Nonlocal Form Research Articles

Josephson Critical Currents and Related Effects in Ultracold Atomic Superfluid Sytems

The Josephson and Proximity effects play a pivotal role in the design of superconducting devices for the implementation of quantum technology, ranging from the standard Al based to the more exotic twisted high-Tc junctions. Josephson critical currents have been recently investigated also in ultracold atomic systems where a potential barrier acts as a weak link. The unifying feature of the above systems, apart from being superconducting/superfluid, is the presence of spatial inhomogeneity, a feature that has to be properly taken into account in any theoretical approach employed to investigate them. In this work, we review the novel (dubbed LPDA for Local Phase Density Approximation) approach based on a coarse graining of the Bogoliubov–de Gennes (BdG) equations. Non-local and local forms of this coarse graining were utilized when investigating Proximity and Josephson effects. Moreover, the LPDA approach was further developed to include pairing fluctuations at the level of the non-self-consistent t-matrix approximation. The resulting approach, dubbed mLPDA (modified LPDA), can be used whenever inhomegeneity and fluctuations effects simultaneously play an important role.

Warriors from the south? Arrowheads from the Tollense Valley and Central Europe

Investigations in the Tollense Valley in north-eastern Germany have provided evidence of a large and violent conflict in the thirteenth century BC. Typological analysis of arrowheads from the valley (10 flint and 54 bronze specimens) and comparison with type distributions in Central Europe, presented here for the first time, emphasise the supra-regional nature of the conflict. While the flint arrowheads are typical for the local Nordic Bronze Age, the bronze arrowheads show a mixture of local and non-local forms, adding to the growing evidence for a clash between local groups and at least one incoming group from southern Central Europe.

Numerical modeling of earthquake-induced landslides using updated Lagrangian nonlocal general particle dynamics method

Developing a robust numerical method to model earthquake-induced landslides has long been a persistent challenge in the field of computational geotechnical engineering. Recently, the meshless methods based on nonlocal theory have piqued the interest of researchers. However, the application of nonlocal theory in seismic analysis is currently limited. This paper proposed a numerical framework based on the updated Lagrangian nonlocal general particle dynamics (UL-NGPD) method to analyze earthquake-induced landslide problems. The UL-NGPD method benefiting from the update support domain can capture the whole process of slope run-out induced by earthquakes. To enhance the numerical stability of the proposed method, several optimizing strategies are proposed. In the current framework, the seismic waves are input through the proposed boundary treatments of nonlocal form. Besides, a nonlocal friction model with velocity-weakening is proposed to accurately simulate the movement process of soils on a rocky sliding bed. The proposed framework is validated by the simulations of several classic problems, including the collapse of sand and the shake table test. The performance of the proposed approach is further demonstrated through simulating the landslides induced by earthquakes. The numerical results consistent with recorded data indicate that the UL-NGPD method has an excellent capacity to deal with earthquake-induced landslide problems.

Anomalous thresholds in B → (P, V)γ* form factors

We study the effects of anomalous thresholds on the non-local form factors describing the hadronization of the light-quark contribution to B → (P, V)γ* transitions. Starting from a comprehensive discussion of anomalous thresholds in the triangle loop function for different mass configurations, we detail how the dispersion relation for ππ intermediate states is affected by contour deformations mandated by the anomalous branch points. Phenomenological estimates of the size of the anomalous contributions to the form factors are provided with couplings determined from measured branching fractions and Dalitz plot distributions. Our key finding is that anomalous effects are suppressed on the ρ(770) resonance, while off-peak the effects can become as large as O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10%) of the full (light-quark-loop induced) non-local form factors. We comment on future generalizations towards higher intermediate states and the charm loop, outlining how the dispersive framework established in this work could help improve the non-local form factors needed as input for a robust interpretation of B → (P, V)ℓ+ℓ− decays.

