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This article is concerned with a thermoelastic response in a non-local micro-stretch completely covered in the endless non-viscous fluid under temperature dependent, the medium is investigated employing the theory of Green-Naghdi (G-N III) and the model of three-phase-lag (3PHL).Basic equations are derived based on these models. The normal mode technique is employed to achieve an analysis solution to the problem. The study used a magnesium crystal element to compare non-local measurements of thermo-micro-stretch elasticity in water using the (G-N III) theory and the (3PHL) model. The non-local effect has been discovered to have a considerable impact on all physical quantities. Furthermore, comparisons are made between three different frequency values. [ABSTRACT FROM AUTHOR]

Atherosclerotic plaques are fatty deposits that form in the walls of major arteries and are one of the major causes of heart attacks and strokes. Macrophages are the main immune cells in plaques and macrophage dynamics influence whether plaques grow or regress. Macrophage proliferation is a key process in atherosclerosis, particularly in the development of mid-stage plaques, but very few mathematical models include proliferation. In this paper we reframe the lipid-structured model of Ford et al. (J Theor Biol 479:48–63, 2019. ) to account for macrophage proliferation. Proliferation is modelled as a non-local decrease in the lipid structural variable. Steady state analysis indicates that proliferation assists in reducing eventual necrotic core lipid content and spreads the lipid load of the macrophage population amongst the cells. The contribution of plaque macrophages from proliferation relative to recruitment from the bloodstream is also examined. The model suggests that a more proliferative plaque differs from an equivalent (defined as having the same lipid content and cell numbers) recruitment-dominant plaque in the way lipid is distributed amongst the macrophages. The macrophage lipid distribution of an equivalent proliferation-dominant plaque is less skewed and exhibits a local maximum near the endogenous lipid content. [ABSTRACT FROM AUTHOR]

In this manuscript, a two-dimensional axi-symmetric problem within a thermoelastic medium featuring fractional order derivatives, focusing on the Moore-Gibson-Thompson heat equation (MGT) in response to mechanical loading is investigated. The study assesses the problem's applicability under the influence of hyperbolic two temperature (HTT) and the non-local parameter resulting from ring and disc loads. The governing equations are rendered dimensionless, simplified through the introduction of potential functions, and solved using Laplace and Hankel transforms. Analytical expressions for displacement, stresses, conductive temperature, and temperature distribution components are derived in the transformed domain. Numerical inversion techniques are employed to obtain solutions in the physical domain. The purpose of the manuscript is to analyze the effects of non-local parameters, HTT, and various thermoelasticity theories graphically on resulting stresses, conductive temperature, and temperature distributions. It is observed that the behavior of composite materials under mechanical loading is effected by non-local and HTT. It will provide information about the different constituents of a composite material respond to temperature changes and mechanical stresses, which is crucial for designing and optimizing composite structures. Additionally, specific cases of interest are deduced from the findings of this investigation. [ABSTRACT FROM AUTHOR]

The present paper deals with the propagation of waves in non-local couple stress microploar thermoelastic solid half space lying under an inviscid liquid layer. We found two sets of coupled longitudinal waves and coupled transverse waves which are dispersive in nature and associated with attenuation. In addition to coupled waves, there also exists one independent longitudinal microroational wave which is dispersive in nature. Two types of waves namely coupled longitudinal waves and coupled transverse waves incident at the common interface. The value of various reflection coefficients and their energy ratios are calculated in both cases against the angle of incidence for a specific model. It is found that all reflection coefficients and energy ratios are affected by presence of non-locality, couple stress and angle of incidence. Their impact on various coefficients and energy ratios are studied numerically and depicted graphically. Some special cases are also deduced from the present investigation. The seismic reflection techniques are of great utility in determining the seismic structure of the earth and oceanic crust. Not only this, current findings may also be helpful in forecasting geophysical parameters at greater depths through signal processing, non-destructive testing and seismic data analysis. [ABSTRACT FROM AUTHOR]

The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler–Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate. [ABSTRACT FROM AUTHOR]

