Relevant bibliographies by topics / Nonlocal theorie

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Nonlocal theorie'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Nonlocal theorie"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Nonlocal theorie"

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Nemati, Navid. "Theorie macroscopique de propagation du son dans les milieux poreux 'à structure rigide permettant la dispersion spatiale: principe et validation." Phd thesis, Université du Maine, 2012. http://tel.archives-ouvertes.fr/tel-00848603.

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Ce travail présente et valide une théorie nonlocale nouvelle et généralisée, de la propagation acoustique dans les milieux poreux à structure rigide, saturés par un fluide viscothermique. Cette théorie linéaire permet de dépasser les limites de la théorie classique basée sur la théorie de l'homogénéisation. Elle prend en compte non seulement les phénomènes de dispersion temporelle, mais aussi ceux de dispersion spatiale. Dans le cadre de la nouvelle approche, une nouvelle procédure d'homogénéisation est proposée, qui permet de trouver les propriétés acoustiques à l'échelle macroscopique, en résolvant deux problèmes d'action-réponse indépendants, posés à l'échelle microscopique de Navier-Stokes-Fourier. Contrairement à la méthode classique d'homogénéisation, aucune contrainte de séparation d'échelle n'est introduite. En l'absence de structure solide, la procédure redonne l'équation de dispersion de Kirchhoff-Langevin, qui décrit la propagation des ondes longitudinales dans les fluides viscothermiques. La nouvelle théorie et procédure d'homogénéisation nonlocale sont validées dans trois cas, portant sur des microgéométries significativement différentes. Dans le cas simple d'un tube circulaire rempli par un fluide viscothermique, on montre que les nombres d'ondes et les impédances prédits par la théorie nonlocale, coïncident avec ceux de la solution exacte de Kirchhoff, connue depuis longtemps. Au contraire, les résultats issus de la théorie locale (celle de Zwikker et Kosten, découlant de la théorie classique d'homogénéisation) ne donnent que le mode le plus attenué, et encore, seulement avec le petit désaccord existant entre la solution simplifiée de Zwikker et Kosten et celle exacte de Kirchhoff. Dans le cas où le milieu poreux est constitué d'un réseau carré de cylindres rigides parallèles, plongés dans le fluide, la propagation étant regardée dans une direction transverse, la vitesse de phase du mode le plus atténué peut être calculée en fonction de la fréquence en suivant les approches locale et nonlocale, résolues au moyen de simulations numériques par la méthode des Eléments Finis. Elle peut être calculée d'autre part par une méthode complètement différente et quasi-exacte, de diffusion multiple prenant en compte les effets viscothermiques. Ce dernier résultat quasi-exact montre un accord remarquable avec celui obtenu par la théorie nonlocale, sans restriction de longueur d'onde. Avec celui de la théorie locale, l'accord ne se produit que tant que la longueur d'onde reste assez grande.
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Iwasaki, Masayuki. "Nonlocal potentials and nuclear resonance scattering /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu148726053195632.

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LOMBARDINI, LUCA. "MINIMIZATION PROBLEMS INVOLVING NONLOCAL FUNCTIONALS: NONLOCAL MINIMAL SURFACES AND A FREE BOUNDARY PROBLEM." Doctoral thesis, Università degli Studi di Milano, 2019. http://hdl.handle.net/2434/607164.

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This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the s-fractional perimeter and its minimizers, the s-minimal sets. We investigate the behavior of sets having (locally) finite fractional perimeter and we establish existence and compactness results for (locally) s-minimal sets. We study the s-minimal sets in highly nonlocal regimes, that correspond to small values of the fractional parameter s. We introduce a functional framework for studying those s-minimal sets that can be globally written as subgraphs. In particular, we prove existence and uniqueness results for minimizers of a fractional version of the classical area functional and we show the equivalence between minimizers and various notions of solution of the fractional mean curvature equation. We also prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. Moreover, we consider a free boundary problem, which consists in the minimization of a functional defined as the sum of a nonlocal energy, plus the classical perimeter. Concerning this problem, we prove uniform energy estimates and we study the blow-up sequence of a minimizer---in particular establishing a Weiss-type monotonicity formula.
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Freitas, Pedro S. C. de. "Some problems in nonlocal reaction-diffusion equations." Thesis, Heriot-Watt University, 1994. http://hdl.handle.net/10399/1401.

