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Journal articles on the topic 'Nonlocal processes'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Delgado, M., A. Suárez, and I. B. M. Duarte. "Nonlocal problems arising from the birth-jump processes." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 2 (2018): 447–69. http://dx.doi.org/10.1017/prm.2018.34.

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In this paper, we prove the existence and uniqueness of a positive solution for a nonlocal logistic equation arising from the birth-jump processes. For this, we establish a sub-super solution method for nonlocal elliptic equations, we perform a study of the eigenvalue problems associated with these equations and we apply these results to the nonlocal logistic equation.

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2

D’Elia, Marta, Qiang Du, Max Gunzburger, and Richard Lehoucq. "Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes." Computational Methods in Applied Mathematics 17, no. 4 (2017): 707–22. http://dx.doi.org/10.1515/cmam-2017-0029.

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AbstractA nonlocal convection-diffusion model is introduced for the master equation of Markov jump processes in bounded domains. With minimal assumptions on the model parameters, the nonlocal steady and unsteady state master equations are shown to be well-posed in a weak sense. Then the nonlocal operator is shown to be the generator of finite-range nonsymmetric jump processes and, when certain conditions on the model parameters hold, the generators of finite and infinite activity Lévy and Lévy-type jump processes are shown to be special instances of the nonlocal operator.

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3

El-Nabulsi, Rami Ahmad. "Nonlocal approach to nonequilibrium thermodynamics and nonlocal heat diffusion processes." Continuum Mechanics and Thermodynamics 30, no. 4 (2018): 889–915. http://dx.doi.org/10.1007/s00161-018-0666-2.

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4

Alcaraz, Francisco C., and Vladimir Rittenberg. "Nonlocal growth processes and conformal invariance." Journal of Statistical Mechanics: Theory and Experiment 2012, no. 05 (2012): P05022. http://dx.doi.org/10.1088/1742-5468/2012/05/p05022.

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5

de Angelis, Fabio, and Donato Cancellara. "Constitutive Equations for a Model of Nonlocal Plasticity which Complies with a Nonlocal Maximum Plastic Dissipation Principle." Applied Mechanics and Materials 217-219 (November 2012): 2362–66. http://dx.doi.org/10.4028/www.scientific.net/amm.217-219.2362.

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In the present paper constitutive equations for a nonlocal plasticity model are presented. Elasticity is considered to be governed by local forces so that only the dissipation processes are adopted as nonlocal. Differing from other proposed models in which the isotropic hardening/softening variables are considered as nonlocal, in the present paper the nonlocality is extended in order to include the kinematic hardening behaviour as well, so that both types of hardening (kinematic and isotropic) are considered as nonlocal. The present formulation satisfies a variational condition representing no

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6

Li, Zhipeng, Hongwu Tang, Saiyu Yuan, Huiming Zhang, Lingzhong Kong, and HongGuang Sun. "Modeling Long-Distance Forward and Backward Diffusion Processes in Tracer Transport Using the Fractional Laplacian on Bounded Domains." Fractal and Fractional 7, no. 11 (2023): 823. http://dx.doi.org/10.3390/fractalfract7110823.

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Recent studies have emphasized the importance of the long-distance diffusion model in characterizing tracer transport occurring within both subsurface and surface environments, particularly in heterogeneous systems. Long-distance diffusion, often referred to as nonlocal diffusion, signifies that tracer particles may experience a considerably long distance in either the forward or backward direction along preferential channels during the transport. The classical advection–diffusion (ADE) model has been widely used to describe tracer transport; however, they often fall short in capturing the int

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Korotaev, S. M., N. M. Budnev, V. O. Serdyuk, Ye O. Kiktenko, and D. A. Orekhova. "New Results of the Baikal Experiment on Forecasting Effect of Macroscopic Nonlocal Correlations." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 4 (85) (August 2019): 56–72. http://dx.doi.org/10.18698/1812-3368-2019-4-56-72.

