Статті в журналах: "Nonlocal theorie"

1

Krasnikov, N. V. "Nonlocal gauge theories." Theoretical and Mathematical Physics 73, no. 2 (November 1987): 1184–90. http://dx.doi.org/10.1007/bf01017588.

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2

Moghtaderi, Saeed H., Alias Jedi, and Ahmad Kamal Ariffin. "A Review on Nonlocal Theories in Fatigue Assessment of Solids." Materials 16, no. 2 (January 15, 2023): 831. http://dx.doi.org/10.3390/ma16020831.

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A review of nonlocal theories utilized in the fatigue and fracture modeling of solid structures is addressed in this paper. Numerous papers have been studied for this purpose, and various nonlocal theories such as the nonlocal continuum damage model, stress field intensity model, peridynamics model, elastic-plastic models, energy-based model, nonlocal multiscale model, microstructural sensitive model, nonlocal lattice particle model, nonlocal high cycle fatigue model, low cycle fatigue model, nonlocal and gradient fracture criteria, nonlocal coupled damage plasticity model and nonlocal fracture criterion have been reviewed and summarized in the case of fatigue and fracture of solid structures and materials.

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3

KAVIANI, FAREED, and HAMID REZA MIRDAMADI. "SNAP-THROUGH AND BIFURCATION OF NANO-ARCHES ON ELASTIC FOUNDATION BY THE STRAIN GRADIENT AND NONLOCAL THEORIES." International Journal of Structural Stability and Dynamics 13, no. 05 (May 28, 2013): 1350022. http://dx.doi.org/10.1142/s0219455413500223.

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This paper presents the snap-through and bifurcation elastic stability analysis of nano-arch type structures with the Winkler foundation under transverse loadings by the strain gradient and stress gradient (nonlocal) theories. The equations of equilibrium are derived by using the variational method and virtual displacement theorem of minimum total potential energy. In the elastic stability analysis, von Karman's nonlinear strain component is included, with the deformation represented by a series solution. It is concluded that in general, the strain gradient theory pushes the system away from instability as compared to the classical theory. However, the nonlocal theory does the reverse and causes the system to experience instability earlier than that of the classical theory. Moreover, theories with different small-size considerations change the mechanism of instability in different ways. For example, in similar conditions, the strain gradient theory causes the system to reach a snap-through point, while the nonlocal theory causes the system to stop at a bifurcation critical point.

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4

Eringen,, AC, and JL Wegner,. "Nonlocal Continuum Field Theories." Applied Mechanics Reviews 56, no. 2 (March 1, 2003): B20—B22. http://dx.doi.org/10.1115/1.1553434.

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5

Calcagni, Gianluca, Michele Montobbio, and Giuseppe Nardelli. "Localization of nonlocal theories." Physics Letters B 662, no. 3 (April 2008): 285–89. http://dx.doi.org/10.1016/j.physletb.2008.03.024.

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6

Carmi, Avishy, and Eliahu Cohen. "Relativistic independence bounds nonlocality." Science Advances 5, no. 4 (April 2019): eaav8370. http://dx.doi.org/10.1126/sciadv.aav8370.

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If nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum nonlocality. However, none of them can explain the set of quantum correlations arising in the simplest scenarios. Here, it is shown that generalized uncertainty relations, as well as a specific notion of locality, give rise to both familiar and new characterizations of quantum correlations. In particular, we identify a condition, relativistic independence, which states that uncertainty relations are local in the sense that they cannot be influenced by other experimenters’ choices of measuring instruments. We prove that theories with nonlocal correlations stronger than the quantum ones do not satisfy this notion of locality, and therefore, they either violate the underlying generalized uncertainty relations or allow experimenters to nonlocally tamper with the uncertainty relations of their peers.

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7

Byszewski, Ludwik. "Existence of a solution of a Fourier nonlocal quasilinear parabolic problem." Journal of Applied Mathematics and Stochastic Analysis 5, no. 1 (January 1, 1992): 43–67. http://dx.doi.org/10.1155/s1048953392000042.