The images and videos of the high-voltage copper contact are disturbed by various noises in the factory. In this paper, an improved Non-local Self-similarity Recurrent Neural Network(NSRNN) is proposed for image denoising. The sparse representation is used for initializing the images, and then NSRNN is trained and tested based on the image datasets with different noise levels and magnification. Due to the similarity and the time correlation between the sequential images, RNN is used to improve the parameter utilization and model robustness. By measuring the self-similarity of the neighborhood features, NSRNN model outperforms other state-of-the-art methods in term of image denoising performance. [ABSTRACT FROM AUTHOR]

We have discussed reflection and refraction phenomenon of wave propagation from a plane interface dividing the non-local couple stress micropolar thermoelastic medium into two half-spaces. we have examined the problem by making incidence of two sets of coupled longitudinal waves and two sets of coupled transverse waves. Here, we observed that there exist five waves, viz., two sets of coupled longitudinal waves, two sets of coupled transverse waves and a longitudinal microrotational wave in non-local couple stress thermoelastic micropolar solid. One of them is propagating independently while others are set of coupled waves. We have also observed that these waves are propagating with different speeds. By making incidence of different waves; the reflection and refraction coefficients of numerous waves against the angle of incidence and angular frequency has been evaluated and portrayed graphically. [ABSTRACT FROM AUTHOR]

The key challenge of sequence representation learning is to capture the long-range temporal dependencies. Typical methods for supervised sequence representation learning are built upon recurrent neural networks to capture temporal dependencies. One potential limitation of these methods is that they only model one-order information interactions explicitly between adjacent time steps in a sequence, hence the high-order interactions between nonadjacent time steps are not fully exploited. It greatly limits the capability of modeling the long-range temporal dependencies since the temporal features learned by one-order interactions cannot be maintained for a long term due to temporal information dilution and gradient vanishing. To tackle this limitation, we propose the non-local recurrent neural memory (NRNM) for supervised sequence representation learning, which performs non-local operations by means of self-attention mechanism to learn full-order interactions within a sliding temporal memory block and models global interactions between memory blocks in a gated recurrent manner. Consequently, our model is able to capture long-range dependencies. Besides, the latent high-level features contained in high-order interactions can be distilled by our model. We validate the effectiveness and generalization of our NRNM on three types of sequence applications across different modalities, including sequence classification, step-wise sequential prediction and sequence similarity learning. Our model compares favorably against other state-of-the-art methods specifically designed for each of these sequence applications. [ABSTRACT FROM AUTHOR]

The main objective of this work is to extend finite element-based topology optimization problem to the two-dimensional, size-dependent structures described using weakly non-local Cosserat (micropolar) and strongly non-local Eringen’s theories, the latter of which finds an application for the first time, to the best of Authors’ knowledge. The optimum material layouts that minimize the structural compliance are attained by means of Solid Isotropic Material with Penalization approach, while the desired smooth, mesh-independent, binary solutions are obtained using density filter accompanied by volume preserving Heaviside projection method. The algorithms are enhanced by including an element removal and reintroduction strategy to reduce the computational cost, and to prevent spurious excessive distortion of elements with very low density. Example problems of practical importance are investigated under the assumption of linear elasticity to validate the code and to clearly demonstrate the influence of internal length scales and different non-locality mechanisms on final configurations. Obtained macro-scale optimum topologies admit the characteristics of corresponding continuum theories, and appear to be in agreement with the mechanical response governed by particle interactions in micro/nanoscale. [ABSTRACT FROM AUTHOR]

Analysis of non-local, phase-lag, and temperature-dependent properties of modified couple stress thermoelastic diffusive medium is examined in conditions of exciting by thermomechanical sources. The governing equations are framed involving non-local, phase-lag, and temperature-dependent properties. These equations are simplified by using the potential functions and employing the Laplace and Fourier transforms for further study. The problem is solved by deploying suitable thermomechanical loads. A specific type of normal and thermal loading of the ramp-type is considered. The transformed components of the physical field like the displacements, stresses, temperature change, and chemical potential are derived. A numerical analysis is performed for these quantities using the numerical technique. The graphs of the resulting quantities are shown to analyze the impact of non-local, phase-lag, and temperature-dependent properties. The specific cases are also mentioned. [ABSTRACT FROM AUTHOR]