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The long-term deep-sea experiment on study of macroscopic quantum nonlocal correlations of natural large-scale random dissipative processes has been conducted in Lake Baikal since 2012. Correlations of the probe processes in detectors insulated from classical local impacts, between each other and with the large-scale source-processes are studied. These correlations are observed at extremely low frequencies and characterized by the large time shifts. The most important feature of random process nonlocal correlations is presence of a considerable advanced component in them. The dominant source i

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8

Hicks, Will. "PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black–Scholes Equation." Entropy 21, no. 2 (2019): 105. http://dx.doi.org/10.3390/e21020105.

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The Accardi–Boukas quantum Black–Scholes framework, provides a means by which one can apply the Hudson–Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers–Moyal expansion, and this provides useful tools to understand their behaviour. In this paper we develop further links between quantum stochastic processes, and nonlocal diffusions, by inverting the question, and showing how certain nonlocal diffusions can be written as quantum stochastic processes. We then go on to show how one can us

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9

Hardcastle, Valerie Gray. "ERPs and the modularity of cognitive processes." Behavioral and Brain Sciences 20, no. 3 (1997): 520–21. http://dx.doi.org/10.1017/s0140525x97261509.

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Farah argues that nonlocal models explain clinical data better. However, the locality assumption does not seem so implausible if different sorts of data are taken into account. In particular, priming experiments using evoked response potentials support modularity. I describe some ERP studies relevant to this issue.

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10

NAKAO, HIROYA, TSUYOSHI MISHIRO, and MICHIO YAMADA. "VISUALIZATION OF CORRELATION CASCADE IN SPATIOTEMPORAL CHAOS USING WAVELETS." International Journal of Bifurcation and Chaos 11, no. 05 (2001): 1483–93. http://dx.doi.org/10.1142/s0218127401002833.

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We propose a simple method to visualize spatiotemporal correlation between scales using wavelets, and apply it to two typical spatiotemporally chaotic systems, namely to coupled complex Ginzburg–Landau oscillators with diffusive interaction, and those with nonlocal interaction. Reflecting the difference between underlying dynamical processes, our method provides distinctive results for those two systems. Especially, for the nonlocally interacting case where the system exhibits fractal amplitude patterns and power-law spectrum, it clearly visualizes the dynamical cascade process of spatiotempor

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11

Brú, A., D. Gómez-Castro, and J. C. Nuño. "Visibility to discern local from nonlocal dynamic processes." Physica A: Statistical Mechanics and its Applications 471 (April 2017): 718–23. http://dx.doi.org/10.1016/j.physa.2016.12.078.

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12

Li, Zenghu. "Path-valued branching processes and nonlocal branching superprocesses." Annals of Probability 42, no. 1 (2014): 41–79. http://dx.doi.org/10.1214/12-aop759.

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13

Huang, Qiao, Jinqiao Duan, and Jiang-Lun Wu. "Maximum principles for nonlocal parabolic Waldenfels operators." Bulletin of Mathematical Sciences 09, no. 03 (2019): 1950015. http://dx.doi.org/10.1142/s1664360719500152.

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As a class of Lévy type Markov generators, nonlocal Waldenfels operators appear naturally in the context of investigating stochastic dynamics under Lévy fluctuations and constructing Markov processes with boundary conditions (in particular the construction with jumps). This work is devoted to prove the weak and strong maximum principles for ‘parabolic’ equations with nonlocal Waldenfels operators. Applications in stochastic differential equations with [Formula: see text]-stable Lévy processes are presented to illustrate the maximum principles.

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14

Almoneef, Areej A., Shreen El-Sapa, Kh Lotfy, A. El-Bary, and Abdulkafi M. Saeed. "Laser Short-Pulse Effect on Thermodiffusion Waves of Fractional Heat Order for Excited Nonlocal Semiconductor." Advances in Condensed Matter Physics 2022 (August 12, 2022): 1–15. http://dx.doi.org/10.1155/2022/1523059.