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The aim of this paper is to give a theorem about the existence of a classical solution of a Fourier third nonlocal quasilinear parabolic problem. To prove this theorem, Schauder's theorem is used. The paper is a continuation of papers [1]-[8] and the generalizations of some results from [9]-[11]. The theorem established in this paper can be applied to describe some phenomena in the theories of diffusion and heat conduction with better effects than the analogous classical theorem about the existence of a solution of the Fourier third quasilinear parabolic problem.

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8

Santos, J. V. Araújo dos, and J. N. Reddy. "Vibration of Timoshenko Beams Using Non-classical Elasticity Theories." Shock and Vibration 19, no. 3 (2012): 251–56. http://dx.doi.org/10.1155/2012/307806.

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This paper presents a comparison among classical elasticity, nonlocal elasticity, and modified couple stress theories for free vibration analysis of Timoshenko beams. A study of the influence of rotary inertia and nonlocal parameters on fundamental and higher natural frequencies is carried out. The nonlocal natural frequencies are found to be lower than the classical ones, while the natural frequencies estimated by the modified couple stress theory are higher. The modified couple stress theory results depend on the beam cross-sectional size while those of the nonlocal theory do not. Convergence of both non-classical theories to the classical theory is observed as the beam global dimension increases.

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9

Barci, D. G., and L. E. Oxman. "Asymptotic States in Nonlocal Field Theories." Modern Physics Letters A 12, no. 07 (March 7, 1997): 493–500. http://dx.doi.org/10.1142/s0217732397000510.

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Asymptotic states in field theories containing nonlocal kinetic terms are analyzed using the canonical method, naturally defined in Minkowski space. We apply our results to study the asymptotic states of a nonlocal Maxwell–Chern–Simons theory coming from bosonization in (2+1) dimensions. We show that in this case the only asymptotic state of the theory, in the trivial (non-topological) sector, is the vacuum.

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10

DI CECIO, G., and G. PAFFUTI. "SOME PROPERTIES OF RENORMALONS IN GAUGE THEORIES." International Journal of Modern Physics A 10, no. 10 (April 20, 1995): 1449–63. http://dx.doi.org/10.1142/s0217751x95000693.

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We find the explicit operatorial form of renormalon type singularities in Abelian gauge theory. Local operators of dimension six take care of the first UV renormalon; nonlocal operators are needed for IR singularities. In the effective Lagrangian constructed with these operators nonlocal imaginary parts appearing in the usual perturbative expansion at large orders are canceled.

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11

Mikki, Said. "On the Topological Structure of Nonlocal Continuum Field Theories." Foundations 2, no. 1 (December 31, 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 physical processes, such as the electromagnetic ones, take place. The added structures, essentially fibered spaces, model the topological microdomains of physics-based nonlocality and provide a fine-grained geometrical picture of field–matter interactions in nonlocal metamaterials. We utilize standard techniques in the theory of smooth manifolds to construct the Banach bundle structure by paying careful attention to the relevant physics. The electromagnetic response tensor is then reformulated as a superspace bundle homomorphism and the various tools needed to proceed from the local topology of microdomains to global domains are developed. For concreteness and simplicity, our presentations of both the fundamental theory and the examples given to illustrate the mathematics all emphasize the case of electromagnetic field theory, but the superspace formalism developed here is quite general and can be easily extended to other types of nonlocal continuum field theories. An application to fundamental theory is given, which consists of utilizing the proposed superspace theory of nonlocal metamaterials in order to explain why nonlocal electromagnetic materials often require additional boundary conditions or extra input from microscopic theory relative to local electromagnetism, where in the latter case such extra input is not needed. Real-life case studies quantitatively illustrating the microdomain structure in nonlocal semiconductors are provided. Moreover, in a series of connected appendices, we outline a new broad view of the emerging field of nonlocal electromagnetism in material domains, which, together with the main superspace formalism introduced in the main text, may be considered a new unified general introduction to the physics and methods of nonlocal metamaterials.

