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Relevant bibliographies by topics / Homogenization Theorem

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Academic literature on the topic 'Homogenization Theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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Journal articles on the topic "Homogenization Theorem"

1

Diakhaby, Aboubakary, and Youssef Ouknine. "Locally periodic homogenization of reflected diffusion." Journal of Applied Mathematics and Stochastic Analysis 2006 (July 6, 2006): 1–17. http://dx.doi.org/10.1155/jamsa/2006/37643.

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We study the homogenization of reflected SDEs with locally periodic coefficients and highly oscillating drift. Our method is entirely probabilistic, and builds upon earlier works of Tanaka, Benchérif-Madani and Pardoux, and Bensoussan et al We extend, to Tanaka's theorem locally periodic case.

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Gutierrez, Cristian E., and Ireneo Peral. "A real analysis theorem and applications to homogenization." Indiana University Mathematics Journal 50, no. 4 (2001): 1651–74. http://dx.doi.org/10.1512/iumj.2001.50.2101.

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BRAIDES, ANDREA, and MARGHERITA SOLCI. "INTERFACIAL ENERGIES ON PENROSE LATTICES." Mathematical Models and Methods in Applied Sciences 21, no. 05 (2011): 1193–210. http://dx.doi.org/10.1142/s0218202511005295.

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In this paper we prove a homogenization theorem for interfacial discrete energies defined on an a-periodic Penrose tiling in ℝ2. A general result on the homogenization of surface energies cannot be directly adapted to this case; the existence of the limit interfacial energy is therefore proved by showing some refined "quasi-periodic" properties of the tilings.

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Alvarez, Felipe, and Jean-Philippe Mandallena. "Multi-parameter homogenization by localization and blow-up." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 5 (2004): 801–14. http://dx.doi.org/10.1017/s0308210500003498.

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We give an alternative self-contained proof of the homogenization theorem for periodic multi-parameter integrals that was established by the authors. The proof in that paper relies on the so-called compactness method for Γ-convergence, while the one presented here is by direct verification: the candidate to be the limit homogenized functional is first exhibited and the definition of Γ-convergence is then verified. This is done by an extension of bounded gradient sequences using the Acerbi et al. extension theorem from connected sets, and by the adaptation of some localization and blow-up techn

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Lukkassen, Dag, Gabriel Nguetseng, Hubert Nnang, and Peter Wall. "Reiterated homogenization of nonlinear monotone operators in a general deterministic setting." Journal of Function Spaces and Applications 7, no. 2 (2009): 121–52. http://dx.doi.org/10.1155/2009/102486.

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We study reiterated homogenization of a nonlinear non-periodic elliptic differential operator in a general deterministic setting as opposed to the usual stochastic setting. Our approach proceeds from an appropriate notion of convergence termed reiterated Σ-convergence. A general deterministic homogenization theorem is proved and several concrete examples are studied under various structure hypotheses ranging from the classical periodicity hypothesis to more complicated, but realistic, structure hypotheses.

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Zubova, M. N., and T. A. Shaposhnikova. "Homogenization limit for the Diffusion Equation in a domain Perforated along (n - 1)-Dimensional Manifold with Dynamic Conditions on the Boundary of the Perforations: Critical Case." Доклады Академии наук 486, no. 1 (2019): 12–19. http://dx.doi.org/10.31857/s0869-5652486112-19.

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The problem of homogenization the diffusion equation in a domain perforated along an (n - 1)-dimensional manifold with dynamic boundary conditions on the boundary of the perforations is studied. A homogenization model is constructed that is a transmission problem for the diffusion equation with the transmission conditions containing a term with memory. A theorem on the convergence of solutions of the original problem to the solution of the homogenized one is proved.

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Sánchez Morgado, Héctor. "Homogenization for sub-riemannian Lagrangians." Nonlinearity 36, no. 6 (2023): 3043–67. http://dx.doi.org/10.1088/1361-6544/accdae.