Purpose: It is intended to investigate the modes of vibration of single-walled and double-walled carbon nanotubes with an attached mass, to gain knowledge useful for the application of CNTs for mass and cell detection. A related goal is the development and validation of a shell model that can be applied for the former purpose. Methods: A p-version finite element method model based on Sanders–Koiter's shell theory and considering the small size effects by employing Eringen's non-local theory is employed. Van der Waals forces are included in the interlayer stiffness of DWCNTs. Concentrated attached masses are included through their inertia, which is affected by non-local terms. The convergence and validity of the models are tested by comparisons to Molecular Dynamics simulations and atomistic–continuum hybrid finite element analysis. Results: Studies are conducted on the influence of the non-local parameter, which is calibrated for natural frequencies of different order and CNTs of different lengths. Critical values of length for which the non-local theory remains relevant depend upon the equivalent material and geometric properties employed, but more important is the verification that the non-local shell theory can be used to improve the accuracy of continuum CNT models. The dynamic behaviour of bridged SWCNTs and DWCNTs is studied, examining their applicability in mass detection devices. Conclusion: The large influence a localised mass has on the mode shapes of vibration is illustrated. Sensitivity increases more significantly in lower length carbon nanotubes. Furthermore, it is found that SWCNTs have a higher sensitivity to attached concentrated masses than DWCNTs with similar diameter, making the former more appealing candidates for mass detection nanodevices. [ABSTRACT FROM AUTHOR]

Purpose: In recent years, Non-Local-based methods have been successfully applied to lung nodule classification. However, these methods offer 2D attention or limited 3D attention to low-resolution feature maps. Moreover, they still depend on a convenient local filter such as convolution as full 3D attention is expensive to compute and requires a big dataset, which might not be available. Methods: We propose to use 3D Axial-Attention, which requires a fraction of the computing power of a regular Non-Local network (i.e., self-attention). Unlike a regular Non-Local network, the 3D Axial-Attention network applies the attention operation to each axis separately. Additionally, we solve the invariant position problem of the Non-Local network by proposing to add 3D positional encoding to shared embeddings. Results: We validated the proposed method on 442 benign nodules and 406 malignant nodules, extracted from the public LIDC-IDRI dataset by following a rigorous experimental setup using only nodules annotated by at least three radiologists. Our results show that the 3D Axial-Attention model achieves state-of-the-art performance on all evaluation metrics, including AUC and Accuracy. Conclusions: The proposed model provides full 3D attention, whereby every element (i.e., pixel) in the 3D volume space attends to every other element in the nodule effectively. Thus, the 3D Axial-Attention network can be used in all layers without the need for local filters. The experimental results show the importance of full 3D attention for classifying lung nodules. [ABSTRACT FROM AUTHOR]

A new mathematical model of modified couple stress thermoelastic (MCT) diffusion is constructed where non-local and dual-phase-lag effects are considered. These impacts are analyzed due to thermomechanical loading. Governing equations are simplified by using Laplace and Fourier transform techniques. Normal and thermal loading of ramp-type are taken into account to demonstrate the application. Numerical results are calculated for displacements, stresses, temperature change and chemical potential and are disucussed by displaying graphically. Particular cases are also deduced. [ABSTRACT FROM AUTHOR]

Non-local patch-based methods were until recently the state of the art for image denoising but are now outperformed by CNNs. In video denoising, however, they are still competitive with CNNs, as they can effectively exploit the video temporal redundancy, which is a key factor to attain high denoising performance. The problem is that CNN architectures are not compatible with the search for self-similarities. In this work, we propose a simple, yet efficient way to feed video self-similarities to a CNN. The non-locality is incorporated into the network via a first non-trainable layer which finds for each patch in the input image its most similar patches in a search region. The central values of these patches are then gathered in a feature vector which is assigned to each image pixel. This information is presented to a CNN which is trained to predict the clean image. We apply the proposed method to image and video denoising. In the case of video, the patches are searched for in a 3D spatiotemporal volume. The proposed method achieves state-of-the-art results. [ABSTRACT FROM AUTHOR]