Peridynamic computations of wave propagation and reflection at material interfaces

Peridynamics describes the material in a non-local form and is very suited for the simulation of dynamic fracture. However, one significant effect regarding dynamic fracture is the correct handling of elastic deformation, like the pressure and tension waves inside a body, due to dynamic boundary conditions like an impact or impulse. Many peridynamic material formulations have been developed with differences in this regard. This study investigates the elastic wave propagation characteristics of bond-based, ordinary state-based, continuum kinematics-inspired peridynamics and a local continuum consistent correspondence formulation. Multiple parameters of a longitudinal pressure wave inside an elastic bar are studied. While all formulations demonstrate adequate wave propagation handling, all except the correspondence formulation are sensitive to incomplete horizons. The local continuum consistent formulation does not suffer from the surface effect and models the wave propagation with perfect accuracy.

Effect of nonlocality on the dispersion relations of mechanical metamaterials

The advent of mechanical metamaterials, with their unconventional and programmable properties, has revolutionised the field of engineering across length scales. Their design remains an area of interest to researchers requiring careful analysis of unit cells so as to achieve desired mechanical and wave dispersion behaviour. While metamaterials are known to extract their unique properties from the internal geometry of the unit cells, the contributions of the constituent materials are typically accounted for via their local material properties in the form of Young’s modulus and Poisson’s ratio. In this article, we demonstrate that material nonlocality of the constituents can also play a crucial role in modulating the nontrivial properties of metamaterials. Such nonlocality can arise from various sources, such as finer scale inhomogeneity like defects, inclusions etc. Towards this, we propose a nonlocal continuum model by upscaling a discrete potential through a stochastic gradient estimator (SGE) interpreted herein as a generalised Cauchy–Born rule. The nonlocal parameters can also be estimated from experimental data by solving an inverse problem, similar to the estimation of constitutive parameters in classical continuum mechanics. The proposed model accurately captures the dispersion behaviour at the continuum level as compared to its discrete counterpart. We further incorporate the model within the transfer matrix method to derive the dispersion relations of a metabar as a function of the constituent material nonlocality. We envisage that the present study introduces a new handle in the form of constituent material nonlocality for designing architected metamaterials with unprecedented mechanical functionalities.

A peridynamic differential operator modeling approach for ceramic matrix composites microstructure with uniform or non-uniform discretization

Based on the theory of peridynamic differential operator (PDDO), a novel three-dimensional (3D) peridynamic (PD) model for isotropic and orthotropic material is proposed to investigate the elastic mechanical behaviors and stress distribution of Ceramic Matrix Composites (CMC) microstructure. The non-local expressions of strain and stress tensors are derived by employing PDDO and the classical constitutive equations. The bond forces in interface region crossing two different constituent materials are obtained by converting the partial differential terms into the non-local forms. The weak form of PD equations of motion is derived by using the principle of virtual work and PDDO. The validity of this approach is verified by predicting the elastic response and stress distributions of isotropic and orthotropic materials under uniaxial tension and pure shear deformation. Finally, simulations are conducted on a CMC microstructure with fiber and matrix under periodic boundary conditions. It is demonstrated that the current approach can effectively build 3D CMC microstructure with uniform or non-uniform discretization, and accurately predict the stress fields and effective elastic properties.

Peridynamics thermomechanical coupling simulation of damage in engineered cementitious composite-concrete bonding specimens under high temperature

The current application of Peridynamics (PD) models in addressing thermally induced failures within Engineered Cementitious Composites (ECC) and concrete bonding specimens is relatively limited. This study introduces a novel semi-discrete PD model for ECC and a random heterogeneous PD model for concrete. These models are grounded in the microscopic constitutive relationships between ECC and concrete materials and incorporate the strain softening behavior of cement-based materials. The effectiveness of the interface model is evaluated through splitting tensile tests on ECC-concrete bonding specimens, employing a series model alongside PD surface effects for material interface correction. Considering the performance degradation of materials at elevated temperatures, a PD thermo-mechanical coupling model, which integrates PD thermal diffusion and motion equations, is proposed to analyze the failure of ECC and concrete under high thermal loads. The validity of both the thermo-mechanical coupling and concrete heterogeneity models is confirmed via thermal cracking tests on heated concrete columns subjected to drilling. Lastly, considering the dynamic response of fire, the Navier-Stokes equation are reformulated into a non-local form utilizing the Peridynamic differential operator (PDDO) to simulate fire environment. A thermo-fluid-mechanical coupling model is developed, and applied to analyze ECC and concrete bonding specimens’ failure behaviors under fire scenarios.