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12

SAAIDI, KHALED, and MOHAMMAD KHORRAMI. "NONLOCAL TWO-DIMENSIONAL YANG–MILLS AND GENERALIZED YANG–MILLS THEORIES." International Journal of Modern Physics A 15, no. 30 (December 10, 2000): 4749–59. http://dx.doi.org/10.1142/s0217751x0000197x.

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A generalization of the two-dimensional Yang–Mills and generalized Yang–Mills theory is introduced in which the building B-F theory is nonlocal in the auxiliary field. The classical and quantum properties of this nonlocal generalization are investigated and it is shown that for large gauge groups, there exists a simple correspondence between the properties of the nonlocal theory and its corresponding local theory.

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13

Alishahiha, Mohsen, and Alok Kumar. "PP-waves from Nonlocal Theories." Journal of High Energy Physics 2002, no. 09 (September 12, 2002): 031. http://dx.doi.org/10.1088/1126-6708/2002/09/031.

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14

Evens, D., J. W. Moffat, G. Kleppe, and R. P. Woodard. "Nonlocal regularizations of gauge theories." Physical Review D 43, no. 2 (January 15, 1991): 499–519. http://dx.doi.org/10.1103/physrevd.43.499.

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15

Addazi, Andrea. "Unitarization and causalization of nonlocal quantum field theories by classicalization." International Journal of Modern Physics A 31, no. 04n05 (February 3, 2016): 1650009. http://dx.doi.org/10.1142/s0217751x16500093.

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We suggest that classicalization can cure nonlocal quantum field theories from acausal divergences in scattering amplitudes, restoring unitarity and causality. In particular, in “trans-nonlocal” limit, the formation of nonperturbative classical configurations, called classicalons, in scatterings like [Formula: see text], can avoid typical acausal divergences.

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16

GRISARU, M. T., and P. VAN NIEUWENHUIZEN. "LOOP CALCULATIONS IN TWO-DIMENSIONAL NONLOCAL FIELD THEORIES." International Journal of Modern Physics A 07, no. 23 (September 20, 1992): 5891–915. http://dx.doi.org/10.1142/s0217751x92002684.

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We perform one-loop calculations in chiral induced W3 gravity in momentum space. Unlike a previous one-loop calculation in x space, which reduced the problem to one in local field theory, we work directly with the nonlocal action. We use Polyakov’s exponential regularization, and obtain agreement with the x-space calculation. We discuss the extension of our methods to higher-loop calculations in more-general chiral nonlocal field theories.

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17

Liu, Cai Ping, Qing Quan Duan, and Jian Ping Zuo. "Theoretical Research on the Dynamic Crack Propagation Velocity Based on Nonlocal Field Theories." Key Engineering Materials 417-418 (October 2009): 953–56. http://dx.doi.org/10.4028/www.scientific.net/kem.417-418.953.

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The purpose of this paper is to discuss the nonlocal effect on dynamic crack propagation velocity. Some experimental phenomena in dynamic fracture and simulative results using molecular & atom dynamics were analyzed and discussed in this paper. The authors found that there were still some disagreements on the dynamic crack propagation velocity. Based on these researches, we introduced nonlocal field theories into the estimation of dynamic crack propagation velocity. The dynamic crack propagation velocity is affected not only by the crack instability, but by characteristic length of material. A nonlocal characteristic length parameter M is defined through a double pile-up dislocation model. According to the Mott’s research method for crack velocity in dynamic fracture and the nonlocal field theories, an approximate theoretical dynamic propagation velocity is obtained. And we conclude that the velocity is related to the combined activity of the nonlocal characteristic length parameter M, the velocity of longitudinal wave, constant k, crack length and Poisson’s ratio.

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18

Diem, Dang Huan. "Existence for a Second-Order Impulsive Neutral Stochastic Integrodifferential Equations with Nonlocal Conditions and Infinite Delay." Chinese Journal of Mathematics 2014 (February 27, 2014): 1–13. http://dx.doi.org/10.1155/2014/143860.

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The current paper is concerned with the existence of mild solutions for a class of second-order impulsive neutral stochastic integrodifferential equations with nonlocal conditions and infinite delays in a Hilbert space. A sufficient condition for the existence results is obtained by using the Krasnoselskii-Schaefer-type fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. Finally, an application to the stochastic nonlinear wave equation with infinite delay is given.

