Nonlocal Effects Research Articles

Vibration of embedded restrained composite tube shafts with nonlocal and strain gradient effects

Torsional vibration response of a circular nanoshaft, which is restrained by the means of elastic springs at both ends, is a matter of great concern in the field of nano-/micromechanics. Hence, the complexities arising from the deformable boundary conditions present a formidable obstacle to the attainment of closed-form solutions. In this study, a general method is presented to calculate the torsional vibration frequencies of functionally graded porous tube nanoshafts under both deformable and rigid boundary conditions. Classical continuum theory, upgraded with nonlocal strain gradient elasticity theory, is employed to reformulate the partial differential equation of the nanoshaft. First, torsional vibration equation based on the nonlocal strain gradient theory is derived for functionally graded porous nanoshaft embedded in an elastic media via Hamilton’s principle. The ordinary differential equation is found by discretizing the partial differential equation with the separation of variables method. Then, Fourier sine series is used as the rotation function. The necessary Stokes' transformation is applied to establish the general eigenvalue problem including the different parameters. For the first time in the literature, a solution that can analyze the torsional vibration frequencies of functionally graded porous tube shafts embedded in an elastic media under general (elastic and rigid) boundary conditions on the basis of nonlocal strain gradient theory is presented in this study. The results obtained show that while the increase in the material length scale parameter, elastic media and spring stiffnesses increase the frequencies of nanoshafts, the increase in the nonlocal parameter and functionally grading index values decreases the frequencies of nanoshafts. The detailed effects of these parameters are discussed in the article.

Apparent and emergent dark matter around a Schwarzschild black hole

Inspired by the two different dark matter frameworks that were studied recently: one that arises from the non-local effects of entanglement entropy as emergent gravity (characterized by the parameter ξ(M), and zero-point scale length l), and one from dark energy viewed as a superconducting medium (characterized by η(M), and screening length parameter λG), two black hole solutions spherically surrounded with these dark matter models were derived. The effect of these two frameworks on SMBH was analyzed through the resulting deviations in the null regions and the black hole shadow. In addition, constraints to the parameters ξ and η (at 3σ level) were found using the available EHT data for Sgr. A* and M87*. These constraints allow one to deduce the effective mass M, which causes uncertainties in the measurement. On the other hand, if the effective mass is known, one can also deduce the constants associated with ξ, and η. The former framework also introduces an Appell function, a hypergeometric function of two variables that separately allows the analysis of macroscopic and (hypothetical) microscopic black holes. This first framework was found to decrease the radii of the null regions respective to the Schwarzschild counterpart. The shadow radius, however, behaves reversibly. The result of the numerical analysis for the latter framework revealed increased values for the photonsphere and shadow radii. Remarkably, the study also showed that for SMBHs, the amplifying effects of λG are stronger than the scale length l. Finally, results of constraints, as an example, for the upper bound in ξ for M87* indicated that the effective mass causing the deviation was around 2.4×1020M⊙ given that the observed Milgrom’s constant is 5.4×10−10m/s2.

Effect of the porous structure on the hygrothermal vibration analysis of functional graded nanoplates using nonlocal high-order continuum plate model

This study delves into the thermomechanical vibration behavior of functionally graded porous nanoplates under extreme thermal temperature and humidity conditions. The equation of motion of the nanoplate was derived using advanced theories in elasticity and deformation. The nanoplate consists of metal (SUS304) on the bottom surface and ceramic (Ni3S4) on the top surface, with the material distribution changing according to the power law across the plate thickness. The nanoplate was modeled with uniform and symmetric distributions of porosity reaching as high as 60%. Upon incorporating the thermal and moisture loads from the humid surroundings into the equations of motion derived from Hamilton's principle, the equations were solved using Navier's method and simplified to the eigenvalue equation. Analyzed within a broad framework are the thermomechanical vibration behavior of the nanoplate, temperature impact, humidity influence, porosity and its distribution, material grading parameter effects, and nonlocal integral elasticity effects. Observations indicate that variations in thermal temperature, humidity, and nonlocal parameters can lower the thermomechanical vibration frequency of the nanoplate, whereas porosity has the opposite effect. The effects mentioned are influenced by factors, such as the porosity ratio, porosity distribution, material ratios, and the size of the nonlocal parameter in the plate. The primary objective of this work is to uncover the nonlinear frequency response of nanoplates with high porosity in conditions characterized by high temperature and humidity.