Peridynamic differential operator for stress analysis of imperfect functionally graded porous sandwich beams based on refined zigzag theory

This study focuses on the stress analysis of imperfect functionally graded porous (FGP) sandwich beams using the Peridynamic Differential Operator (PDDO) and Refined Zigzag Theory (RZT). Functionally graded materials (FGMs) can be found in diverse engineering applications since they offer smooth transitions in the mechanical properties of distinct materials, unlike traditional composite materials. Micro-voids and porosities may appear inside the FGMs due to technical challenges during the manufacturing process of such materials. Therefore, understanding the stress variations of the FG sandwich beams with porosities/micro-voids, which are called imperfect FGMs, under loads is of vital importance. In order to achieve the porous configuration in the FG structures, the modified rule of mixtures is applied to calculate the effective material properties of FGMs. The RZT is very suitable for stress analysis of laminated composites, especially for thick and moderately thick beams. It contains only four kinematic variables and eliminates the use of the shear correction factors. In this study, the equilibrium equations of the RZT are solved by means of the PDDO for the stress analysis of imperfect FG sandwich beams having uniform and non-uniform porosity distributions. The PDDO transforms the differential equations into their nonlocal form, namely integral form, providing highly accurate approximations of the derivatives. A comprehensive PDDO analysis is performed for the investigation of the influence of the material variation, and even and uneven porosity distributions on the stress variations of the imperfect FG sandwich beams. It is noted that when the FG core exhibits soft material distributions, the effect of porosity is evident. The even type porosity distribution pattern is more influential on the axial displacement and stress variations in comparison with those of the uneven type porosity distribution pattern.

Nonlocal modelling of piezoelectric solid with cracks based on peridynamic differential operator

The paper establishes a nonlocal model for piezoelectric solids using the Peridynamic differential operator. The method transforms the displacement-electric potential equation, constitutive equation, and boundary conditions of piezoelectric solids from a local differential form to a nonlocal integral form. The solution for the displacement and electric potential distributions in piezoelectric solids is obtained using variational principles and the Lagrange multiplier method. The correctness and effectiveness of the model are validated through a comparison of the deformation analysis of piezoelectric solid square plates with analytical solutions. Analysis of piezoelectric solid square plates with edge cracks proves the applicability of this model for solving discontinuous problems. Furthermore, the paper explores the suitability of the model in analysing problems involving multiple cracks in piezoelectric solid plates, highlighting its capability to address defective piezoelectric solid problems. This model provides a new perspective for solving problems involving defects under electro-mechanical coupling conditions.

A non-ordinary state-based peridynamic model for creep–fatigue behavior and damage evolution

A peridynamic creep–fatigue model is proposed to study creep–fatigue mechanical responses and damage behaviors. A non-unified constitutive model is reformulated in a nonlocal form in the peridynamic-based framework. A probabilistic peridynamic damage criterion is proposed for characterizing creep–fatigue damage. The simulated mechanical responses are in good agreement with the results of creep–fatigue experiments conducted at high temperatures, which confirms the accuracy of the model. In addition, the damage evolution and morphology are well characterized by the model, and the damage mechanism is revealed. The model exhibits excellent potential for simulating nonlinear damage behaviors.

