well the teleportation or nonlocal nature of the MZMs. More specifically, the characteristic structure of coherent peaks in the power spectrum of the cross correlation is analyzed to identify the nonlocal and coherent coupling mechanism between the MZMs and the quantum dots. We also display the behaviors of peak shift with variation of the Majorana coupling energy, which can be realized by modulating parameters such as the magnetic field.

A Review of Peridynamics (PD) Theory of Diffusion Based Problems

The study of heat conduction phenomena using peridynamic (PD) theory has a paramount significance on the development of computational heat transfer. This is because PD theory has got an interesting feature to deal with the inherent nonlocal nature of heat transfer processes. Since the revolutionary work on PD theory by Silling (2000), extensive investigations have been devoted to PD theory. This paper provides a survey on the recent developments of PD theory mainly focusing on diffusion based peridynamic (PD) formulation. Both the bond-based and state-based PD formulations are revisited, and numerical examples of two-dimensional problems are presented.

Single-copy activation of Bell nonlocality via broadcasting of quantum states

Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state:ρα=α|Φ+⟩⟨Φ+|+(1−α)14.We present two main results, considering that Nature allows for (i) the most general no-signalling correlations, and (ii) the most general quantum correlations at the level of any hidden variable theory. We show that the state does not admit a local hidden variable description for α>0.559 and α>12, in cases (i) and (ii) respectively, which in both cases provides a device-independent certification of the entanglement of the state. These bounds are significantly lower than the previously best-known bound of 0.697 for both Bell nonlocality and device-independent entanglement certification using a single copy of the state. Our results show that strong examples of non-classicality are possible with a small number of resources.

Chaotic Dynamics in a Novel COVID-19 Pandemic Model Described by Commensurate and Incommensurate Fractional-Order Derivatives

Mathematical models based on fractional-order differential equations have recently gained interesting insights into epidemiological phenomena, by virtue of their memory effect and nonlocal nature. This paper investigates the nonlinear dynamic behaviour of a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives. The model is based on the Caputo operator and takes into account the daily new cases, the daily additional severe cases and the daily deaths. By analysing the stability of the equilibrium points and by continuously varying the values of the fractional order, the paper shows that the conceived COVID-19 pandemic model exhibits chaotic behaviours. The system dynamics are investigated via bifurcation diagrams, Lyapunov exponents, time series and phase portraits. A comparison between integer-order and fractional-order COVID-19 pandemic models highlights that the latter is more accurate in predicting the daily new cases. Simulation results, besides to confirm that the novel fractional model well fit the real pandemic data, also indicate that the numbers of new cases, severe cases and deaths undertake chaotic behaviours without any useful attempt to control the disease.

Nonlocal plasticity-based damage modeling in quasi-brittle materials using an isogeometric approach

Purpose This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. Such an approach requires C1 continuous approximation. This is achieved by using an isogeometric approximation (IGA). Numerical examples in one and two dimensions are presented. Design/methodology/approach In this work, the authors propose a nonlocal elastic plastic damage model. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. An additive decomposition of strains in to elastic and inelastic or plastic part is considered. To obtain stable damage, a higher gradient order is considered for an integral equation, which is obtained by the Taylor series expansion of the local inelastic strain around the point under consideration. The higher-order continuity of nonuniform rational B-splines (NURBS) functions used in isogeometric analysis are adopted here to implement in a numerical scheme. To demonstrate the validity of the proposed model, numerical examples in one and two dimensions are presented. Findings The proposed nonlocal elastic plastic damage model is able to predict the damage in an accurate manner. The numerical results are mesh independent. The nonlocal terms add a regularization to the model especially for strain softening type of materials. The consideration of nonlocality in inelastic strains is more meaningful to the physics of damage. The use of IGA framework and NURBS basis functions add to the nonlocal nature in approximations of the field variables. Research limitations/implications The method can be extended to 3D. The model does not consider the effect of temperature and the dissipation of energy due to temperature. The method needs to be implemented for more real practical problems and compare with experimental work. This is an ongoing work. Practical implications The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately. Social implications The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately. Originality/value The present work includes the formulation and implementation of a nonlocal damage plasticity model using an isogeometric discretization, which is the novel contribution of this paper. An implicit gradient enhancement is considered to the inelastic strain. During inelastic deformations, the proposed strain tensor partitioning allows the use of a distinct potential surface and distinct failure criterion for both damage and plasticity models. The use of NURBS basis functions adds to more nonlocality in the approximation.

Valley-selective energy transfer between quantum dots in atomically thin semiconductors

In monolayers of transition metal dichalcogenides the nonlocal nature of the effective dielectric screening leads to large binding energies of excitons. Additional lateral confinement gives rise to exciton localization in quantum dots. By assuming parabolic confinement for both the electron and the hole, we derive model wave functions for the relative and the center-of-mass motions of electron–hole pairs, and investigate theoretically resonant energy transfer among excitons localized in two neighboring quantum dots. We quantify the probability of energy transfer for a direct-gap transition by assuming that the interaction between two quantum dots is described by a Coulomb potential, which allows us to include all relevant multipole terms of the interaction. We demonstrate the structural control of the valley-selective energy transfer between quantum dots.

Investigation of DNA Breather Dynamics in A Model with Non-Local Inter-Site Interaction

A variant of the Peyrard-Bishop-Dauxois model is proposed, which takes account of the partially delocalized nature of DNA stacking interactions. It is shown that the nonlocal nature of the inter-site potential can lead to an increase in the local cooperativity of the base pairs' opening an increasing in the number of simultaneously opening adjacent nucleotide pairs during the denaturation bubble's nucleation. The process of the formation and propagation of mobile breathers excited by the initial displacements of a number of nucleotide pairs has been studied. It is revealed that taking account of the non-local coupling in the Peyrard-Bishop-Dauxois model, while maintaining the remaining parameters of the model, leads to a decrease in the speed of the mobile breather and an increase in the probability of nucleation of the denaturation bubble.

Existence of normalized solutions for nonlinear fractional Schrödinger equations with trapping potentials

In this paper, we study the existence, nonexistence and mass concentration of L2-normalized solutions for nonlinear fractional Schrödinger equations. Comparingwith the Schrödinger equation, we encounter some new challenges due to the nonlocal nature of the fractional Laplacian. We first prove that the optimal embedding constant for the fractional Gagliardo–Nirenberg–Sobolev inequality can be expressed by exact form, which improves the results of [17, 18]. By doing this, we then establish the existence and nonexistence of L2-normalized solutions for this equation. Finally, under a certain type of trapping potentials, by using some delicate energy estimates we present a detailed analysis of the concentration behavior of L2-normalized solutions in the mass critical case.