Nonlocal Effects Research Articles

Microstructural smoothed particle hydrodynamics model and simulations of discontinuous shear-thickening fluids

Despite the recent interest in the discontinuous shear-thickening (DST) behavior, few computational works tackle the rich hydrodynamics of these fluids. In this work, we present the first implementation of a microstructural DST model in smoothed particle hydrodynamic (SPH) simulation. The scalar model was implemented in an SPH scheme and tested in two flow geometries. Three distinct ratios of local to non-local microstructural effects were probed: zero, moderate, and strong non-locality. Strong and moderate cases yielded excellent agreement with flow curves constructed via the Wyart–Cates (WC) model, with the moderate case exhibiting banding patterns. We demonstrate that a local model is prone to a stress-splitting instability, resulting in discontinuous stress fields and poor agreement with the WC model. The mechanism of stress splitting has been explored and contextualized by the interaction of local microstructure evolution and the stress-control scheme. Analytic solutions for a body-force-driven DST channel flow have been derived and used to validate the SPH simulations with excellent agreement in velocity profiles. Simulations carried out at increasing driving forces exhibited a decrease in flow. We showed that even the simple scalar model can capture some of the key properties of DST materials, laying the foundation for further SPH study of instabilities and pattern formation.

A thermodynamically consistent strain difference-based nonlocal damage mechanics approach for failure analysis of quasi-brittle materials

The nonlocal integral approaches are established methods known for their effectiveness in dealing with the challenges of ill-posed behaviour and mesh sensitivity during the strain softening process, especially within classical continuum theories. The present work extends the strain difference-based nonlocal approach to continuum damage mechanics (CDM) theories for predicting the failure behaviour of quasi-brittle materials. The strain difference approach is adopted for two reasons: (i) it maintains physical realism and indirectly incorporates nonlocal effects while computing both the damage variable and the damage energy release rate, and (ii) the constitutive model maintains a symmetry nature in constructing the nonlocal part of the stiffness matrix, reducing the computational cost in strain-softening problems. The state and damage evolution equations for the present nonlocal approach are formulated within the thermodynamic framework. Numerical examples involving 2D and 3D cases are solved: (i) to study the influence of nonlocal parameter ‘α’ on the damage distribution while capturing the post-peak behaviours, (ii) to demonstrate the effectiveness of the present methodology by obtaining mesh-independent results and accurately predicting damage propagation paths, and (iii) to compare the experimental results and numerical structural response for coarse mesh, highlighting both computational efficiency and reduction of mesh-bias dependency. The results obtained by the strain difference-based nonlocal damage model agree well with the experimental results in the literature.

Flood teleconnections from levees undermine disaster resilience

Inland levees can amplify flood risk in unprotected communities by altering floodwater levels away from their location. While these nonlocal effects of levees, which we term flood teleconnections, have been studied for specific river segments, their impact on flood risks along a river network remains underexplored. By combining data-driven, hydrodynamic, and economic models, we quantify the magnitude, spatial distribution, and economic damages associated with flood teleconnections for a large river network system with extensive levees. We find that due to levees, the 100-year flood inundation extent grows by 25% of the total levee-protected area regionally, and the flood inundation depth increases by up to 2 m at specific locations. Levees also increase the vulnerability of unprotected, marginalized communities to flooding. Our results demonstrate that flood teleconnections are spatially widespread, involve unaccounted costs, and can lead to flood inequities. These findings will be critical to climate adaptation efforts in flood-prone regions.

Surface recoil force on dielectric nanoparticle enhancement via graphene acoustic surface plasmon excitation: non-local effect consideration.

Controlling optomechanical interactions at sub-wavelength levels is of great importance in academic science and nanoparticle manipulation technologies. This Letter focuses on the improvement of the recoil force on nanoparticles placed close to a graphene-dielectric-metal structure. The momentum conservation involving the non-symmetric excitation of acoustic surface plasmons (ASPs), via near-field circularly polarized dipolar scattering, implies the occurrence of a huge momentum kick on the nanoparticle. Owing to the high wave vector values entailed in the near-field scattering process, it has been necessary to consider the non-locality of the graphene electrical conductivity to explore the influence of the scattering loss on this large wave vector region, which is neglected by the semiclassical model. Surprisingly, the contribution of ASPs to the recoil force is negligibly modified when the non-local effects are incorporated through the graphene conductivity. On the contrary, our results show that the contribution of the non-local scattering loss to this force becomes dominant when the particle is placed very close to the graphene sheet and that it is mostly independent of the dielectric thickness layer. Our work can be helpful for designing new and better performing large plasmon momentum optomechanical structures using scattering highly dependent on the polarization for moving dielectric nanoparticles.