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In this work, the thermal effect of a laser pulse is taken into account when mechanical-thermodiffusion (METD) waves are studied. The nonlocal semiconductor material is used when interference between holes and electrons occurs. The fractional technique is applied on the heat equation according to the photo-thermoelasticity theory. The governing equations describe the photo-excitation processes according to the overlapping between the thermoelasticity and photothermal theories. The thermoelastic deformation (TD) and the electronic deformation (ED) for the dimensionless fields are taken in one d

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15

Blasone, M., S. De Siena, G. Lambiase, C. Matrella, and B. Micciola. "Local and Nonlocal Quantum Correlations in QED Scattering Processes." Journal of Physics: Conference Series 3017, no. 1 (2025): 012030. https://doi.org/10.1088/1742-6596/3017/1/012030.

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Abstract We summarize recent findings on the generation and distribution of entanglement in Quantum Electrodynamics (QED) scattering processes. We explore both the generation of entanglement in fundamental QED interactions and the role of complete complementarity relations (CCR) in characterizing the local and nonlocal properties of these quantum processes, and in accounting for their intertwining.

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16

Wu, Chih-Ping, and Yen-Jung Chen. "Cylindrical Bending Vibration of Multiple Graphene Sheet Systems Embedded in an Elastic Medium." International Journal of Structural Stability and Dynamics 19, no. 04 (2019): 1950035. http://dx.doi.org/10.1142/s0219455419500354.

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Based on the Eringen nonlocal elasticity theory and multiple time scale method, an asymptotic nonlocal elasticity theory is developed for cylindrical bending vibration analysis of simply-supported, [Formula: see text]-layered, and uniformly or nonuniformly-spaced, graphene sheet (GS) systems embedded in an elastic medium. Both the interactions between the top and bottom GSs and their surrounding medium and the interactions between each pair of adjacent GSs are modeled as one-parameter Winkler models with different stiffness coefficients. In the formulation, the small length scale effect is int

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17

Xu, Xin-Jian, and Chuan-Fu Yang. "Inverse nodal problem for nonlocal differential operators." Tamkang Journal of Mathematics 50, no. 3 (2019): 337–47. http://dx.doi.org/10.5556/j.tkjm.50.2019.3361.

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Inverse nodal problem consists in constructing operators from the given zeros of their eigenfunctions. The problem of differential operators with nonlocal boundary condition appears, e.g., in scattering theory, diffusion processes and the other applicable fields. In this paper, we consider a class of differential operators with nonlocal boundary condition, and show that the potential function can be determined by nodal data.

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18

Du, Qiang, Zhan Huang, and Richard B. Lehoucq. "Nonlocal convection-diffusion volume-constrained problems and jump processes." Discrete & Continuous Dynamical Systems - B 19, no. 2 (2014): 373–89. http://dx.doi.org/10.3934/dcdsb.2014.19.373.

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19

Popov, N. S. "Nonlocal integro-differential problems of multi-dimensional wave processes." Journal of Physics: Conference Series 1268 (July 2019): 012060. http://dx.doi.org/10.1088/1742-6596/1268/1/012060.

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20

Aguilar, J. F. Gómez, T. Córdova-Fraga, J. Tórres-Jiménez, R. F. Escobar-Jiménez, V. H. Olivares-Peregrino, and G. V. Guerrero-Ramírez. "Nonlocal Transport Processes and the Fractional Cattaneo-Vernotte Equation." Mathematical Problems in Engineering 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/7845874.

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The Cattaneo-Vernotte equation is a generalization of the heat and particle diffusion equations; this mathematical model combines waves and diffusion with a finite velocity of propagation. In disordered systems the diffusion can be anomalous. In these kinds of systems, the mean-square displacement is proportional to a fractional power of time not equal to one. The anomalous diffusion concept is naturally obtained from diffusion equations using the fractional calculus approach. In this paper we present an alternative representation of the Cattaneo-Vernotte equation using the fractional calculus

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21

Raković, D., M. Dugić, M. B. Plavšić, G. Keković, Irena Ćosić, and David Davidović. "Quantum Decoherence and Quantum-Holographic Information Processes: From Biomolecules to Biosystems." Materials Science Forum 518 (July 2006): 485–90. http://dx.doi.org/10.4028/www.scientific.net/msf.518.485.