Local and Nonlocal Biophysical Effects of Historical Land Use and Land Cover Changes in CMIP6 Models and the Intermodel Uncertainty

AbstractLand use and land cover changes (LULCCs) can influence surface temperature through local and nonlocal biophysical processes, which remain inadequately addressed. In this study, we separate the local and nonlocal effects of historical (1850–2014) LULCCs based on model outputs from the Coupled Model Intercomparison Project Phase 6. We also attempt to explore the sources of intermodel differences in the effects of LULCCs. The multimodel mean shows a cooling effect of −0.05°C (with an intermodel range of −0.24–0.06°C) at the global scale due to cropland and pastureland expansion, consisting of dominant nonlocal cooling of −0.06°C (with an intermodel range of −0.26–0.06°C) and slight local warming of 0.01°C (with an intermodel range of −0.01–0.05°C). The modeling results show some clear consistency in the effects of LULCCs despite considerable intermodel uncertainties. The local effects cause warming at low latitudes and cooling in boreal regions via changes in upward shortwave radiation and sensible and latent heat fluxes. The nonlocal effects mainly cause cooling via decreases in downward longwave radiation and increases in upward shortwave radiation. Intermodel differences in the total effects are dominated by those in the nonlocal effects, which are further attributed to divergent changes in downward longwave radiation and sensible heat flux across the models. This study highlights the importance of the nonlocal effects of LULCCs in terms of strength and intermodel uncertainty, with implications for designing land‐based solutions aimed at climate change mitigation.

The Duration of Non-Local Muscle Fatigue Effects.

Non-local muscle fatigue (NLMF) refers to a transient decline in the functioning of a non-exercised muscle following the fatigue of a different muscle group. Most studies examining NLMF conducted post-tests immediately after the fatiguing protocols, leaving the duration of these effects uncertain. The aim of this study was to investigate the duration of NLMF (1-, 3-, and 5-minutes). In this randomized crossover study, 17 recreationally trained participants (four females) were tested for the acute effects of unilateral knee extensor (KE) muscle fatigue on the contralateral homologous muscle strength, and activation. Each of the four sessions included testing at either 1-, 3-, or 5-minutes post-test, as well as a control condition for non-dominant KE peak force, instantaneous strength (force produced within the first 100-ms), and vastus lateralis and biceps femoris electromyography (EMG). The dominant KE fatigue intervention protocol involved two sets of 100-seconds maximal voluntary isometric contractions (MVIC) separated by 1-minute of rest. Non-dominant KE MVIC forces showed moderate and small magnitude reductions at 1-min (p < 0.0001, d = 0.72) and 3-min (p = 0.005, d = 0.30) post-test respectively. The KE MVIC instantaneous strength revealed large magnitude, significant reductions between 1-min (p = 0.021, d = 1.33), and 3-min (p = 0.041, d = 1.13) compared with the control. In addition, EMG data revealed large magnitude increases with the 1-minute versus control condition (p = 0.03, d = 1.10). In summary, impairments of the non-exercised leg were apparent up to 3-minutes post-exercise with no significant deficits at 5-minutes. Recovery duration plays a crucial role in the manifestation of NLMF.