Non-factorisable contributions of strong-penguin operators in Λb→ Λℓ+ℓ− decays

We investigate for the first time a certain class of non-factorisable contributions of the four-quark operators O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}3−6 in the weak effective Hamiltonian to the Λb → Λℓ+ℓ− decay amplitude. We focus on the case where a virtual photon is radiated from one of the light constituents of the Λb baryon, in the kinematic situation of large hadronic recoil with an energetic Λ baryon in the final state. The effect on the suitably defined “non-local form factors” is calculated using the light-cone sum rule approach for a correlator with an interpolating current for the light Λ baryon. We find that this approach requires the introduction of new soft functions that generalise the standard light-cone distribution amplitudes (LCDAs) for the heavy Λb baryon. We give a heuristic discussion of their properties and a model that relates them to the standard LCDAs. Within this framework, we provide numerical results for the size of the non-local form factors considered.

Thermo-mechanical coupled peridynamics simulation of concrete failure under fire scenarios

A coupled thermo-mechanical bond-based peridynamical (PD) method is developed to simulate thermal cracking processes in concrete. Based on the bond-based PD heat conduction and motion equations, the PD differential operator (PDDO) is used to express the classical computational fluid dynamics basic equations in a non-local integral form, establishing a PD model for the thermo-mechanical coupling problems. In this model, concrete is considered a heterogeneous material composed of aggregates and mortar, with material parameters assumed to be temperature-dependent. The multi-rate explicit time integration scheme is proposed to overcome the multi-scale time problem in coupled thermo-mechanical systems. The model is applied to simulate the transient heat transfer problem of a homogeneous plate. The results show good agreement with the analytical solution, providing evidence for the correctness and accuracy of the proposed coupled numerical method. The damage behavior of the borehole heated concrete plate is analyzed, followed by the simulation of the damage to the concrete plate under a fire scenario. The numerical results accurately predict the temperature distribution within the heterogeneous concrete and the resulting material damage. This study provides new theoretical basis for the fire resistance design and high-temperature performance improvement of concrete materials and structures.

Probabilistic Characterization of Weakly Harmonic Maps with Respect to Non-Local Dirichlet Forms

AbstractWe characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemannian manifolds from the image of symmetric stable processes under fractional harmonic maps in a weak sense. Based on this characterization, we also consider the continuity of weakly harmonic maps along the paths of Markov processes and describe the condition for the continuity of harmonic maps by quadratic variations of martingales in some situations containing cases of energy minimizing maps.

Analyzing non-isothermal phase transition problems with natural convection using peridynamic differential operator

In this study, a developed model for non-isothermal phase transition with natural convection is proposed by using peridynamic differential operator (PDDO). The dimensionless governing equations of heat source approach and vorticity-stream function approach are reconstructed into the non-local integral form. The Euler forward difference is used for time integration. The application of the developed PDDO model extends to simulations involving pure phase transition, pure natural convection, and non-isothermal phase transition coupled with natural convection. The validity and accuracy of the developed non-isothermal phase transition model are verified by comparing the PDDO simulation results with results in published literature. This research provides a new alternative approach for simulating phase transition and convection problems.

Nonlocal anisotropic model for deformation and fracture using peridynamic operator method

This paper proposes a nonlocal anisotropic model for deformation and fracture based on peridynamic operator method. The classic anisotropic theory is reformulated from its local form into nonlocal form by using peridynamic operator method. The final solution formulation is developed by employing variational principles and Lagrange's equations. In the case of the circular interaction domain, this model can be regarded as a novel anisotropic ordinary state-based peridynamic model. Moreover, we present for the first time the energetic failure criterion for the weak anisotropic fracture. Unlike the existing anisotropic peridynamic models that consider only two fracture toughness constants for orthogonal orientation, the fracture toughness in this criterion is an orientation-dependent function. Additionally, we develop an implicit static solution procedure to investigate corresponding crack propagation problems. Several numerical examples demonstrate the effectiveness and ability of the proposed model in handling the deformation and fracture behaviours of anisotropic materials.

Validity and failure of the integral representation of Γ-limits of convex non-local functionals

We prove an integral-representation result for limits of non-local quadratic forms on H01(Ω), with Ω a bounded open subset of Rd, extending the representation on Cc∞(Ω) given by the Beurling-Deny formula in the theory of Dirichlet forms. We give a counterexample showing that a corresponding representation may not hold if we consider analogous functionals in W01,p(Ω), with p≠2 and 1<p⩽d.