Theory of nonlocal modal hydrodynamic functions for beam and plate vibrations in viscous fluids

In this paper, we introduce a new nonlocal modal hydrodynamic theory for fluid–structure interactions (FSI) of light, flexible cantilever beams and plates undergoing small amplitude vibrations in Newtonian, incompressible, viscous, heavy fluids otherwise at rest. For low aspect ratio flexible structures and high mode numbers, three dimensional (3D) and nonlocal fluid effects become prominent drivers of the coupled dynamics, to the point that existing local hydrodynamic theories based on two dimensional (2D) fluid approximations become inadequate to predict the system response. On the other hand, our approach is based on a rigorous, yet efficient, 3D treatment of the hydrodynamic loading on cantilevered thin structures. The off-line solution of the FSI problem results in the so-called nonlocal modal hydrodynamic function matrix, that is, the representation of the nonlocal hydrodynamic load operator on a basis formed by the structural modes. Our theory then integrates the nonlocal hydrodynamics within a fully coupled structural modal model in the frequency domain. We compare and discuss our theory predictions in terms of frequency response functions, mode shapes, hydrodynamic loads, quality factors, added mass ratios with the predictions of the classical local approaches, for different actuation scenarios, identifying the limitations of the hypotheses underlying existing treatments. Importantly, we also validate our new model with experiments conducted on flexible square plates. While computationally efficient, our fully coupled theory is exact up to numerical truncation and can bridge knowledge gaps in the design and analysis of FSI systems based on low aspect ratio flexible beams and plates.

Learning fast, accurate, and stable closures of a kinetic theory of an active fluid

Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the kinetic model serve as an efficient alternative, but typically require closure assumptions to model unrepresented higher-order moments. In this study, we present a learning framework based on neural networks that exploits rotational symmetries in the closure terms to learn accurate closure models directly from kinetic simulations. The data-driven closures demonstrate excellent a-priori predictions comparable to the state-of-the-art Bingham closure. We provide a systematic comparison between different neural network architectures and demonstrate that nonlocal effects can be safely ignored to model the closure terms. We develop an active learning strategy that enables accurate prediction of the closure terms across the entire parameter space using a single neural network without the need for retraining. We also propose a data-efficient training procedure based on time-stepping constraints and a differentiable pseudo-spectral solver, which enables the learning of stable closures suitable for a-posteriori inference. The coarse-grained simulations equipped with data-driven closure models faithfully reproduce the mean velocity statistics, scalar order parameters, and velocity power spectra observed in simulations of the kinetic theory. Our differentiable framework also facilitates the estimation of parameters in coarse-grained descriptions conditioned on data.

Small-dependent nonlinear analysis of functionally graded triply periodic minimal surface nanoplates

This paper introduces an effective and simple approach to analyze functionally graded triply periodic minimal surface (FG-TPMS) nanoplates, taking advantage of a novel nonlocal strain gradient nonlinear analysis. TPMS has recently gained attention as an extraordinary solution for constructing structures, drawing inspiration from natural architectures. It offers remarkable features, including high interconnectivity porous architectures, smooth surfaces, and the ability to achieve mathematically controllable geometry features. However, the extensive potential and benefits of TPMS structures have not been fully explored in current research. Hence, this study aims to address this limitation and unlock new possibilities for FG-TPMS nanoplates. Three patterns of FG-TPMS nanoplates, namely Primitive (P), Gyroid (G), and I-gragh and Wrapped Package-graph (IWP), are utilized in this investigation. The proposed model effectively incorporates the nonlocal,strain gradient and nonlinear effects into nanoplate structures. It enables a comprehensive understanding of the mechanisms responsible for both reducing and enhancing stiffness in the nanoplate by fine-tuning the nonlocal and strain gradient parameters. This research offers promising prospects for future design and optimization, providing a robust approach to address the intricate nonlinear behavior observed in FG-TPMS nanoplates.

Fractional dual-phase-lag thermal-mechanical response of an functionally graded spherical microshell with size-dependent effect

Functionally graded materials (FGM) have attracted much attention due to their superior thermal shock resistance in extreme thermal environment. In addition, the memory-dependent feature of transient heat transfer progress can’t be reflected in the frame of integer-order heat conduction model due to the inability of depicting the effect of the past states on the current state. It is noticed that the size-dependent effect of elastic deformation has become significant due to the development of micro-devices. To describe the memory-dependent effect and the size-dependent effect in the functionally graded microstructures, the work aims a thermoelastic model by incorporating the fractional dual-phase-lag heat conduction model and the Eringen’s nonlocal model. To illustrate its application values, the modified model is used to investigate the dynamic performance of an functionally graded spherical microshell subjected to a thermal-mechanical loading. Governing equations including the modified parameters are derived and solved by Laplace transformation. The achieved results show that considering the influences of nonlocal effect and ceramic composition will reduce the thermal deformation under ultrafast heating condition.