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Magleby, Stephanie Allred. "The Violation of Bell's Inequality in a Deterministic but Nonlocal Model." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1197.pdf.

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Oterkus, Erkan. "Peridynamic Theory for Modeling Three-Dimensional Damage Growth in Metallic and Composite Structures." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/145366.

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A recently introduced nonlocal peridynamic theory removes the obstacles present in classical continuum mechanics that limit the prediction of crack initiation and growth in materials. It is also applicable at different length scales. This study presents an alternative approach for the derivation of peridynamic equations of motion based on the principle of virtual work. It also presents solutions for the longitudinal vibration of a bar subjected to an initial stretch, propagation of a pre-existing crack in a plate subjected to velocity boundary conditions, and crack initiation and growth in a plate with a circular cutout. Furthermore, damage growth in composites involves complex and progressive failure modes. Current computational tools are incapable of predicting failure in composite materials mainly due to their mathematical structure. However, the peridynamic theory removes these obstacles by taking into account non-local interactions between material points. Hence, an application of the peridynamic theory to predict how damage propagates in fiber reinforced composite materials subjected to mechanical and thermal loading conditions is presented. Finally, an analysis approach based on a merger of the finite element method and the peridynamic theory is proposed. Its validity is established through qualitative and quantitative comparisons against the test results for a stiffened composite curved panel with a central slot under combined internal pressure and axial tension. The predicted initial and final failure loads, as well as the final failure modes, are in close agreement with the experimental observations. This proposed approach demonstrates the capability of the PD approach to assess the durability of complex composite structures.
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Zhang, You-Kuan. "A quasilinear theory of time-dependent nonlocal dispersion in geologic media." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185039.

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A theory is presented which accounts for a particular aspect of nonlinearity caused by the deviation of plume "particles" from their mean trajectory in three-dimensional, statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities. Quasilinear expressions for the time-dependent nonlocal dispersivity and spatial covariance tensors of ensemble mean concentration are derived, as a function of time, variance σᵧ² of log hydraulic conductivity, degree of anisotropy, and flow direction. One important difference between existing linear theories and the new quasilinear theory is that in the former transverse nonlocal dispersivities tend asymptotically to zero whereas in the latter they tend to nonzero Fickian asymptotes. Another important difference is that while all existing theories are nominally limited to situations where σᵧ² is less than 1, the quasilinear theory is expected to be less prone to error when this restriction is violated because it deals with the above nonlinearity without formally limiting σᵧ². The theory predicts a significant drop in dimensionless longitudinal dispersivity when σᵧ² is large as compared to the case where σᵧ² is small. As a consequence of this drop the real asymptotic longitudinal dispersivity, which varies in proportion to σᵧ² when σᵧ² is small, is predicted to vary as σᵧ when σᵧ² is large. The dimensionless transverse dispersivity also drops significantly at early dimensionless time when σᵧ² is large. At late time this dispersivity attains a maximum near σᵧ² = 1, varies asymptotically at a rate proportional to σᵧ² when σᵧ² is small, and appears inversely proportional to σᵧ when σᵧ² is large. The actual asymptotic transverse dispersivity varies in proportion to σᵧ⁴ when σᵧ² is small and appears proportional to σᵧ when σᵧ² is large. One of the most interesting findings is that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the orientation of longitudinal spread is generally offset from μ toward the direction of largest log hydraulic conductivity correlation scale. When local dispersion is active, a plume starts elongating parallel to μ. With time the long axis of the plume rotates toward the direction of largest correlation scale, then rotates back toward μ, and finally stabilizes asymptotically at a relatively small angle of deflection. Application of the theory to depth-averaged concentration data from the recent tracer experiment at Borden, Ontario, yields a consistent and improved fit without any need for parameter adjustment.
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AUGELLO, RICCARDO. "Advanced FEs for the micropolar and geometrical nonlinear analyses of composite structures." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2872330.