On the Pair-instability Supernova Origin of J1010+2358* * Based on observations made with the Very Large Telescope (VLT) of the ESO at the La Silla Paranal Observatory under the program ID 112.26WJ.001

The first (Population III) stars formed only out of H and He and were likely more massive than present-day stars. Massive Population III stars in the range 140–260 M ⊙ are predicted to end their lives as pair-instability supernovae (PISNe), enriching the environment with a unique abundance pattern, with high ratios of odd to even elements. Recently, the most promising candidate for a pure descendant of a zero-metallicity massive PISN (260 M ⊙) was discovered by the LAMOST survey, the star J1010+2358. However, key elements to verify the high PISN contribution, C and Al, were missing from the analysis. To rectify this, we obtained and analyzed a high-resolution Very Large Telescope/UVES spectrum, correcting for 3D and/or non-local thermodynamic equilibrium effects. Our measurements of both C and Al give much higher values (∼1 dex) than expected from a 260 M ⊙ PISN. Furthermore, we find significant discrepancies with the previous analysis and therefore a much less pronounced odd–even pattern. Our results show that J1010+2358 cannot be a pure descendant of a 260 M ⊙ PISN. Instead, we find that the best-fit model consists of a 13 M ⊙ Population II core-collapse supernova combined with a Population III supernova. Alternative, less favored solutions ( χ2/χbest2≈2.3 ) include a 50% contribution from a 260 M ⊙ PISN or a 40% contribution from a Population III Type Ia supernova. Ultimately, J1010+2358 is certainly a unique star giving insights into the earliest chemical enrichment; however, this star is not a pure PISN descendant.

Incorporating non-local anyonic statistics into a graph decomposition

In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev’s toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.

Electromechanical coupling characteristics of multilayered piezoelectric quasicrystal plates in an elastic medium

AbstractQuasicrystals (QCs) have attracted tremendous attention of researchers for their unusual properties. In this paper, an exact electric‐elastic solution of the simply supported and multilayered three‐dimensional (3D) cubic piezoelectric quasicrystal (PQC) nanoplate with the nonlocal effect is derived. Based on the basic elasticity equation of 3D QCs, we construct the linear eigenvalue system in terms of the pseudo‐Stroh formalism, from which the general solutions of the extended displacements and stresses in any homogeneous layer can be obtained. The two‐parameter foundation model is utilized to simulate the interaction between the nanoplate and elastic medium. The propagator matrices are employed to connect the field variables at the upper interface to those at the lower interface of each layer. Based on the boundary conditions of the upper and lower surfaces of the laminate and foundation model, the solutions are employed to derive from the global propagator matrix. Compared with the conventional propagator matrix method, a new propagator method is reestablished to deal with numerical instabilities of the case of large aspect ratio and high‐order frequencies for QC laminates. Finally, typical numerical examples are presented to illustrate the influence of nonlocal parameters and elastic medium coefficients on phonon, phason, and electric variables of 3D PQC nanoplates.

DESIGN AND IMPLEMENTATION OF FUZZY-FRACTIONAL WU–ZHANG SYSTEM USING HE–MOHAND ALGORITHM

In recent years, fuzzy and fractional calculus are utilized for simulating complex models with uncertainty and memory effects. This study is focused on fuzzy-fractional modeling of (2+1)-dimensional Wu–Zhang (WZ) system. Caputo-type time-fractional derivative and triangular fuzzy numbers are employed in the model to observe uncertainties in the presence of non-local and memory effects. The extended He–Mohand algorithm is proposed for the solution and analysis of the current model. This approach is based on homotopy perturbation method along with Mohand transformation. Effectiveness of proposed methodology at upper and lower bounds is confirmed through residual errors. The theoretical convergence of proposed algorithm is proved alongside numerical computations. Existence and uniqueness of solution are also theoretically proved in the given paper. Current investigation considers three types of fuzzifications i.e. fuzzified equations, fuzzified conditions, and finally fuzzification in both model and conditions. Different physical aspects of WZ system profiles are analyzed through 2D and 3D illustrations at upper and lower bounds. The obtained results highlight the impact of uncertainty on WZ system in fuzzy-fractional space. Hence, the proposed methodology can be used for other fuzzy-fractional systems for better accuracy with lesser computational cost.

