Nonlocal Effects Research Articles

A unified nonlocal method for capturing discontinuous and multi‐physical behaviors of quasi‐brittle materials

AbstractA unified nonlocal method (UNM) is developed to simulate discontinuous and multi‐physical coupling dynamic behaviors for quasi‐brittle materials. In the proposed method, unified nonlocal momentum equations and constitutive laws are proposed to capture the nonlocal fluid transport effect and loading‐rate effect of quasi‐brittle materials. A general multiscale framework, which couples the proposed nonlocal method and the finite element method (FEM), is presented to accelerate the computational efficiency. The effectiveness and accuracy of this method are verified by comparing its results with experimental observations. Numerical examples show that the proposed model can well simulate the discontinuous and multi‐physical behaviors of quasi‐brittle materials, which can serve an effective numerical method for the simulation of engineering problems such as failure of concrete structures.

Effect of the microstructure-dependent nonlocality on acoustic black holes

To obtain a well-damped structure, the concept of “acoustic black hole (ABH)” is proposed to trap bending waves at the edge of the wedge shape. However, in the current practice, the remarkable effect of intrinsic lengths is not incorporated. This study aims to reveal the remarkable contribution due to the interplay between intrinsic and extrinsic lengths, which is of fundamental scientific interest. The nonlocal theory is employed to examine the dynamical behaviors of the ABH incorporating the effect of intrinsic lengths. The theoretical model is established for microstructure-dependent power-law plates, and the solution method is developed for analyzing the reflection coefficient of microstructure-dependent power-law plates and bars. It is found that the effect of the microstructure-dependent nonlocality becomes significant and the ABH shows a better absorption of acoustic energy when the nonlocal intrinsic length tends to be lager. Furthermore, the reflection coefficient of traditional works is underestimated. Also, the relationship between the reflection coefficient and wedge truncation length, and frequency is discussed in detail.

Investigation on the thermoelastic response of a porous microplate in a modified fractional-order heat conduction model incorporating the nonlocal effect

In recent years, the application of porous materials in practical engineering has become increasingly common. Under extreme thermal conditions, how to accurately describe the heat conduction and structural response of porous materials is a key issue in the structural safety and functional design of porous materials. Among them, it is particularly important to consider the size-dependent and memory-dependent effects for small-sized structures or microdevices of porous materials. To address these issues of porous structures and to guide their applications as well as optimization, this paper first investigates the thermoelastic transient response of porous microplates subjected to thermal and stress shocks at the left boundary based on the Atangana-Baleanu (AB) fractional-order generalized thermoelastic theory by considering nonlocal effects and fractional-order strain, which is combined with the thermoelasticity theory of porous materials and the dual-phase-lag (DPL) heat conduction model. The governing equations are then established and solved using the Laplace transform and its numerical inversion. Finally, the effects of newly defined fractional order parameters, nonlocal parameters and the initial magnitude of the mechanical shock on the dimensionless temperature, volume fraction field, displacement and stress distribution are discussed and displayed graphically.

Non-local dielectric effects in nanoscience.

The physical properties of charges and excitations in nanoscale materials are influenced both by the dielectric properties of the material itself and the surrounding environment. This non-local dielectric effect was first discussed in the context of molecules in solvents over a century ago. In this perspective, we discuss non-local dielectric effects in zero-dimensional, one-dimensional, and two-dimensional nanoscale systems.

Dynamic of Some Relapse in a Giving Up Smoking Model Described by Fractional Derivative

Smoking is associated with various detrimental health conditions, including cancer, heart disease, stroke, lung illnesses, diabetes, and fatal diseases. Motivated by the application of fractional calculus in epidemiological modeling and the exploration of memory and nonlocal effects, this paper introduces a mathematical model that captures the dynamics of relapse in a smoking cessation context and presents the dynamic behavior of the proposed model utilizing Caputo fractional derivatives. The model incorporates four compartments representing potential, persistent (heavy), temporally recovered, and permanently recovered smokers. The basic reproduction number R0 is computed, and the local and global dynamic behaviors of the free equilibrium smoking point (Y0) and the smoking-present equilibrium point (Y*) are analyzed. It is demonstrated that the free equilibrium smoking point (Y0) exhibits global asymptotic stability when R0≤1, while the smoking-present equilibrium point (Y*) is globally asymptotically stable when R0>1. Additionally, analytical results are validated through a numerical simulation using the predictor–corrector PECE method for fractional differential equations in Matlab software.