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Our recently proposed quantum approach to biomolecular recognition processes is hereby additionally supported by biomolecular Resonant Recognition Model and by quantum-chemical theory of biomolecular non-radiative resonant transitions. Previously developed general quantumdecoherence framework for biopolymer conformational changes in very selective ligandproteins/ target-receptors key/lock biomolecular recognition processes (with electron-conformational coupling, giving rise to dynamical modification of many-electron energy-state hypersurface of the cellular quantum-ensemble ligand-proteins/tar

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22

Vasiliev, Valery V., and Sergey A. Lurie. "To the Problem of Discontinuous Solutions in Applied Mathematics." Mathematics 11, no. 15 (2023): 3362. http://dx.doi.org/10.3390/math11153362.

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This paper addresses discontinuities in the solutions of mathematical physics that describe actual processes and are not observed in experiments. The appearance of discontinuities is associated in this paper with the classical differential calculus based on the analysis of infinitesimal quantities. Nonlocal functions and nonlocal derivatives, which are not specified, in contrast to the traditional approach to a point, but are the results of averaging over small but finite intervals of the independent variable are introduced. Classical equations of mathematical physics preserve the traditional

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23

Birgelis, Karlis, and Uldis Raitums. "STRICTLY CONVERGENT ALGORITHM FOR AN ELLIPTIC EQUATION WITH NONLOCAL AND NONLINEAR BOUNDARY CONDITIONS." Mathematical Modelling and Analysis 17, no. 1 (2012): 128–39. http://dx.doi.org/10.3846/13926292.2012.647100.

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The paper describes a formally strictly convergent algorithm for solving a class of elliptic problems with nonlinear and nonlocal boundary conditions, which arise in modeling of the steady-state conductive-radiative heat transfer processes. The proposed algorithm has two levels of iterations, where inner iterations by means of the damped Newton method solve an appropriate elliptic problem with nonlinear, but local boundary conditions, and outer iterations deal with nonlocal terms in boundary conditions.

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24

Gómez-Aguilar, J. F., R. F. Escobar-Jiménez, V. H. Olivares-Peregrino, M. Benavides-Cruz, and C. Calderón-Ramón. "Nonlocal electrical diffusion equation." International Journal of Modern Physics C 27, no. 01 (2016): 1650007. http://dx.doi.org/10.1142/s0129183116500078.

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In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is [Formula: see text] and for the time domain is [Formula: see text]. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time frac

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25

He, Hui, and Rugang Ma. "Limit Theorems for Continuous-Time Branching Flows." Journal of Applied Probability 51, no. 2 (2014): 317–32. http://dx.doi.org/10.1239/jap/1402578627.

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We construct a flow of continuous-time and discrete-state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses, over the positive half line, studied in Li (2014).

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26

He, Hui, and Rugang Ma. "Limit Theorems for Continuous-Time Branching Flows." Journal of Applied Probability 51, no. 02 (2014): 317–32. http://dx.doi.org/10.1017/s0021900200011268.

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We construct a flow of continuous-time and discrete-state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses, over the positive half line, studied in Li (2014).

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27

Korotaev, S., N. Budnev, V. Serdyuk, E. Kiktenko, D. Orekhova, and J. Gorohov. "Macroscopic nonlocal correlations by new data of the Baikal Experiment." Journal of Physics: Conference Series 2197, no. 1 (2022): 012019. http://dx.doi.org/10.1088/1742-6596/2197/1/012019.