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19

Bougoffa, Lazhar. "A third-order nonlocal problem with nonlocal conditions." International Journal of Mathematics and Mathematical Sciences 2004, no. 28 (2004): 1503–7. http://dx.doi.org/10.1155/s0161171204303017.

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We study an equation with dominated lower-order terms and nonlocal conditions. Using the Riesz representation theorem and the Schauder fixed-point theorem, we prove the existence and uniqueness of a generalized solution.

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20

Jung, Woo-Young, and Sung-Cheon Han. "Nonlocal Elasticity Theory for Transient Analysis of Higher-Order Shear Deformable Nanoscale Plates." Journal of Nanomaterials 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/208393.

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The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringen’s nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT). The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringen’s nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. On the basis of those numerical results, the relations between nonlocal and local theory are investigated and discussed, as are the nonlocal parameter, aspect ratio, side-to-thickness ratio, nano-scale plate size, and time step effects on the dynamic response. In order to validate the present solutions, the reference solutions are employed and examined. The results of nano-scale plates using the nonlocal theory can be used as a benchmark test for the transient analysis.

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21

Norouzzadeh, Amir, Mohammad Faraji Oskouie, Reza Ansari, and Hessam Rouhi. "Integral and differential nonlocal micromorphic theory." Engineering Computations 37, no. 2 (August 19, 2019): 566–90. http://dx.doi.org/10.1108/ec-01-2019-0008.

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Purpose This paper aims to combine Eringen’s micromorphic and nonlocal theories and thus develop a comprehensive size-dependent beam model capable of capturing the effects of micro-rotational/stretch/shear degrees of freedom of material particles and nonlocality simultaneously. Design/methodology/approach To consider nonlocal influences, both integral (original) and differential versions of Eringen’s nonlocal theory are used. Accordingly, integral nonlocal-micromorphic and differential nonlocal-micromorphic beam models are formulated using matrix-vector relations, which are suitable for implementing in numerical approaches. A finite element (FE) formulation is also provided to solve the obtained equilibrium equations in the variational form. Timoshenko micro-/nano-beams with different boundary conditions are selected as the problem under study whose static bending is addressed. Findings It was shown that the paradox related to the clamped-free beam is resolved by the present integral nonlocal-micromorphic model. It was also indicated that the nonlocal effect captured by the integral model is more pronounced than that by its differential counterpart. Moreover, it was revealed that by the present approach, the softening and hardening effects, respectively, originated from the nonlocal and micromorphic theories can be considered simultaneously. Originality/value Developing a hybrid size-dependent Timoshenko beam model including micromorphic and nonlocal effects. Considering the nonlocal effect based on both Eringen’s integral and differential models proposing an FE approach to solve the bending problem, and resolving the paradox related to nanocantilever.

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22

GOVINDARAJAN, T. R., SEÇKIN KÜRKÇÜOǦLU, and MARCO PANERO. "NONLOCAL REGULARISATION OF NONCOMMUTATIVE FIELD THEORIES." Modern Physics Letters A 21, no. 24 (August 10, 2006): 1851–63. http://dx.doi.org/10.1142/s021773230602113x.

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We study noncommutative field theories, which are inherently nonlocal, using a Poincaré-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cutoff scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention on the particular case when the noncommutativity parameter is inversely proportional to the square of the cutoff, via a dimensionless parameter η. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in η-dependent terms. The implications of this approach, which avoids the problems related to uv–ir mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories.

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23

Saravani, Mehdi. "Continuum modes of nonlocal field theories." Classical and Quantum Gravity 35, no. 7 (February 28, 2018): 074001. http://dx.doi.org/10.1088/1361-6382/aaaea8.

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24

Takabayasi, Takehiko. "25. Nonlocal Theories and Related Topics." Progress of Theoretical Physics Supplement 105 (1991): 270–86. http://dx.doi.org/10.1143/ptps.105.270.