Non-local effect of eccentrically simply supported beam on free vibration

Based on the Euler-Bernoulli beam theory, the coupling effect between bending vibration mode shape and longitudinal vibration mode shape of the beam is analyzed when the beam is supported by eccentric simply supported. Under the assumption of small deformation, the vibration control equations and the coupling boundary conditions are obtained through Hamilton's principle and the principle of virtual work variation. The numerical results under three different boundary conditions are given. It shows that the natural frequencies of the beam vary with the eccentricity distances are in complete agreement with the results obtained from finite element analysis and literature. The results strongly proved the validity and correctness of the coupling method in this paper. It also indicates that eccentric simply supported constraints have non-local effects.

Dark Matter in Fractional Gravity II: Tests in Galaxy Clusters

Recently, in Benetti et al. (Astrophys. J. 2023, 949, 65), we suggested that the dark matter (DM) component in galaxies may originate fractional gravity. In such a framework, the DM component exists, but the gravitational potential associated to its density distribution is determined by a modified Poisson equation including fractional derivatives (i.e., derivatives of noninteger type), which are meant to describe nonlocal effects; as such, this scenario is different from theories where baryonic matter emulates DM-like effects via modifications of gravity (e.g., MONDian frameworks). In Benetti et al., we showed that fractional gravity worked very well for reproducing the kinematics of disk-dominated galaxies, especially dwarfs; there is also preliminary evidence that the strength of fractional effects tends to weaken toward more massive systems. Here, we aim to test fractional gravity in galaxy clusters, with a twofold aim: (i) perform an independent sanity check that it can accurately describe such large and massive structures; (ii) derive a clear-cut trend for its strength in systems with different DM masses. To this purpose, we forward model the density and pressure distributions of the intracluster medium (ICM), working out the hydrostatic equilibrium equation in fractional gravity. Then, we perform a Bayesian analysis of the X-COP galaxy cluster sample and infer constraints on the fractional gravity parameters, for individual clusters as well as stacked clusters. We find that fractional gravity performs remarkably well in modeling the ICM profiles for the X-COP sample. We also check that the DM concentration vs. mass relation is still consistent with the expectations of N-body simulations in the standard cosmological scenario. Finally, we confirm the weakening of the fractional gravity effects toward more massive systems and derive the overall scaling of the fractional gravity parameters from dwarf galaxies to massive clusters, spanning six orders of magnitude in DM mass. Such an overall trend implies that fractional gravity can substantially alleviate the small-scale issues of the standard DM paradigm, while remaining successful on large cosmological scales.

Thermo-hydro-mechanical nonlocal response on porous deep-sea sediments under vibration of mining vehicle

The excessive deformation of deep-sea sediments caused by the vibration of the mining machine will adversely affect the efficiency and safety of mining. This paper reports the study of coupled thermo-hydro-mechanical problem for saturated porous deep-sea sediments, subjected to the vibration of the mining vehicle. Based on nonlocal Moore–Gibson–Thompson thermoelastic theory and Darcy’s law, the model for thermo-hydro-mechanical dynamic response for saturated porous deep-sea sediments under the vibration of mining vehicle is established. Analytical solutions for vertical displacement, excess pore water pressure, vertical stress, temperature and the change in the volume fraction field have been obtained on implementing the normal mode analysis, and the numerical results have been depicted graphically. The result provides the direction on how the vibration frequency and the loading amplitude can affect the physical quantities of the foundation of the seabed. The influence of nonlocality and memory effect on the seabed is also reported.