Constructing Mixed Density Functionals for Describing Dissociative Chemisorption on Metal Surfaces: Basic Principles.

The production of a majority of chemicals involves heterogeneous catalysis at some stage, and the rates of many heterogeneously catalyzed processes are governed by transition states for dissociative chemisorption on metals. Accurate values of barrier heights for dissociative chemisorption on metals are therefore important to benchmarking electronic structure theory in general and density functionals in particular. Such accurate barriers can be obtained using the semiempirical specific reaction parameter (SRP) approach to density functional theory. However, this approach has thus far been rather ad hoc in its choice of the generic expression of the SRP functional to be used, and there is a need for better heuristic approaches to determining the mixing parameters contained in such expressions. Here we address these two issues. We investigate the ability of several mixed, parametrized density functional expressions combining exchange at the generalized gradient approximation (GGA) level with either GGA or nonlocal correlation to reproduce barrier heights for dissociative chemisorption on metal surfaces. For this, seven expressions of such mixed density functionals are tested on a database consisting of results for 16 systems taken from a recently published slightly larger database called SBH17. Three expressions are derived that exhibit high tunability and use correlation functionals that are either of the PBE GGA form or of one of two limiting nonlocal forms also describing the attractive van der Waals interaction in an approximate way. We also find that, for mixed density functionals incorporating GGA correlation, the optimum fraction of repulsive RPBE GGA exchange obtained with a specific GGA density functional is correlated with the charge-transfer parameter, which is equal to the difference in the work function of the metal surface and the electron affinity of the molecule. However, the correlation is generally not large and not large enough to obtain accurate guesses of the mixing parameter for the systems considered, suggesting that it does not give rise to a very effective search strategy.

Orchestrating the impact of antisites and vacancy defects on the elastic and optoelectronic properties of boron arsenide.

Cubic boron arsenide (c-BAs), a semiconducting material with ultra-high thermal conductivity and carrier mobilities, has been studied using first-principles calculation. This study examined the elastic and optoelectronic properties of c-BAs. The challenge of subphase boron (B) formation in bulk form owing to the volatile nature of arsenic (As) makes it mandatory to calculate its optoelectronic properties, by producing vacancies and antisite defects with BAs (As atom on a B site) and AsB (B atom on an As site). The mechanical properties including bulk (B), shear (G) moduli, and Poison's ratio of all the systems were studied. It was found that mechanical instability of the structure is observed for the overall vacancy creation, arsenic substitution, and mutual antisite defects. Further, pristine c-BAs showed an indirect bandgap of 1.48eV. Defect formation reduces the bandgap and shifts the absorption peaks, which improves the overall optoelectronic properties of the host material. In addition, B vacancy formation shows the maximum optical absorption and reflectivity and low energy loss, suggesting its potential applications for optoelectronic devices. The obtained anticipated data from this study is for the optoelectronic and elastic properties of c-BAs, for the device applications in photonics and electronics. In this paper, the elastic and optoelectronic properties of the pristine and defected c-BAs were systematically investigated using the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA). The SIESTA program uses pseudopotentials in the norm-conserving nonlocal forms and pseudo-atomic orbital (PAO) basis set with a double-zeta potential (DZP) which are fundamental for calculating the Hamiltonian and overlap matrices in O(N) operations.

Magnetogenesis in Non-Local Models during Inflation

The generation of magnetic fields during the inflation in an electromagnetic model with a non-local form factor in Maxwell’s action is studied. The equations of motion for the electromagnetic field are derived and solved. It is found that the conformal symmetry breaking due to the non-local form factor does not lead to the generation of magnetic fields during the inflation in the absence of an interaction with the inflaton field. If such a coupling takes place, then the presence of the form factor inhibits the generation of primordial magnetic fields compared to the case where the non-local form factor is absent.