A reduced kinetic method for investigating non-local ion heat transport in ideal multi-species plasmas

A reduced kinetic method (RKM) with a first-principles collision operator is introduced in a 1D2V planar geometry and implemented in a computationally inexpensive code to investigate non-local ion heat transport in multi-species plasmas. The RKM successfully reproduces local results for multi-species ion systems and the important features expected to arise due to non-local effects on the heat flux are captured. In addition to this, novel features associated with multi-species, as opposed to single species, cases are found. Effects of non-locality on the heat flux are investigated in mass and charge symmetric and asymmetric ion mixtures with temperature, pressure, and concentration gradients. In particular, the enthalpy flux associated with diffusion is found to be insensitive to sharp pressure and concentration gradients, increasing its significance in comparison to the conductive heat flux driven by temperature gradients in non-local scenarios. The RKM code can be used for investigating other kinetic and non-local effects in a broader plasma physics context. Due to its relatively low computational cost it can also serve as a practical non-local ion heat flux closure in hydrodynamic simulations or as a training tool for machine learning surrogates.

Optoelectronically controlled spin-valley filter and nonlocal switch based on an asymmetrical silicene magnetic superconducting heterostructure

We investigate the effects of the circularly polarized light (CPL) and the electric field (EF) on the nonlocal transport in a silicene-based antiferromagnet/superconductor/ferromagnet (AF/S/F) asymmetrical junction. For case I (II), the CPL and the EF are applied simultaneously in the antiferromagnetic (ferromagnetic) region, whereas in the ferromagnetic (antiferromagnetic) region, only a constant EF is considered. The spin-valley-resolved conductance can be turned on or off by adjusting the CPL or the EF. The AF/S/F junction can be manipulated as a spin-locked valley filter for case I, while for case II, it can be used not only as a valley-locked spin filter but also as a nonlocal switch between two pure nonlocal processes. Such interesting nonlocal switch effect can be effectively controlled by reversing the direction of the incident energy axis, the handedness of the CPL, or the direction of the EF. These findings may open an avenue to the design and manufacture of the spintronic and valleytronic devices based on the asymmetrical silicene magnetic superconducting heterostructure.

Analysis to the dynamic response of a functionally graded spherical microshell in consideration of fractional-order dual-phase-lag heat conduction and nonlocal effect

Functionally graded materials (FGMs) stand as one of the most representative composite materials due to the superior thermal resistance in non-isothermal environment. On another front, the applicability of integer-order heat conduction models is increasingly questionable because the heat transfer shares the history-dependent property at time microscale. It is noted that the small-scale effect of elastic deformation has become significant due to the development of micro-devices. To capture the small-scale effect of elastic deformation and the memory-dependent effect of heat conduction in the FGM microstructures, as a first attempt, the present study focuses on developing a thermoelastic model by incorporating the fractional-order dual-phase-lag (FODPL) heat conduction model and the Eringen’s nonlocal model. Moreover, the extension of the Caputo definition, i.e., the Tempered-Caputo (TC) definition of fractional derivative ruling out singular kernel is adopted to depict the memory-dependent effect of the heat conduction. Then, the modified model is used to investigating the dynamic response of a FGM spherical microshell subjected to a sinusoidal thermal-mechanical loading. The corresponding governing equations are formulated and then solved by Laplace transform techniques. Some parametric results are demonstrated to display the influences of the fractional-order parameter, the nonlocal parameter and the power-law index on the considered physical quantities.

Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response

The paper’s primary objective is to examine the dynamic behavior of an integer and noninteger predator–prey system with a Holling type IV functional response in the Caputo sense. Our focus is on understanding how harvesting influences the stability, equilibria, bifurcations, and limit cycles within this system. We employ qualitative and quantitative analysis methods rooted in bifurcation theory, dynamical theory, and numerical simulation. We also delve into studying the boundedness of solutions and investigating the stability and existence of equilibrium points within the system. Leveraging Sotomayor’s theorem, we establish the presence of both the saddle-node and transcritical bifurcations. The analysis of the Hopf bifurcation is carried out using the normal form theorem. The model under consideration is extended to the fractional reaction–diffusion model which captures non-local and long-range effects more accurately than integer-order derivatives. This makes fractional reaction–diffusion systems suitable for modeling phenomena with anomalous diffusion or memory effects, improving the fidelity of simulations in turn. An adaptable numerical technique for solving this class of differential equations is also suggested. Through simulation results, we observe that one of the Lyapunov exponents has a negative value, indicating the potential for the emergence of a stable-limit cycle via bifurcation as well as chaotic and complex spatiotemporal distributions. We supplement our analytical investigations with numerical simulations to provide a comprehensive understanding of the system’s behavior. It was discovered that both the prey and predator populations will continue to coexist and be permanent, regardless of the choice of fractional parameter.