Single-image dehazing is an ill-posed problem. Most previous methods focused on estimating intermediate parameters for input hazy images. In this paper, we propose a novel end-to-end Simplified Non-locally Dense Network (SNDN) which does not rely on intermediate parameters. To capture long-range dependencies, we propose a Simplified Non-local Dense Block (SNDB) which is lightweight and outperforms traditional non-local method. Our SNDB will be embedded into a densely connected encoder–decoder network. To avoid gradients vanishing problem, we propose a simple branch network which only have five convolution layers. The effectiveness of our proposed network is proved through ablation experiment. In addition, we enhanced our training set by synthesizing colored hazy images, which helps restore the original color of the hazy image. The experimental results demonstrate that our network have better performance than most of the pervious state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we analyse Mickens’ type non-standard finite difference schemes (NSFD) and establish their convergence. We then apply these schemes on Lane Emden equations. The numerical results thus obtained are compared with existing analytical solutions or with solutions computed with standard finite difference (FD) schemes. NSFD and FD solutions and their errors have also been compared graphically and observed that the errors in NSFD tends to zero as step size tends to zero. The result shows that the NSFD behave qualitatively in the same way as the original equations. NSFD approximate solution near singular point efficiently where FD fails to do so (Buckmire in Numer Methods Partial Differ Equ 19:380-398, 2003). [ABSTRACT FROM AUTHOR]

The highly nonlinear mechanical behaviour of soft tissues solicited within the physiological range usually involves degradation of the material properties. Mechanically, having these biostructures undergoing such stretch patterns may bring about pathological conditions related to the steady deterioration of both collagen fibres and material's ground substance. Tissue and subject variability observed in the phenomenological mechanical characterisation of soft tissues often hinder the choice of the computational constitutive model. Therefore, this contribution brings forth a detailed overview of the constitutive implementation in a computational framework of anisotropic hyperelastic materials with damage. Surmounting the challenge posed by the mesh dependency pathology requires the incorporation of an integral-type non-local averaging, which seeks to include the effects of the microstructure in order to limit the localisation phenomena of the damage variables. By adopting this approach, one can make use of multiple developed material models available in the literature, a combination of those, or even propose new models within the same numerical framework. The numerical examples of three-dimensional displacement and force-driven boundary value problems highlight the possibility of using multiple material models within the same numerical framework. Particularities concerning the considered material models and the damage effect implications to represent the Mullins effect, induced anisotropy, hysteresis, and mesh dependency are discussed. [ABSTRACT FROM AUTHOR]

The peridynamic theory of solid mechanics offers an integral based alternative to traditional continuum models based on partial differential equations. This formulation is particularly advantageous when applied to material failure problems that result in discontinuous displacement fields. This paper presents a meshfree implementation of a state-based peridynamic bending model based on the idea of rotational springs between pairs of peridynamic bonds. Energy-based analysis determines the properties of these bond pairs for a brittle material, resulting in a constitutive model that naturally gives rise to localized damage and crack propagation. [ABSTRACT FROM AUTHOR]

A general mathematical model of steady-state transport driven by spatially non-local driving potential differences is proposed. The porous medium is considered to be a network of short-, medium-, and long-range interstitial channels with impermeable walls and at a continuum of length scales, and the flow rate in each channel is assumed to be linear with respect to the pressure difference between its ends. The flow rate in the model is thus a functional of the non-local driving pressure differences. As special cases, the model reduces to familiar forms of transport equations that are commonly used. An important situation arises when the phenomenon is almost, but not quite, locally dependent. The one-dimensional form of the model discussed here can be extended to multiple dimensions, temporal non-locality, and to heat, mass, and momentum transfer. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-population continuous integro-differential model of cell differentiation, using a non-local term to describe the influence of the local environment on differentiation. We investigate three different versions of the model, with differentiation being cell autonomous, regulated via a community effect, or weakly dependent on the local cellular environment. We consider the spatial patterns that such different modes of differentiation produce, and investigate the formation of both stripes and spots by the model. We show that pattern formation only occurs when differentiation is regulated by a strong community effect. In this case, permanent spatial patterns only occur under a precise relationship between the parameters characterising cell dynamics, although transient patterns can persist for biologically relevant timescales when this condition is relaxed. In all cases, the long-lived patterns consist only of stripes, not spots. [ABSTRACT FROM AUTHOR]