A general finite element based non-local theory for the medium-long-range correlation of metallic glasses

Mean-field theory is extensively used in statistical physics, solid-state physics, and biophysics to compress a large number of interacting multi-body problems into an effective single-body problem, providing some insight into the system’s behavior at a lower computing cost. Nonetheless, the mean-field approximation always suppresses the non-local effects, hence obscuring the underlying mechanisms involving unit interactions between microscopic events, such as competition, co-evolution, and self-organized criticality. This paper presents a general, non-local mean-field approximation for the medium-long-range correlation of materials based on the finite element method, which has excellent compatibility and scalability with existing theories. It ties the evolution of a deformation unit to the status of other spatial domain elements, which is analogous to the fundamental principle of cellular automata. When applied to metallic glasses, the model demonstrates excellent spatial–temporal agreement between the shear band evolution measurements and simulation findings. Excitingly, the self-organized criticality of amorphous systems and the self-adaptive evolution mechanism of shear bands are realized in both two and three dimensions for the first time. Without restriction to amorphous systems, this work explores the application of mean-field theories to non-local phenomena. Future research into new mathematical types of medium-long range interaction is conceivable through multiscale simulation techniques.

A size-dependent meshfree approach for magneto-electro-elastic functionally graded nanoplates based on nonlocal strain gradient theory

In this paper, we introduce a novel size-dependent meshfree approach for analyzing free vibrations of magneto-electro-elastic (MEE) functionally graded (FG) nanoplates. This approach combines the nonlocal strain gradient theory (NSGT), the higher-order shear deformation theory (HSDT), and meshfree method for the first time. MEE materials are essentially mixed by the barium titanate and cobalt ferrite which are definitely coupled by both piezoelectric and piezomagnetic effects. Our approach captures both the nonlocal and strain gradient effects in nanoplates, which result in the reduced stiffness and increased stiffness, respectively, by adjusting two parameters. The kind of effective material properties of MEE-FG nanoplates are expressed using a power-law scheme. The coupled governing equations, based on the principle of extended virtual displacement, are solved using the moving Kriging (MK) meshfree method. Numerical examples are given to investigate the effect of geometrical parameters, initial electric voltage, power index, initial magnetic potential, strain gradient parameter, and nonlocal parameter on the natural frequency of MEE-FG nanoplates.

Distillation of non-locality in porous solids

Non-local interactions are intrinsic to multiscale heterogeneous solids. The strength of the interactions exhibits a position-dependent character whose spatial distribution strongly correlates with the underlying microstructure. In this work, a variable-order fractional calculus-based framework to distill the position-dependent non-local effects is developed. By considering the example of porous plates, theoretical and numerical analyses will illustrate the ability of variable-order mechanics to enable parsimonious and causal models via a synthetic variable-order map that naturally measures the heterogeneous non-locality induced by the microstructure; in other terms, the non-classical role of the microstructure in determining the macroscopic response. The characteristic measure for non-locality, different from the local entanglement resulting from the porosity map, allows distillation of the macroscopic non-locality, analogous to quantum non-locality distillation. The macroscopic distillation also enables the additivity of the order map, that is the ability of assembled order maps to capture the response of combined porous plates.

Precipitation governing vegetation patterns in an arid or semi-arid environment.

In an arid or semi-arid environment, precipitation plays a vital role in vegetation growth. Recent researches reveal that the response of vegetation growth to precipitation has a lag effect. To explore the mechanism behind the lag phenomenon, we propose and investigate a water-vegetation model with spatiotemporal nonlocal effects. It is shown that the temporal kernel function does not affect Turing bifurcation. For better understanding the influences of lag effect and nonlocal competition on the vegetation pattern formation, we choose some special kernel functions and obtain some insightful results: (i) Time delay does not trigger the vegetation pattern formation, but can postpone the evolution of vegetation. In addition, in the absence of diffusion, time delay can induce the occurrence of stability switches, while in the presence of diffusion, spatially nonhomogeneous time-periodic solutions may emerge, but there are no stability switches; (ii) The spatial nonlocal interaction may trigger the pattern onset for small diffusion ratio of water and vegetation, and can change the number and size of isolated vegetation patches for large diffusion ratio. (iii) The interaction between time delay and spatial nonlocal competition may induce the emergence of traveling wave patterns, so that the vegetation remains periodic in space, but is oscillating in time. These results demonstrate that precipitation can significantly affect the growth and spatial distribution of vegetation.