Normal form and Hopf bifurcation for the memory‐based reaction‐diffusion equation with nonlocal effect

In this paper, we provide the normal form for the Hopf bifurcation of a class of the reaction‐diffusion equation with memory‐based diffusion and nonlocal effect, where the delay is present in the differential term, similar to the chemotaxis model with time delay. The eigenvalue problems and the decomposition of the phase space are discussed in detail. Through a series of variable transformations, we obtain the third‐order truncated normal form of the model constrained on the central manifold and its equivalent equation in polar coordinates. Then, with the help of the dynamic analysis for the finite dimensional equations, the key parameters for determining the direction and stability of the Hopf bifurcation are given. These theoretical results are applied to the Bazykin's model, the stability, Turing bifurcation and Hopf bifurcation of the equilibrium are demonstrated through both theoretical and numerical methods.

Non-Local Cosmology: From Theory to Observations

We examine the key aspects of gravitational theories that incorporate non-local terms, particularly in the context of cosmology and spherical symmetry. We thus explore various extensions of General Relativity, including non-local effects in the action through the function F(R,□−1R), where R denotes the Ricci curvature scalar and the operator □−1 introduces non-locality. By selecting the functional forms using Noether Symmetries, we identify exact solutions within a cosmological framework. We can thus reduce the dynamics of these chosen models and obtain analytical solutions for the equations of motion. Therefore, we study the capability of the selected models in matching cosmological observations by evaluating the phase space and the fixed points; this allows one to further constrain the non-local model selected by symmetry considerations. Furthermore, we also investigate gravitational non-local effects on astrophysical scales. In this context, we seek symmetries within the framework of f(R,□−1R) gravity and place constraints on the free parameters. Specifically, we analyze the impact of non-locality on the orbits of the S2 star orbiting SgrA*.

Can nonlocal gravity really explain dark energy?

In view to scrutinize the idea that nonlocal modifications of General Relativity could dynamically address the dark energy problem, we investigate the evolution of the Universe at infrared scales as an Infinite Derivative Gravity model of the Ricci scalar, without introducing the cosmological constant Λ or any scalar field. The accelerated expansion of the late Universe is shown to be compatible with the emergence of nonlocal gravitational effects at sufficiently low energies. A technique for circumventing the mathematical complexity of the nonlocal cosmological equations is developed and, after drawing a connection with the Starobinsky gravity, verifiable predictions are considered, like a possible decreasing in the strength of the effective gravitational constant. In conclusion, the emergence of nonlocal gravity corrections at given scales could be an efficient mechanism to address the dark energy problem.

Hilbert transform view of water-wave theory

A general rethinking of the mathematical foundations of water surface waves from the perspective of the Hilbert transform uncovers shortcomings of the standard multiple-scale approach as well as elucidates the interplay of non-local and dispersive effects. Application of the Hilbert transforms to planar and cylindrical settings allows us to deduce new weakly nonlinear models, including an alternative to Zakharov's equation and an envelope equation for cylindrical waves on deep water, as well as to highlight the crucial differences between these geometries.