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Abstract The long-term Baikal experiment on study of macroscopic nonlocal correlations between random dissipative heliogeophysical processes and probe ones in the detectors have revealed prominent features of macroscopic entanglement predicted by action-at-a-distance electrodynamics. These correlations have both the retarded and advanced components with large time shifts. The correlations occur at extremely low frequencies and require long series of observations, so the Baikal experiment is continuing to study their unusual properties. In 2019-2021 new data were obtained on correlation of the

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28

El-Sapa, Shreen, Khaled Lotfy, Alaa A. El-Bary, and M. H. Ahmed. "Photo Thermal Diffusion of Excited Nonlocal Semiconductor Circular Plate Medium with Variable Thermal Conductivity." Advances in Condensed Matter Physics 2023 (April 26, 2023): 1–12. http://dx.doi.org/10.1155/2023/1106568.

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To examine the effects of the nonlocal thermoelastic parameters in a nanoscale semiconductor material, a novel nonlocal model with variable thermal conductivity is provided in this study. The photothermal diffusion (PTD) processes in a chemical action are utilized in the framework of the governing equations. When elastic, thermal, and plasma waves interact, the nonlocal continuum theory is used to create this model. For the main formulations to get the analytical solutions of the thermal stress, displacement, carrier density, and temperature during the nanoscale thermo-photo-electric medium, t

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29

Zhao, Yanxiang, Jiakou Wang, Yanping Ma, and Qiang Du. "Generalized local and nonlocal master equations for some stochastic processes." Computers & Mathematics with Applications 71, no. 11 (2016): 2497–512. http://dx.doi.org/10.1016/j.camwa.2015.09.030.

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30

Almet, Axel A., Michael Pan, Barry D. Hughes, and Kerry A. Landman. "When push comes to shove: Exclusion processes with nonlocal consequences." Physica A: Statistical Mechanics and its Applications 437 (November 2015): 119–29. http://dx.doi.org/10.1016/j.physa.2015.05.031.

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31

Khantuleva, T. A., and Yu I. Mescheryakov. "Nonlocal theory of the high-strain-rate processes instructured media." International Journal of Solids and Structures 36, no. 21 (1999): 3105–29. http://dx.doi.org/10.1016/s0020-7683(98)00013-4.

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32

Khantuleva, T., and D. Shalymov. "Nonlocal hydrodynamic modeling high-rate shear processes in condensed matter." Journal of Physics: Conference Series 1560 (June 2020): 012057. http://dx.doi.org/10.1088/1742-6596/1560/1/012057.

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33

Siregar, E., A. F. Viñas, and M. L. Goldstein. "Coarse-graining and nonlocal processes in proton cyclotron resonant interactions." Physics of Plasmas 5, no. 2 (1998): 333–44. http://dx.doi.org/10.1063/1.872715.

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34

Grzywny, Tomasz, Moritz Kassmann, and Łukasz Leżaj. "Remarks on the Nonlocal Dirichlet Problem." Potential Analysis 54, no. 1 (2020): 119–51. http://dx.doi.org/10.1007/s11118-019-09820-9.

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AbstractWe study translation-invariant integrodifferential operators that generate Lévy processes. First, we investigate different notions of what a solution to a nonlocal Dirichlet problem is and we provide the classical representation formula for distributional solutions. Second, we study the question under which assumptions distributional solutions are twice differentiable in the classical sense. Sufficient conditions and counterexamples are provided.

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35

Kayali, Nour. "“Does this make sense?”: The effect of matching guise in regional accent on grammatical acceptability judgments." Proceedings of the Linguistic Society of America 8, no. 1 (2023): 5525. http://dx.doi.org/10.3765/plsa.v8i1.5525.

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Syntax and sociophonetics are typically treated as wildly disjointed (possibly even incompatible) theoretical pursuits. This paper seeks to unite sociophonetic speech perception and syntax research by presenting participants with matching or mismatching social expectations during a structural grammaticality judgment task. Place is the unifying social association between guise and structure. Participants completed a between-subjects matched guise survey with place-based grammatical structures spoken in either a matching place-based, local accent or a nonlocal accent. Place-based structures are

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36

Chen, Chaorong, Jun Ge, Weidong Guo, et al. "The Biophysical Impacts of Idealized Afforestation on Surface Temperature in China: Local and Nonlocal Effects." Journal of Climate 35, no. 23 (2022): 4233–52. http://dx.doi.org/10.1175/jcli-d-22-0144.1.