Mechanical behavior of nanocircular plates under coupled surface and nonlocal effects by using molecular dynamics simulations

The equations of control for a circular thin plate under simple support are obtained by coupling the surface effect and non-local effect using the equilibrium method. Molecular dynamics simulations were used to calculate the residual surface strain energies at different crystal orientations. Different crystal orientations of the same material would affect its surface energy and thus result in different mechanical behaviors. The effects of residual surface strain energy and non-local parameters on the mechanical behavior of circular thin plates were analyzed. The analysis reveals that the surface effect and non-local effect on the deflection of the nanoplates are significant. The surface effect parameter of tensile stress increases the deflection, while the opposite is true for the surface effect parameter of compressive stress, and the non-local parameter decreases the deflection. The influence of surface effect and non-local effect is significant for smaller thicknesses and weakens for larger thicknesses.

The effect of forest cover changes on the regional climate conditions in Europe during the period 1986–2015

Abstract. Afforestation affects the earth's climate system by changing the biogeochemical and biogeophysical characteristics of the land surface. While the regional effects of afforestation are well understood in the tropics and the high latitudes, its climate impact on the midlatitudes is still the subject of scientific discussions. The general impact of afforestation on the regional climate conditions in Europe during the last decades is investigated in this study. For this purpose, regional climate simulations are performed with different forest cover fractions over Europe. In a first simulation, afforestation in Europe is considered, while this is not the case for a second simulation. We focus on the years 1986–2015, a period in which the forest cover in Europe increased comparatively strongly, accompanied by a strong general warming over the continent. Results show that afforestation has both local and non-local effects on the regional climate system in Europe. Due to an increased transport of turbulent heat (latent + sensible) into the atmosphere, afforestation leads to a significant reduction of the mean local surface temperatures in summer. In northern Europe, mean local surface temperatures were reduced about −0.3 K with afforestation, in central Europe about −0.5 K, and in southern Europe about −0.8 K. During heat periods, this local cooling effect can reach −1.9 K. In winter, afforestation results in a slight local warming in both northern and southern Europe because of the albedo effect of forests. However, this effect is rather small and the mean temperature changes are not significant. In the downwind direction, locally increased evapotranspiration rates with afforestation increase the general cloud cover, which results in a slight non-local warming in winter in several regions of Europe, particularly during cold spells. Thus, afforestation had a discernible impact on the climate change signal in Europe during the period 1986–2015, which may have mitigated the general warming trend in Europe, especially on the local scale in summer.

Effect of temporal nonlocality on wave propagation behaviors of viscoelastic FGM nanoshells

Effect of temporal nonlocality on wave propagation behaviors of viscoelastic FGM nanoshells

Modeling and Simulating an Epidemic in Two Dimensions with an Application Regarding COVID-19

We derive a reaction–diffusion model with time-delayed nonlocal effects to study an epidemic’s spatial spread numerically. The model describes infected individuals in the latent period using a structured model with diffusion. The epidemic model assumes that infectious individuals are subject to containment measures. To simulate the model in two-dimensional space, we use the continuous Runge–Kutta method of the fourth order and the discrete Runge–Kutta method of the third order with six stages. The numerical results admit the existence of traveling wave solutions for the proposed model. We use the COVID-19 epidemic to conduct numerical experiments and investigate the minimal speed of spread of the traveling wave front. The minimal spreading speeds of COVID-19 are found and discussed. Also, we assess the power of containment measures to contain the epidemic. The results depict a clear drop in the spreading speed of the traveling wave front after applying containment measures to at-risk populations.

Impact of nonlocal effects on plasmonic quasi-bandgap in asymmetric IMI waveguides

In this paper, we theoretically investigate the impact of nonlocal effects on the formation of plasmonic quasi-bandgap in an asymmetric insulator-metal-insulator (A-IMI) waveguide composed of a metal thin film and two insulators with different permittivities. The nonlocal response of metal thin film is described by a generalized nonlocal optical response (GNOR) model including both Thomas-Fermi kinetic energy and diffusion kinetic energy of free electrons. The results show that, under the influence of nonlocal effects, the plasmonic quasi-bandgap exhibits an obvious blueshift and narrowing compared with that under local response. In addition, the quasi-bandgap can be tuned conveniently by changing the metal film thickness and insulator material permittivity.