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25

CALCAGNI, GIANLUCA, and GIUSEPPE NARDELLI. "COSMOLOGICAL ROLLING SOLUTIONS OF NONLOCAL THEORIES." International Journal of Modern Physics D 19, no. 03 (March 2010): 329–38. http://dx.doi.org/10.1142/s0218271810016440.

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We find nonperturbative solutions of a nonlocal scalar field equation, with cubic or exponential potential on a cosmological background. The former case corresponds to the lowest level effective tachyon action of cubic string field theory. While the well known Minkowski solution is wildly oscillating, due to Hubble friction its cosmological counterpart describes smooth rolling toward the local minimum of the potential.

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26

Cushman, J. H., and B. X. Hu. "A resumé of nonlocal transport theories." Stochastic Hydrology and Hydraulics 9, no. 2 (June 1995): 105–16. http://dx.doi.org/10.1007/bf01585601.

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27

Buoninfante, Luca, Gaetano Lambiase, and Masahide Yamaguchi. "Enlarging local symmetries: A nonlocal Galilean model." International Journal of Geometric Methods in Modern Physics 17, supp01 (May 26, 2020): 2040009. http://dx.doi.org/10.1142/s0219887820400095.

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We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing how the ultraviolet behavior of loop integrals can be ameliorated. We also discuss the pole structure of the propagator which has infinitely many complex conjugate poles, but satisfies tree level unitarity. Moreover, we will introduce the same kind of nonlocal operators in the context of linearized gravity. In such a scenario, the graviton propagator turns out to be ghost-free and the spacetime metric generated by a point-like source is non-singular.

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28

Byszewski, Ludwik. "Impulsive nonlocal nonlinear parabolic differential problems." Journal of Applied Mathematics and Stochastic Analysis 6, no. 3 (January 1, 1993): 247–60. http://dx.doi.org/10.1155/s1048953393000206.

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The aim of the paper is to prove a theorem about a weak impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities. A weak maximum principle for an impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities and an uniqueness criterion for the existence of the classical solution of an impulsive nonlocal nonlinear parabolic differential problem are obtained as a consequence of the theorem about the weak impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities.

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29

Barakat, M. A., Ahmed H. Soliman, and Abd-Allah Hyder. "Langevin Equations with Generalized Proportional Hadamard–Caputo Fractional Derivative." Computational Intelligence and Neuroscience 2021 (December 8, 2021): 1–18. http://dx.doi.org/10.1155/2021/6316477.

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We look at fractional Langevin equations (FLEs) with generalized proportional Hadamard–Caputo derivative of different orders. Moreover, nonlocal integrals and nonperiodic boundary conditions are considered in this paper. For the proposed equations, the Hyres–Ulam (HU) stability, existence, and uniqueness (EU) of the solution are defined and investigated. In implementing our results, we rely on two important theories that are Krasnoselskii fixed point theorem and Banach contraction principle. Also, an application example is given to bolster the accuracy of the acquired results.

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30

Askari, Hassan, Davood Younesian, Ebrahim Esmailzadeh, and Livija Cveticanin. "Nonlocal effect in carbon nanotube resonators: A comprehensive review." Advances in Mechanical Engineering 9, no. 2 (February 2017): 168781401668692. http://dx.doi.org/10.1177/1687814016686925.

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This article provides a comprehensive review about the use of nonlocal theory in modeling of the vibrations of the carbon nanotube resonators. It is fully described how the nonlocal effect has been exploited by researchers to mathematically model vibrations of carbon nanotube resonators. Fusion of different classical beam theories with nonlocal theory is discussed. Also, the article presents the combination of nonlocal models with different physical phenomena which have influence in the vibrations of carbon nanotube resonators.

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31

Barnaby, Neil. "Nonlocal inflationThis paper was prsented at the Theory CANADA 4 conference, held at the Centre de Recherches Mathématiques at the Université de Montréal, Québec, Canada on 4–7 June 2008." Canadian Journal of Physics 87, no. 3 (March 2009): 189–94. http://dx.doi.org/10.1139/p08-089.