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Foghem, Gounoue Guy Fabrice [Verfasser]. "$L^2$-Theory for nonlocal operators on domains / Guy Fabrice Foghem Gounoue." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1219215139/34.

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BRASSEUR, JULIEN. "ANALYSIS OF SOME NONLOCAL MODELS IN POPULATION DYNAMICS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/597755.

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This thesis is mainly devoted to the mathematical analysis of some nonlocal models arising in population dynamics. In general, the study of these models meets with numerous difficulties owing to the lack of compactness and of regularizing effects. In this respect, their analysis requires new tools, both theoretical and qualitative. We present several results in this direction. In the first part, we develop a functional analytic toolbox which allows one to handle some quantities arising in the study of these models. In the first place, we extend the characterization of Sobolev spaces due to Bourgain, Brezis and Mironescu to low regularity function spaces of Besov type. This results in a new theoretical framework that is more adapted to the study of some nonlocal equations of Fisher-KPP type. In the second place, we study the regularity of the restrictions of these functions to hyperplanes. We prove that, for a large class of Besov spaces, a surprising loss of regularity occurs. Moreover, we obtain an optimal characterization of the regularity of these restrictions in terms of spaces of so-called “generalized smoothness”. In the second part, we study qualitative properties of solutions to some nonlocal reaction-diffusion equations set in (possibly) heterogeneous domains. In collaboration with J. Coville, F. Hamel and E. Valdinoci, we consider the case of a perforated domain which consists of the Euclidean space to which a compact set, called an “obstacle”, is removed. When the latter is convex (or close to being convex), we prove that the solutions are necessarily constant. In a joint work with J. Coville, we study in greater detail the influence of the geometry of the obstacle on the classification of the solutions. Using tools of the type of those developed in the first part of this thesis, we construct a family of counterexamples when the obstacle is no longer convex. Lastly, in a work in collaboration with S. Dipierro, we study qualitative properties of solutions to nonlinear elliptic systems in variational form. We establish various monotonicity results in a fairly general setting that covers both local and fractional operators.
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Books on the topic "Nonlocal theorie"

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Eringen, A. Cemal, ed. Nonlocal Continuum Field Theories. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/b97697.

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Nonlocal continuum field theories. New York: Springer, 2002.

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Chen, Jingkai. Nonlocal Euler–Bernoulli Beam Theories. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4.

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S, Ilʹi͡ashenko I͡U. Nonlocal bifurcations. Providence, R.I: American Mathematical Society, 1999.

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Ilyashenko, Yu S. Nonlocal bifurcations. Providence, R.I: American Mathematical Society, 1999.

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Nonlocal quantum field theory and stochastic quantum mechanics. Dordrecht: D. Reidel pub. Co., 1986.

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Boyd, J. P. Weakly nonlocal solitary waves and beyond-all-orders asymptotics: Generalized solitons and hyperasymptotic perturbation theory. Dordrecht: Kluwer Academic Publishers, 1998.

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Ordinary differential equations: Qualitative theory. Providence, R.I: American Mathematical Society, 2010.

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Kloeden, Peter E. Nonautonomous dynamical systems. Providence, R.I: American Mathematical Society, 2011.

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Eringen, A. Cemal. Nonlocal Continuum Field Theories. Springer, 2002.

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Book chapters on the topic "Nonlocal theorie"

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Jirásek, Milan. "Nonlocal Theories." In Encyclopedia of Continuum Mechanics, 1–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2018. http://dx.doi.org/10.1007/978-3-662-53605-6_148-1.

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Jirásek, Milan. "Nonlocal Theories." In Encyclopedia of Continuum Mechanics, 1869–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-55771-6_148.

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Meher, Ramakanta. "Nonlocal Existence Theorem." In Textbook on Ordinary Differential Equations, 47–80. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003360643-4.

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Chen, Jingkai. "Nonlocal Beam Equations." In Nonlocal Euler–Bernoulli Beam Theories, 5–7. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_2.

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Askes, Harm, Terry Bennett, and Sivakumar Kulasegaram. "Meshless discretisation of nonlocal damage theories." In IUTAM Symposium on Discretization Methods for Evolving Discontinuities, 3–20. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6530-9_1.