Effects of porosity and nonlocality on the low- and high-frequency vibration characteristics of Al/Si3N4 functionally graded nanoplates using quasi-3D theory

Effects of porosity and nonlocality on the low- and high-frequency vibration characteristics of Al/Si3N4 functionally graded nanoplates using quasi-3D theory

Effect of Nonlocality and Internal Heat Source on an Initially Stressed Thermoelastic Medium Under MGL Model

Effect of Nonlocality and Internal Heat Source on an Initially Stressed Thermoelastic Medium Under MGL Model

On the shock wave approximation to fractional generalized Burger–Fisher equations using the residual power series transform method

The time-fractional generalized Burger–Fisher equation (TF-GBFE) has various applications across various scientific and engineering disciplines. It is used for investigating various phenomena, including the dynamics of fluid flow, gas dynamics, shock-wave formation, heat transfer, population dynamics, and diffusion transport, among other areas of research. By incorporating fractional calculus into these models, researchers can more effectively represent the non-local and memory-dependent effects frequently observed in natural phenomena. Due to the importance of the family of TF-GBFEs, this work introduces a changed iterative method for analyzing this family analytically to gain a deep understanding of many nonlinear phenomena described by this family (e.g., shock waves). The proposed approach combines two algorithms: the Laplace transform and the residual power series method. The suggested technique is thoroughly discussed. Two numerical problems are discussed to check the effectiveness and accuracy of the proposed method. The approximations for integer and fractional orders are compared with the exact solution for integer-order problems. Finally, to investigate how the fractional order affects these problems, the obtained results are discussed graphically and numerically in the tables.

The Small-Amplitude Dynamics of Spontaneous Tropical Cyclogenesis. Part I: Experiments with Amplified Longwave Radiative Feedback

Abstract What determines the vortex size at the small-amplitude stage of spontaneous tropical cyclogenesis remains unclear. A doubly periodic domain is a standard setup for numerically studying this problem, but the convectively coupled standing waves inherent to the setup could directly trigger vortices, rendering an unrealistic path for tropical cyclogenesis. We increase the Coriolis parameter to suppress the wave and double the longwave radiative feedback to make the more realistic moisture–radiation instability dominant. Experiments show that the moisture–radiation instability has a short-wavelength cutoff due to the smoothing effect of convective dynamics, which includes the nonlocal convective triggering by cold pools and the nonlocal longwave radiative effect of anvil clouds. By approximating the spread of convective activity as a Gaussian filter on the column humidity, we derive a bulk convective spreading length lcp+av to parameterize the combined effect of cold pools and anvils. Using a novel diagnostic method, lcp+av is shown to be around 10 km. The contribution of cold pools and anvil clouds to convective spreading is comparable in the doubled radiative feedback experiments. An extrapolation to the normal radiative feedback state shows the anvil clouds play a smaller yet nonnegligible role.

Beam-type acoustic black holes incorporating the microstructure-dependent nonlocal effect

Acoustic black holes (ABHs) are effective passive damping structures for capturing bending waves at wedge edges. However, as the wedge shape continuously reduces in size, the intrinsic length scale of the ABH's tip gradually approaches the external length scale, such as the wavelength of wave, which causes a phenomenon known as the "scale effect" to take hold of the ABH. Despite gaining considerable attention in the past two decades, the influence of intrinsic length on the energy aggregation of ABHs has not been thoroughly investigated. This study aims to explore the significant contribution of microstructure-dependent nonlocal effects on the dynamic behavior of ABHs, which holds great scientific importance. The nonlocality arises from the inherent length of the material being studied. A nonlocal elastic theory (NET) is employed to model the dynamic behavior of one-dimensional ABH beams. Geometric acoustic method is proposed to analyze the power-law beam wave number and microstructure-related reflection coefficient. Results indicate a significant impact of nonlocality on the acoustic energy of beam-type ABHs, particularly when the nonlocal intrinsic length approaches the truncation length of the wedge. Moreover, a comparison between the present study and classical theory reveals an overestimation of the reflection coefficient in conventional works for small truncation lengths. The relationship between the reflection coefficient, truncation length, and nonlocal characteristic lengths is thoroughly examined. Additionally, the influence of the damping layer and different power-law exponents m on ABH behavior is extensively studied.

Thermodynamic costs of temperature stabilization in logically irreversible computation

Abstract In recent years, great efforts are devoted to reducing the work cost of the bit operation, but it is still unclear whether these efforts are sufficient for resolving the temperature stabilization problem in computation. By combining information thermodynamics and a generalized constitutive model which can describe Fourier heat conduction as well as non-Fourier heat transport with nonlocal effects, we here unveil two types of the thermodynamic costs in the temperature stabilization problem. Each type imposes an upper bound on the amount of bits operated per unit time per unit volume, which will eventually limit the speed of the bit operation. The first type arises from the first and second laws of thermodynamics, which is independent of the boundary condition and can be circumvented in Fourier heat conduction. The other type is traceable to the third law of thermodynamics, which will vary with the boundary condition and is ineluctable in Fourier heat conduction. These thermodynamic costs show that reducing the work cost of the bit operation is insufficient for resolving the temperature stabilization problem in computation unless the work cost vanishes.

Understanding 2D Semiconductor Edges by Combining Local and Nonlocal Effects: The Case of MoSi2N4

Understanding 2D Semiconductor Edges by Combining Local and Nonlocal Effects: The Case of MoSi₂N₄