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We consider the possibility of realizing inflation in nonlocal field theories containing infinitely many derivatives. Such constructions arise naturally in string field theory and also in a number of toy models, such as the p-adic string. After reviewing the complications (ghosts and instabilities) that arise when working with high-derivative theories, we discuss the the initial value problem and perturbative stability of theories with infinitely many derivatives. Next, we examine the inflationary dynamics and phenomenology of such theories. Nonlocal inflation can proceed even when the potential is naively too steep and generically predicts large non-Gaussianity in the cosmic microwave background.

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32

Li, Fang, Jin Liang, Tzon-Tzer Lu, and Huan Zhu. "A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/901942.

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This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach spaceX. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a concrete integrodifferential equation is obtained.

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33

GHIRARDI, GIANCARLO, and RAFFAELE ROMANO. "CLASSICAL, QUANTUM AND SUPERQUANTUM CORRELATIONS." International Journal of Modern Physics B 27, no. 01n03 (November 26, 2012): 1345011. http://dx.doi.org/10.1142/s0217979213450112.

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A deeper understanding of the origin of quantum correlations is expected to allow a better comprehension of the physical principles underlying quantum mechanics. In this work, we reconsider the possibility of devising "crypto-nonlocal theories", using a terminology firstly introduced by Leggett. We generalize and simplify the investigations on this subject which can be found in the literature. At their deeper level, such theories allow nonlocal correlations which can overcome the quantum limit.

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34

Benchohra, Mouffak, and Mohammed Souid. "L1-solutions for implicit fractional order differential equations with nonlocal conditions." Filomat 30, no. 6 (2016): 1485–92. http://dx.doi.org/10.2298/fil1606485b.

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In this paper we study the existence of integrable solutions of the nonlocal problem for fractional order implicit differential equations with nonlocal condition. Our results are based on Schauder?s fixed point theorem and the Banach contraction principle fixed point theorem.

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35

Cardinali, Tiziana, and Serena Gentili. "An existence theorem for a non-autonomous second order nonlocal multivalued problem." Studia Universitatis Babes-Bolyai Matematica 62, no. 1 (March 1, 2017): 101–17. http://dx.doi.org/10.24193/subbmath.2017.0008.

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36

Guo, Junhong, Tuoya Sun, and Ernian Pan. "Three-dimensional buckling of embedded multilayered magnetoelectroelastic nanoplates/graphene sheets with nonlocal effect." Journal of Intelligent Material Systems and Structures 30, no. 18-19 (September 22, 2019): 2870–93. http://dx.doi.org/10.1177/1045389x19873397.

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This article presents an exact analysis for the three-dimensional buckling problem of embedded multilayered magnetoelectroelastic and simply supported nanoplates/graphene sheets with nonlocal effect. The interaction between the multilayered nanoplates/graphene sheets and their surrounding medium is simulated by a Pasternak-type foundation. The critical loads for embedded multilayered magnetoelectroelastic nanoplates/graphene sheets under uniaxial and biaxial compression at small scale are then derived by solving the linear eigensystem and making use of the propagator matrix method. A comparison between the present anisotropic three-dimensional model and previous results (an asymptotic nonlocal elasticity theory for single elastic graphene sheet and classical orthotropic plate theories) is made to show the effectiveness and correctness of the present anisotropic three-dimensional model. Numerical examples are then presented for the variation of the dimensionless critical buckling loads for the homogeneous elastic graphene sheet with nonlocal effect, the homogeneous orthotropic thick plate without nonlocal effect, and the sandwich magnetoelectroelastic nanoplates made of piezoelectric and magnetostrictive materials with nonlocal effect. Furthermore, the effects of the thickness of nanoplates, nonlocal parameter, Winkler stiffness, and shear modulus of the elastic medium on the critical load of sandwich magnetoelectroelastic nanoplates/graphene sheets are demonstrated. These results should be very useful as benchmarks for the future development of approximate nanoplate/graphene sheet theories and numerical methods for modeling and simulation of multilayered nanoplates/graphene sheets with nonlocal effect.