Nonlocal quasi-3d vibration/ analysis of three-layer nanoplate surrounded by Orthotropic Visco-Pasternak foundation by considering surface effects and neutral surface concept

The present article deals with the application of refined plate theory and surface effects to investigate the nonlocal free vibration behavior of a functionally graded nano-plate composed of two piezoelectric face sheets resting on Orthotropic Visco-Pasternak. Surface and nonlocal effects are applied using the surface piezoelectricity and stress-strain gradient theories. Surface effects, refined quasi-3D higher-order theory, neutral surface position and in-plane mechanical preloads are considered to study piezoelectric sandwich nano-plate with a functionally graded core in this study for the first time, simultaneously. The size-dependent governing equations are derived based on 2D and 3D refined theory using Hamilton’s principle and different boundary conditions are studied and investigated according to the semi-analytical solution method. Comparing the results of the vibration behavior of 2D and quasi-3D models, local and non-local models, and also, examining different foundations simultaneously can be said as one of the innovations of the current research. Finally, a parametric study is presented to examine the effects of different parameters such as surface effects, small scale parameters, mechanical preloads, thickness stretching effects, neutral surface position, non-homogeneous coefficient, applied voltage, different foundation constants, boundary conditions, geometrical ratios and different theories in details. It is indicated that the inclusion of surface effects and thickness stretching effects leads to a significant influence on the vibration behavior of three-layered nano-scale plates. The presented results in this article may provide useful guidance for the design and development of the next generation of nano-devices.

Understanding the Disparities of PM2.5 Air Pollution in Urban Areas via Deep Support Vector Regression.

In densely populated urban areas, PM2.5 has a direct impact on the health and quality of residents' life. Thus, understanding the disparities of PM2.5 is crucial for ensuring urban sustainability and public health. Traditional prediction models often overlook the spillover effects within urban areas and the complexity of the data, leading to inaccurate spatial predictions of PM2.5. We propose Deep Support Vector Regression (DSVR) that models the urban areas as a graph, with grid center points as the nodes and the connections between grids as the edges. Nature and human activity features of each grid are initialized as the representation of each node. Based on the graph, DSVR uses random diffusion-based deep learning to quantify the spillover effects of PM2.5. It leverages random walk to uncover more extensive spillover relationships between nodes, thereby capturing both the local and nonlocal spillover effects of PM2.5. And then it engages in predictive learning using the feature vectors that encapsulate spillover effects, enhancing the understanding of PM2.5 disparities and connections across different regions. By applying our proposed model in the northern region of New York for predictive performance analysis, we found that DSVR consistently outperforms other models. During periods of PM2.5 surges, the R-square of DSVR reaches as high as 0.729, outperforming non-spillover models by 2.5 to 5.7 times and traditional spatial metric models by 2.2 to 4.6 times. Therefore, our proposed model holds significant importance for understanding disparities of PM2.5 air pollution in urban areas, taking the first steps toward a new method that considers both the spillover effects and nonlinear feature of data for prediction.

WITHDRAWN: Accurate and efficient analytical simulation of free vibration for embedded nonlocal CNTRC beams with general boundary conditions

This study aims to evaluate the free vibrational response of restrained nanobeam enriched by nanocomposites based on an exact Fourier series approach. In order to capture the small size effects on the dynamical response, Eringen’s differential form of nonlocal elasticity is used which employs the one size (nonlocal) parameter. Within the framework of Rayleigh and Bernoulli-Euler beam theories to include the effect of nonlocality and by employing Fourier sine series together with Stokes’ transformation, a system of linear equations is obtained then solved by using the coefficient matrix. The combined effects of elastic boundary conditions, elastic medium, dispersion patterns and nonlocal effects are examined by solving this eigen-value problem constructed with Fourier infinite series. Free vibration frequencies are calculated for carbon nanotube reinforced nanobeam under different rigid or restrained boundary conditions, including an elastic medium Winkler-Pasternak type. A comprehensive parametric study is performed, with the particular focus on the influences of distribution pattern, elastic boundary and medium parameter on the free vibrational response of the composite nanobeam with different graded distributions. It is concluded that the addition of a small amount of carbon nanotube material can reinforce the stiffness of the nanobeam, and its free vibration performance is significantly affected by the distribution patterns, elastic medium and boundary conditions.