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Chadan, K., P. C. Sabatier, and R. G. Newton. "Nonlocal Separable Interactions." In Inverse Problems in Quantum Scattering Theory, 112–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83317-5_8.

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Chen, Jingkai. "Peridynamics Beam Equation." In Nonlocal Euler–Bernoulli Beam Theories, 9–21. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_3.

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Chen, Jingkai. "Analytical Solution to Benchmark Examples." In Nonlocal Euler–Bernoulli Beam Theories, 23–47. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_4.

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Chen, Jingkai. "Numerical Solutions to Peridynamic Beam." In Nonlocal Euler–Bernoulli Beam Theories, 49–57. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_5.

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Chen, Jingkai. "Conclusion." In Nonlocal Euler–Bernoulli Beam Theories, 59. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_6.

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Conference papers on the topic "Nonlocal theorie"

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Li, Shi-Ming, and Danesh K. Tafti. "A Mean-Field Free-Energy Lattice Boltzmann Model for Liquid-Vapor Interfaces." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98021.

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A nonlocal pressure equation is proposed for liquid-vapor interfaces based on mean-field theory. The new nonlocal pressure equation is shown to be a generalized form of the nonlocal pressure equation of the van der Waals theory or the “square-gradient theory”. The proposed nonlocal pressure is implemented in the mean-field free-energy lattice Boltzmann method (LBM) proposed by Zhang et al (2004). The modified LBM is applied to simulate equilibrium interface properties and the interface dynamics of capillary waves. Computed results are validated with Maxwell constructions of liquid-vapor coexistence densities, theoretical relationship of variation of surface tension with temperature, theoretical planar interface density profiles, and the dispersion relation between frequency and wave number describing the dynamics of capillary waves. It is shown that the modified LBM gives very good agreement with the theories. In addition, preliminary calculations of phase transition and binary droplet coalescence are also presented.
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Pasharavesh, Abdolreza, Y. Alizadeh Vaghasloo, M. T. Ahmadian, and Reza Moheimani. "Nonlinear Vibration Analysis of Nano to Micron Scale Beams Under Electric Force Using Nonlocal Theory." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47615.

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Electrostatically actuated beams are fundamental blocks of many different nano and micro electromechanical devices. Accurate design of these devices strongly relies on recognition of static and dynamic behavior and response of mechanical components. Taking into account the effect of internal forces between material particles nonlocal theories become highly important. In this paper nonlinear vibration of a micro\nano doubly clamped and cantilever beam under electric force is investigated using nonlocal continuum mechanics theory. Implementing differential form of nonlocal constitutive equation the nonlinear partial differential equation of motion is reformulated. The equation of motion is nondimentioanalized to study the effect of applied nonlocal theories. Galerkin decomposition method is used to transform governing equation to a nonlinear ordinary differential equation. Homotopy perturbation method is implemented to find semi-analytic solution of the problem. Size effect on vibration frequency for various applied voltages is studied. Results indicate as size decreases the dimensionless frequency increases for a cantilever beam and decreases for a doubly clamped beam. Size effect is specially significant as the beam size tends toward nano scale in the analysis.
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Suzuki, Takashi, and Futoshi Takahashi. "Non-topological condensates in self-dual Chern-Simons gauge theory." In Nonlocal Elliptic and Parabolic Problems. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc66-0-22.

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Alavinasab, Ali, Goodarz Ahmadi, and Ratneshwar Jha. "Nonlocal Continuum Theory Based Modeling of Carbon Nanotube Composites." In ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2008. http://dx.doi.org/10.1115/smasis2008-595.

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Analytical modeling of Carbon Nanotube (CNT) composite based on the nonlocal continuum theory is investigated. This approach accounts for nonlocal stress-strain relationships, that is, stress at any point in a structure is a function of strain in the entire structure. Finite element analysis of a representative volume element (RVE) of CNT composite is used to evaluate unknown constant in the nonlocal theory based solution. Stress distributions are obtained from finite element method (FEM), nonlocal theory, and standard (local) elasticity. Nonlocal theory and FEM stress distributions yield the same total force and first moment, whereas standard elasticity gives less accurate results.
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MORAWETZ, KLAUS, VÁCLAV ŠPIČKA, and PAVEL LIPAVSKÝ. "NONLOCAL KINETIC THEORY." In Proceedings of the 10th International Conference. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792754_0054.