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37

Barretta, Raffaele, Francesco Marotti de Sciarra, and Marzia Sara Vaccaro. "Nonlocal Elasticity for Nanostructures: A Review of Recent Achievements." Encyclopedia 3, no. 1 (February 27, 2023): 279–310. http://dx.doi.org/10.3390/encyclopedia3010018.

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Recent developments in modeling and analysis of nanostructures are illustrated and discussed in this paper. Starting with the early theories of nonlocal elastic continua, a thorough investigation of continuum nano-mechanics is provided. Two-phase local/nonlocal models are shown as possible theories to recover consistency of the strain-driven purely integral theory, provided that the mixture parameter is not vanishing. Ground-breaking nonlocal methodologies based on the well-posed stress-driven formulation are shown and commented upon as effective strategies to capture scale-dependent mechanical behaviors. Static and dynamic problems of nanostructures are investigated, ranging from higher-order and curved nanobeams to nanoplates. Geometrically nonlinear problems of small-scale inflected structures undergoing large configuration changes are addressed in the framework of integral elasticity. Nonlocal methodologies for modeling and analysis of structural assemblages as well as of nanobeams laying on nanofoundations are illustrated along with benchmark applicative examples.

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38

Tomboulis, E. T. "Renormalization and unitarity in higher derivative and nonlocal gravity theories." Modern Physics Letters A 30, no. 03n04 (January 30, 2015): 1540005. http://dx.doi.org/10.1142/s0217732315400052.

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We review and discuss higher derivative and nonlocal theories of quantum gravity focusing on their UV and unitarity properties. We first consider the general fourth-order gravitational action, then actions containing derivatives up to any given fixed order, and discuss their UV divergences, fixed points and concomitant unitarity issues. This leads to a more general discussion of "asymptotic safety" and unitarity, which motivates the introduction of nonlocal theories containing derivatives to all orders arising from the expansion of entire functions. For such theories good UV behavior is visible at any finite truncation, but unitarity emerges only when derivatives to all orders are included.

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39

PRADHAN, S. C., and J. K. PHADIKAR. "NONLOCAL THEORY FOR BUCKLING OF NANOPLATES." International Journal of Structural Stability and Dynamics 11, no. 03 (June 2011): 411–29. http://dx.doi.org/10.1142/s021945541100418x.

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Classical plate theory (CLPT) and first-order shear deformation plate theory (FSDT) of plates are reformulated using the nonlocal elasticity theory. Developed nonlocal plate theories have been applied to study buckling behavior of nanoplates. Nonlocal elasticity theory, unlike traditional elasticity theory introduces a length scale parameter into the formulation to take into account the discrete structure of the material to some extent. Both single-layered and multilayered nanoplates have been included in the analysis. Navier's approach has been used to obtain exact solutions for buckling loads for simply supported boundary conditions. Dependence of the small scale effect on various geometrical and material parameters has been investigated. Present study reveals the presence of significant small scale effect on the buckling response of nanoplates. The theoretical development and the numerical results presented in the present work are expected to promote the use of nonlocal theories for more accurate prediction of stability behavior of nanoplates and nanoshells.

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40

Vasiliev, V. V., and S. A. Lurie. "On correct nonlocal generalized theories of elasticity." Physical Mesomechanics 19, no. 3 (July 2016): 269–81. http://dx.doi.org/10.1134/s102995991603005x.

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41

Sladek, Jan, Vladimir Sladek, Jozef Kasala, and Ernian Pan. "Nonlocal and Gradient Theories of Piezoelectric Nanoplates." Procedia Engineering 190 (2017): 178–85. http://dx.doi.org/10.1016/j.proeng.2017.05.324.

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42

Iannece, Donatella, and Antonio Romano. "Solidification of small crystals and nonlocal theories." International Journal of Engineering Science 28, no. 6 (January 1990): 535–42. http://dx.doi.org/10.1016/0020-7225(90)90055-n.

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43

Iannece, D., and A. Romano. "Growth of macroscopic crystals and nonlocal theories." International Journal of Engineering Science 28, no. 11 (January 1990): 1199–204. http://dx.doi.org/10.1016/0020-7225(90)90117-2.