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Abstract Afforestation can impact surface temperature through local and nonlocal biophysical effects. However, the local and nonlocal effects of afforestation in China have rarely been explicitly investigated. In this study, we separate the local and nonlocal effects of idealized afforestation in China based on a checkerboard method and the regional Weather Research and Forecasting (WRF) Model. Two checkerboard pattern–like afforestation simulations (AFF1/4 and AFF3/4) with regularly spaced afforested and unaltered grid cells are performed; afforestation is implemented in one out of every four

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37

Chacón-Cortés, Leonardo Fabio, and Oscar Francisco Casas-Sánchez. "Non-radial functions, nonlocal operators and Markov processes over p-adic numbers." Universitas Scientiarum 24, no. 2 (2019): 381–406. http://dx.doi.org/10.11144/javeriana.sc24-2.nrfn.

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The main goal of this article is to study a new class of nonlocal operators and the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated with them. The fundamental solutions of these equations are transition functions of Markov processes on an n-dimensional vector space over the p-adic numbers. We also study some properties of these Markov processes, including the first passage time problem.

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38

Chen, Ru, Glenn R. Flierl, and Carl Wunsch. "A Description of Local and Nonlocal Eddy–Mean Flow Interaction in a Global Eddy-Permitting State Estimate." Journal of Physical Oceanography 44, no. 9 (2014): 2336–52. http://dx.doi.org/10.1175/jpo-d-14-0009.1.

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Abstract The assumption that local baroclinic instability dominates eddy–mean flow interactions is tested on a global scale using a dynamically consistent eddy-permitting state estimate. Interactions are divided into local and nonlocal. If all the energy released from the mean flow through eddy–mean flow interaction is used to support eddy growth in the same region, or if all the energy released from eddies through eddy–mean flow interaction is used to feed back to the mean flow in the same region, eddy–mean flow interaction is local; otherwise, it is nonlocal. Different regions have different

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39

Yang, Leiyu, Yuzhou Han, Yuchen Li, Jiashuo Wu, Jiejie Cai, and Jihou Yang. "Chain reaction of wave splitting based on roton-like dispersion in graded nonlocal periodic structures." Physica Scripta 100, no. 6 (2025): 065401. https://doi.org/10.1088/1402-4896/adcfd2.

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Abstract Although rotons are fundamental to quantum fluid dynamics, their classical analogues in engineered systems remain underexploited for wave control applications. This study explores wave manipulation mechanisms of one-dimensional nonlocal periodic structures with roton-like dispersion characteristics. A nonlocal model with long-range interactions is established. It can produce roton-like dispersion relations. Theoretical analysis is conducted to explore the influence of nonlocal effects on the dispersion characteristics. The multiple wavevector regions where positive and negative slopes

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40

Brener, A. M. "Nonlocal equations of the heat and mass transfer in technological processes." Theoretical Foundations of Chemical Engineering 40, no. 6 (2006): 564–72. http://dx.doi.org/10.1134/s0040579506060029.

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41

Peters, Vanessa N., Srujana Prayakarao, Samantha R. Koutsares, Carl E. Bonner, and Mikhail A. Noginov. "Control of Physical and Chemical Processes with Nonlocal Metal–Dielectric Environments." ACS Photonics 6, no. 12 (2019): 3039–56. http://dx.doi.org/10.1021/acsphotonics.9b00734.

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42

Gurevich, P. L. "Unbounded perturbations of two-dimensional diffusion processes with nonlocal boundary conditions." Doklady Mathematics 76, no. 3 (2007): 891–95. http://dx.doi.org/10.1134/s1064562407060221.