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MORAWETZ, K., V. ŠPIČKA, and P. LIPAVSKÝ. "NONLOCAL KINETIC THEORY." In Proceedings of the Conference “Kadanoff-Baym Equations: Progress and Perspectives for Many-Body Physics”. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812793812_0004.

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MOFFAT, J. W. "NONLOCAL GAUGE INVARIANT FIELD THEORIES." In Proceedings of the International Seminar. WORLD SCIENTIFIC, 1991. http://dx.doi.org/10.1142/9789814439336_0017.

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Rafati, Jacob, Mohsen Asghari, and Sachin Goyal. "Effects of DNA Encapsulation on Buckling Instability of Carbon Nanotube Based on Nonlocal Elasticity Theory." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34430.

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Abstract:
Carbon nanotubes (CNTs) are capable to absorb and encapsulate some molecules to create new hybrid nano-structures providing a variety of functionally useful properties. CNTs functionalized by encapsulaitng single-stranded deoxy-ribonucleic acid (ssDNA) promise great potentials for applications in nanotechnology and nano-biotechnology. In this paper, buckling instability of ssDNA@CNT i.e. hybrid nano-structure composed of ssDNA encapsulated inside CNT has been investigated using the nonlocal elasticity theory. The nonlocal elasticity theory is capable to capture the small scale effects due to the discontinuity of nano-structures at atomic scales. The nonlocal elastic rod and shell equations are derived for modeling ssDNA and CNT respectively. Providing numerical examples, it is predicted that, ssDNA@(10,10) CNT is more resistant than the pristine (10,10) CNT against the buckling instability under radial pressure due to the inter-atomic van der Waals interactions between DNA and CNT. Furthermore, nonlocal elasticity theory predicts lower critical buckling pressure than does the local elasticity theory.
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Bakhtiari-Nejad, Firooz, and Mostafa Nazemizadeh. "An Investigation on Resonant Characteristics of Micro/Nano-Beams Based on Nonlocal Elasticity Theory." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60458.

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In present paper, resonant characteristics of vibrating micro/nano-beams are investigated based on the nonlocal elasticity theory. The natural frequency and quality factor of the micro/nano-beams are known as important resonant characteristics which play crucial roles in resonant vibration of the beams in air environments. To determine the resonant characterizes of the micro/nano-beams, the governing vibration equation of the nonlocal beam with fixed end supports is derived considering the air damping force. As the beam is modeled the beam as a string of vibrating adjacent spheres in interaction with the ambient air environment, the air damping force is obtained as a function of the resonant frequency. Furthermore, to calculate the quality factor of the size-dependent micro/nano-beams, the time-dependent vibration equation is presented in modal space based on the orthogonality conditions. Therefore, the quality factor obtained as a function of the natural frequencies and size-dependent nonlocal parameter at various resonant modes of vibration. Then, a parametric study investigates the nonlocal effects on the quality factor of the resonant micro/nano-beam. The obtained results indicate that the nonlocal size effects decreases the quality factor. In addition, the size effects play more prominent role at the higher resonant modes of vibration.
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Gulian, Mamikon. "A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus." In Proposed for presentation at the One Nonlocal World. US DOE, 2021. http://dx.doi.org/10.2172/1841821.

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Reports on the topic "Nonlocal theorie"

1

D'Elia, Marta, Mamikon Gulian, George Karniadakis, and Hayley Olson. A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus. Office of Scientific and Technical Information (OSTI), May 2020. http://dx.doi.org/10.2172/1618398.

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Bazant, Zdenek P. Nonlocal Theory for Fracturing of Quasibrittle Materials. Fort Belvoir, VA: Defense Technical Information Center, March 1994. http://dx.doi.org/10.21236/ada278283.

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Silverstein, Eva M. Nonlocal String Theories on AdS{sub 3} x S{sup 3} and Stable Non-Supersymmetric Backgrounds. Office of Scientific and Technical Information (OSTI), January 2002. http://dx.doi.org/10.2172/798959.

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