When formulated properly, most geophysical transport-type process involving passive scalars or motile particles may be described by the same space-time nonlocal field equation which consists of a classical mass balance coupled with a space-time nonlocal convective/dispersive flux. Specific examples employed here include stretched and compressed Brownian motion, diffusion in slit-nanopores, subdiffusive continuous-time random walks (CTRW), super diffusion in the turbulent atmosphere and dispersion of motile and passive particles in fractal porous media. Stretched and compressed Brownian motion, which may be thought of as Brownian motions run with nonlinear clocks, are defined as the limit processes of a special class of random walks possessing nonstationary increments. The limit process has a mean square displacement that increases as t where α > −1 is a constant. If α = 0 the process is classical Brownian, if α < 0 we say the process is compressed Brownian while if α > 0 it is stretched. The Fokker-Planck equations for these processes are classical ade's with dispersion coefficient proportional to t. The Brownian-type walks have fixed time step, but nonstationary spatial increments that are Gaussian with power law variance. With the CTRW, both the time increment and the spatial increment are random. The subdiffusive Fokker-Planck equation is fractional in time for the CTRW's considered in this article. The second moments for a Levy spatial trajectory are infinite while the Fokker-Planck equation is an advective-dispersive equation, ade, with constant diffusion coefficient and fractional spatial derivatives. If the Lagrangian velocity is assumed Levy rather than the position, then a similar Fokker-Planck equation is obtained, but the diffusion coefficient is a power law in time. All these Fokker-Planck equations are special cases of the general non-local balance law. [ABSTRACT FROM AUTHOR]

For each n let $${Y^{(n)}_t}$$ be a continuous time symmetric Markov chain with state space $${n^{-1} \mathbb{Z}^d}$$ . Conditions in terms of the conductances are given for the convergence of the $${Y^{(n)}_t}$$ to a symmetric Markov process Y t on $${\mathbb{R}^d}$$ . We have weak convergence of $$\{{Y^{(n)}_t: t \leq t_0\}}$$ for every t0 and every starting point. The limit process Y has a continuous part and may also have jumps. [ABSTRACT FROM AUTHOR]

A new numerical method of solving integro-differential equations appearing in the theory of atomic and nuclear scattering systems has been devised. It is termed Singular Value Decomposition Method (SVD). It consists in expanding the exchange kernel into a number of separable terms by means of the Singular Value Decomposition and then iterating over the remainder. In this paper, we extend our SVD method to the scattering of low energy electron-helium which has been the subject of interest, both theoretically and experimentally. We compare our results with the Moments Method which is widely used. The Moments Method consists of making an expansion of the solution into an especially favorable basis that takes care of the non-exchange part of the Hamiltonian. [ABSTRACT FROM AUTHOR]

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Moreover, large eddies are able to mix scalar quantities in a manner that is counter to the local gradient. We present a general solution of a two-dimension steady state advection-diffusion equation, considering non-local turbulence closure using the General Integral Laplace Transform Technique. We show some examples of applications of the new solution with different vertical diffusion parameterisations. [ABSTRACT FROM AUTHOR]

We report analytical and numerical solutions describing the evolution of the coherent structure of bubbles and spikes in the Richtmyer–Meshkov instability in supernovae. It is shown that the dynamics of the flow is essentially non-local, and the nonlinear Richtmyer–Meshkov bubble flattens and decelerates. [ABSTRACT FROM AUTHOR]

Finite element analysis of the strain localization behaviors of a voided ductile material has been performed using a non-local plasticity, in which the yield strength depends on both an equivalent plastic strain measure (hardening parameter) and Laplacian equivalent. The introduction of gradient terms to the yield function was found to play an important role in simulating the strain localization behavior of the voided ductile material. The effect of the mesh size and characteristic length on the strain localization were also investigated. An FEM simulation based on the proposed non-local plasticity revealed that the load-strain curves of the voided ductile material subjected to plane strain tension converges to one curve, regardless of the mesh size. In addition, the results using non-local plasticity also showed that the dependence of the deformation behavior of the material on the mesh size was much less sensitive than with classical local plasticity and could be successfully eliminated through the introduction of a large value for the characteristic length. [ABSTRACT FROM AUTHOR]

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit. [ABSTRACT FROM AUTHOR]

We give a new class of examples of non-local, non-symmetric Dirichlet forms. [ABSTRACT FROM AUTHOR]

In this paper, we are going to show existence of branches of bifurcation of positive Wloc1,p(Ω)-solutions for the very singular non-local λ-problem -∫Ωg(x,u)dxrΔpu=λa(x)u-δ+b(x)uβinΩ,u>0inΩandu=0on∂Ω,where Ω⊂RN is a smooth bounded domain, δ>0, 0<β