Hydrodynamic Modification in Channels Densely Populated with Aquaculture Farms

We predicted small-scale hydrodynamics, including the effect of the aquaculture farming infrastructure, for a region within the group of salmon farm concessions identified in the Chilean regulation as ACS-7. The geographical region corresponds to the Caucahue Channel, composed of two branches connected by a constriction on Caucahue Island, Inland Sea of Chiloe, Chilean Patagonia. The prediction methodology considers the interaction of a regional ocean model and a high-resolution local CFD model. The model prediction was validated using available data from ADCP. We find that the Caucahue Channel is characterized by a complex circulation and hydrodynamics, including an unstable shear flow, with meanders and turbulent structures, and retention zones. Results show the aquaculture infrastructure has a non-local hydrodynamic effect. Differences in horizontal and vertical velocity can be quite significant even far from aquaculture centers, reaching up to 300% and 170%, respectively, in simulations without taking its effects into account. The useful characteristics of this predictive approach and its potential use in particle tracking and species diffusion prediction allow for the use of projecting as a tool for strengthening the environmental and productive management of this industry.

Traveling wave solutions in a nonlocal dispersal SIR epidemic model with nonlocal time-delay and general nonlinear incidences

This paper investigates a nonlocal dispersal epidemic model under the multiple nonlocal distributed delays and nonlinear incidence effects. First, the minimal wave speed [Formula: see text] and the basic reproduction number [Formula: see text] are defined, which determine the existence of traveling wave solutions. Second, with the help of the upper and lower solutions, Schauder’s fixed point theorem, and limiting techniques, the traveling waves satisfying some asymptotic boundary conditions are discussed. Specifically, when [Formula: see text], for every speed [Formula: see text] there exists a traveling wave solution satisfying the boundary conditions, and there is no such traveling wave solution for any [Formula: see text] when [Formula: see text] or [Formula: see text] when [Formula: see text]. Finally, we analyze the effects of nonlocal time delay on the minimum wave speed.

Porosity-dependent wave propagation in multi-directional functionally graded nanoplate with nonlinear temperature-dependent characteristics on Kerr-type substrate

The present study investigates the wave propagation characteristics of porous, multi-directional, functionally graded (FG) nanoplates embedded in a Kerr-elastic substrate. A first-order shear deformation model (FSDM) and the nonlocal strain gradient approach (NSGA) are utilized to address this issue. The NSGA is enhanced by considering softening and hardening material effects, leading to improved accuracy in the obtained results. In accordance with the law of mixing, the material properties of the nanoplates exhibit nonlinear temperature-dependent variations along the structural axes. Both even and uneven porosity profiles are considered in this study. The nonclassical governing equations for the proposed structure are derived using Hamilton's approach. The phase velocity and wave frequency are determined through the analytical solution of an eigenvalue problem, which depends on the wave number. The dispersion properties of waves in porous FG nanoplates are examined with respect to various factors, including porosity distributions, wave numbers, nonlocal and strain gradient effects, elastic foundation coefficients, and volume fraction index. The main findings of the study indicate that increasing the volume fraction index in the thickness direction leads to a decrease in the phase velocity and frequency of wave propagation in a porous FG nanoplate for a given wave number. Additionally, regardless of the porosity pattern, an increase in the porosity coefficient results in a decrease in wave frequency and phase velocity.