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43

Alegría, Francisco, Verónica Poblete, and Juan C. Pozo. "Nonlocal in-time telegraph equation and telegraph processes with random time." Journal of Differential Equations 347 (February 2023): 310–47. http://dx.doi.org/10.1016/j.jde.2022.12.001.

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44

Tumbarell Aranda, Orestes, André L. A. Penna, and Fernando A. Oliveira. "Nonlinear self-organized population dynamics induced by external selective nonlocal processes." Communications in Nonlinear Science and Numerical Simulation 93 (February 2021): 105512. http://dx.doi.org/10.1016/j.cnsns.2020.105512.

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45

Bogatov, A. V. "A PROBLEM WITH NONLOCAL CONDITION FOR ONE-DIMENSIONAL HYPERBOLIC EQUATION." Vestnik of Samara University. Natural Science Series 27, no. 1 (2021): 7–14. http://dx.doi.org/10.18287/2541-7525-2021-27-1-7-14.

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In this paper, we study the problem with a dynamic nonlocal condition for the one-dimensional hyperbolic equation, which occurs in the study of rod vibrations. This problem may be used as a mathematical model oflongitudinal vibration in a thick short bar and illustrates a nonlocal approach to such processes. Conditions have been obtained for input data, providing unambiguous resolution of the task, proof of the existence and singularity of the problem in the space of Sobolev. The proof is based on the a priori estimates obtained in this paper, Galerkins procedure and the properties of the Sobo

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46

Ryzhikov, P. S., and V. A. Makarov. "Intrinsic symmetry of nonlocal nonlinear optical susceptibility tensor in degenerate multi-wave mixing." Laser Physics Letters 20, no. 10 (2023): 105401. http://dx.doi.org/10.1088/1612-202x/acf045.

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Abstract Using energy and momentum conservation laws, we obtained the intrinsic symmetry relations for the nonlocal nonlinear optical susceptibility tensor in lossless nth order nonlinear medium of arbitrary symmetry class for the case when less than n + 1 electromagnetic waves with different frequencies interact. Particular attention is devoted to the relations of the components of this tensor, which cannot be obtained as limiting case from the symmetry relations for the nonlocal nonlinear susceptibility tensor describing interaction of exactly n + 1 waves with different frequencies. The exam

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Mikki, Said. "On the Topological Structure of Nonlocal Continuum Field Theories." Foundations 2, no. 1 (2021): 20–84. http://dx.doi.org/10.3390/foundations2010003.

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An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which phy

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Pham Thanh, Tuan. "REGULARITY AND CONVERGENCE TO EQUILIBRIUM FOR A CLASS OF NONLOCAL EVOLUTION EQUATIONS." Journal of Science Natural Science 66, no. 2 (2021): 14–36. http://dx.doi.org/10.18173/2354-1059.2021-0025.

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We study a class of semilinear nonlocal partial differential equations, which model different problems related to processes in materials with memory. Our aim is to derive sufficient conditions ensuring the global solvability, regularity, and convergence to equilibrium of solutions

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Xu, Binbin, and Yuhui Zheng. "Learnable Nonlocal Contrastive Network for Single Image Super-Resolution." Applied Sciences 13, no. 12 (2023): 7160. http://dx.doi.org/10.3390/app13127160.

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Single image super-resolution (SISR) aims to recover a high-resolution image from a single low-resolution image. In recent years, SISR methods based on deep convolutional neural networks have achieved remarkable success, and some methods further improve the performance of the SISR model by introducing nonlocal attention into the model. However, most SISR methods that introduce nonlocal attention focus on more complex attention mechanisms and only use fixed functions for measurement when exploring image similarity. In addition, the model penalizes the algorithm in terms of loss when the output

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Yang, Wenzhi, and Zengtao Chen. "Nonlocal dual-phase-lag heat conduction and the associated nonlocal thermal-viscoelastic analysis." International Journal of Heat and Mass Transfer 156 (August 2020): 119752. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2020.119752.

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