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44

Capri, M. A. L., V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes. "Local renormalizable gauge theories from nonlocal operators." Annals of Physics 323, no. 3 (March 2008): 752–67. http://dx.doi.org/10.1016/j.aop.2007.07.002.

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45

Hasani Baferani, A., and AR Ohadi. "Analytical investigation of the acoustic behavior of nanocomposite porous media by using modified nonlocal Biot’s equations." Journal of Vibration and Control 24, no. 13 (February 20, 2017): 2701–16. http://dx.doi.org/10.1177/1077546317693184.

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In this paper, the modified Biot’s equations based on nonlocal elasticity theory are presented for modeling nanocomposite porous media. The analytical solution of modified Biot’s equations is obtained by using the recently developed potential function method. By doing some mathematical manipulation, the coupled modified Biot’s equations are converted to two decoupled equations. Consequently, the variations of field variables and acoustical properties of a considered nanocomposite foam are studied by changing the nonlocal parameter. The obtained results show that the local Biot’s results are in good agreement with the nonlocal modified Biot’s results for very small values of the nonlocal parameter. In addition, the values of field variables (i.e. pressure) in the thickness direction are decreased by increasing the nonlocal parameter for frequencies below 5000 Hz. Furthermore, by increasing the nonlocal parameter, the differences between local and nonlocal values of field variables and the absorption coefficient increase. Also, the nonlocal parameter has no considerable effect on the absorption coefficient for frequencies lower than 2000 Hz, whereas by increasing the nonlocal parameter the differences between corresponding results of local and nonlocal theories increase for frequencies above 2000 Hz.

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46

Solonukha, O. "On periodic solutions of linear parabolic problems with nonlocal boundary conditions." TAURIDA JOURNAL OF COMPUTER SCIENCE THEORY AND MATHEMATICS, no. 2 (November 29, 2022): 7–11. http://dx.doi.org/10.29039/1729-3901-2021-20-2-7-11.

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47

Kataria, Haribhai R., Prakashkumar H. Patel, and Vishant Shah. "Existence results of noninstantaneous impulsive fractional integro-differential equation." Demonstratio Mathematica 53, no. 1 (January 1, 2020): 373–84. http://dx.doi.org/10.1515/dema-2020-0029.

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Abstract Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.

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48

Polonyi, Janos. "Boost invariant regulator for field theories." International Journal of Modern Physics A 34, no. 03n04 (February 10, 2019): 1950017. http://dx.doi.org/10.1142/s0217751x19500179.

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It is shown that by imposing the relativistic symmetries on the cutoff in field theories, one rules out all known nonperturbative regulators except the point splitting. The relativistic cutoff dynamics is nonlocal in time and thereby unstable, bringing the very existence of relativistic field theory into question. A stable, relativistic regulator is proposed for a scalar field theory model and its semiclassical stability is shown numerically.

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49

İlhan, Onur Alp, Danyal Soybaş, Shakirbay G. Kasimov, and Farhod D. Rakhmanov. "Solvability of mixed problems for heat equations with two nonlocal conditions." Mathematica Slovaca 72, no. 6 (December 1, 2022): 1573–84. http://dx.doi.org/10.1515/ms-2022-0108.

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Abstract In this study, the solvability of a problem of the heat conduction theory with two nonlocal boundary conditions is investigated. Systems of eigenfunctions of the corresponding operator with two nonlocal boundary conditions are taken into consideration. A theorem on the solvability of the problem of the theory of heat conduction with two nonlocal boundary conditions is given

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50

Byszewski, Ludwik. "Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals." Journal of Applied Mathematics and Stochastic Analysis 3, no. 1 (January 1, 1990): 65–79. http://dx.doi.org/10.1155/s1048953390000065.

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In [4] and [5], the author studied strong maximum principles for nonlinear parabolic problems with initial and nonlocal inequalities, respectively. Our purpose here is to extend results in [4] and [5] to strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with integrals. The results obtained in this paper can be applied in the theories of diffusion and heat conduction, since considered here integrals in nonlocal inequalities can be interpreted as mean amounts of the diffused substance or mean temperatures of the investigated medium.

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