Magneto-thermoelastic problem of semi-infinite body considering non-local and memory effects under hydrostatic pressure

Magneto-thermoelastic problem of semi-infinite body considering non-local and memory effects under hydrostatic pressure

Apparent dark matter as a non-local manifestation of emergent gravity

We disclose a close correspondence between Verlinde’s Emergent Gravity (VEG) theory and the non-local gravity theories. Such non-local effects can play crucial role at small distances as well as in large scale structures. In particular, we argue that the emergent gravity effectively is a manifestation of the entanglement entropy and can modify Newton’s law of gravity as well as address the flat rotation curves of spiral galaxies. In the cosmological setup, we have considered three different models for the apparent dark matter density. In the first model, we have found that Friedmann equations get modified due to the presence of the apparent dark matter (DM) in such a way that Newton’s constant of gravity shifts as G→G1+ζ, where ζ is a dimensionless small parameter. Using the flat rotating curves we estimate ζ∼10−7. For such a model, we find out that by rescaling the radial coordinate, r, the curvature space constant, k, and the scale factor of the universe, a, the effect of apparent DM can change the geometry of the universe and can shift the curvature space constant as k⋆=k(1−ζ). To this end, we study a more realistic model with evolving densities where we obtain the ΛCDM model in Verlinde’s gravity and comment on the Hubble tension problem with evolving densities.

Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses.

According to recent new definitions, a multiparty behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. The new definitions differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources. Here, we categorize the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks, highlighting the intimate link to device-independent witnesses of network effects. A key finding is the existence of a behavior in the simplest nontrivial multipartite measurement scenario (three parties, two measurement settings, and two outcomes) that cannot be simulated in a bipartite network prohibiting entangled measurements and superquantum resources-thus witnessing the most general form of GMNL-but can be simulated with bipartite-only quantum states with an entangled measurement, indicating an approach to device-independent certification of entangled measurements with fewer settings than in previous protocols. Surprisingly, we also find that this (3,2,2) behavior, as well as the others previously studied as device-independent witnesses of entangled measurements, can all be simulated at a higher echelon of the GMNL hierarchy that allows superquantum bipartite resources while still prohibiting entangled measurements. This poses a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.

Nonlocality and entanglement in measured critical quantum Ising chains

We study the effects of measurements, performed with a finite density in space, on the ground state of the one-dimensional transverse-field Ising model at criticality. Local degrees of freedom in critical states exhibit long-range entanglement, and as a result, local measurements can have highly nonlocal effects. Our analytical investigation of correlations and entanglement in the ensemble of measured states is based on properties of the Ising conformal field theory (CFT), where measurements appear as $(1+0)$-dimensional defects in the $(1+1)$-dimensional Euclidean spacetime. So that we can verify our predictions using large-scale free-fermion numerics, we restrict ourselves to parity-symmetric measurements. To describe their averaged effects analytically we use a replica approach, and we show that the defect arising in the replica theory is an irrelevant perturbation to the Ising CFT. Strikingly, the asymptotic scalings of averaged correlations and entanglement entropy are therefore unchanged relative to the ground state. In contrast, the defect generated by postselecting on the most likely measurement outcomes is exactly marginal. We then find that the exponent governing postmeasurement order parameter correlations, as well as the ``effective central charge'' governing the scaling of entanglement entropy, vary continuously with the density of measurements in space. Our work establishes connections between the effects of measurements on many-body quantum states and of physical defects on low-energy equilibrium properties.

The impact of urban irrigation on the temperature-carbon feedback in U.S. cities

Urban areas experience numerous environmental challenges, among which the anthropogenic emissions of heat and carbon are two major contributors, the former is responsible for the notorious urban heat effect, the latter longterm climate changes. Moreover, the exchange of heat and carbon dioxide are closely interlinked in the built environment, and can form positive feedback loops that accelerate the degradation of urban environmental quality. Among a handful countermeasures for heat and carbon mitigation, urban irrigation is believed to be effective in cooling, yet the understanding of its impact on the co-evolution of heat and carbon emission remains obscure. In this study, we conducted multiphysics urban climate modeling for all urban areas in the contiguous United States, and evaluated the irrigation-induced cooling and carbon mitigation. Furthermore, we assessed the impact of urban irrigation on the potential heat-carbon feedback loop, with their strength of coupling quantified by an advanced causal inference method using the convergent cross mapping algorithms. It is found that the impact of urban irrigation varies vastly in geographically different cities, with its local and non-local effect unraveling distinct pathways of heat-carbon feedback mechanism.