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Abstract We consider Lagrangians that are defined only on the horizontal distribution of a sub-riemannian manifold. The associated Hamiltonian is neither strictly convex nor coercive. We prove a result on homogenization of the Hamilton–Jacobi equation following the approach in Contreras et al (2015 Calc. Var. Partial Differ. Equ. 52 237–52). To establish the result, we need to extend weak KAM and Aubry–Mather theories to the sub-riemannian setting. We obtain a Tonelli theorem to dispend of the Lagrangian dynamics tools used in standard weak KAM theory. In the way towards our main result we obs

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Gu, Yu. "A central limit theorem for fluctuations in 1D stochastic homogenization." Stochastics and Partial Differential Equations: Analysis and Computations 4, no. 4 (2016): 713–45. http://dx.doi.org/10.1007/s40072-016-0075-0.

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Chechkin, Gregory A., and Tatiana P. Chechkina. "Random Homogenization in a Domain with Light Concentrated Masses." Mathematics 8, no. 5 (2020): 788. http://dx.doi.org/10.3390/math8050788.

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In the paper, we consider an elliptic problem in a domain with singular stochastic perturbation of the density located near the boundary, depending on a small parameter. Using the boundary homogenization methods, we prove the compactness theorem and study the behavior of eigenelements to the initial problem as the small parameter tends to zero.

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Nguyen, Phuong H., Canh V. Le, and Phuc L. H. Ho. "Strength and fatigue analysis of periodic perforated materials using the computational homogenization and ES-FEM approaches." Vietnam Journal of Mechanics 44, no. 1 (2022): 83–95. http://dx.doi.org/10.15625/0866-7136/16852.

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This paper presents a computational homogenization shakedown analysis of periodic perforated materials with von Mises matrices. The plastic behaviors of the perforated materials under cyclic macroscopic loads are studied by means of kinematic shakedown theorem and computational homogenization method. The kinematic micro-fields are approximated by the edge-based smoothed finite element method. The resulting large-scale optimization problem is efficiently solved by using conic solver, enabling a large number of points on the macroscopic strength and fatigue surface to be calculated rapidly. The

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Dissertations / Theses on the topic "Homogenization Theorem"

1

Fabricius, John. "Homogenization theory with applications in tribology." Licentiate thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25720.

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Homogenization is a mathematical theory for studying differential equations with rapidly oscillating coefficents. Many important problems in physics with one or several microscopic length scales give rise to this kind of equations. Hence there is a need for methods that enable an efficient treatment of such problems. To this end several homogenization techniques exist, ranging from the fairly abstract ones to those that are more oriented towards applications. This thesis is concerned with two such methods, namely the "asymptotic expansion method", also known as the "method of multiple scales",

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Tsandzana, Afonso Fernando. "Homogenization with applications in lubrication theory." Licentiate thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-18727.

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In this licentiate thesis we study some mathematical problems in hydrodynamic lubrication theory. It is composed of two papers (A and B) and a complementary appendix. Lubrication theory is devoted to fluid flow in thin domains. The main purpose of lubrication is to reduce friction and wear between two solid surfaces in relative motion. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation which describes the motion of viscous fluids. In thin domains several approximations are possible which leads to the so called Reynolds equation. This equation is crucial

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Chan, Yiu Mo Patton. "Laminated beam theory based on homogenization." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0022/MQ50485.pdf.

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Chen, Ying Ph D. Massachusetts Institute of Technology. "Percolation and homogenization theories for heterogeneous materials." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44389.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2008.<br>Includes bibliographical references (p. 139-145).<br>Most materials produced by Nature and by human beings are heterogeneous. They contain domains of different states, structures, compositions, or material phases. How these different domains are distributed in space, or in other words, how they connect to one another, determines their macroscopic properties to a large degree, making the simple rule-of-mixtures ineffective in most cases. This thesis studies the macroscopic effective diff

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Hirschberger, Claudia Britta. "A treatise on micromorphic continua theory, homogenization, computation." Kaiserslautern Techn. Univ., Lehrstuhl für Techn. Mechanik, 2008. http://d-nb.info/99795261X/34.

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Dasht, Johan. "Some developments of homogenization theory and Rothe's method /." Luleå : Dept. of Mathematics, Univ, 2005. http://epubl.luth.se/1402-1757/2005/05/LTU-LIC-0505-SE.pdf.

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Binci, Massimiliano Kalidindi Surya. "A novel spectral framework for second-order homogenization theories /." Philadelphia, Pa. : Drexel University, 2008. http://hdl.handle.net/1860/2662.

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Lampshire, Gregory B. "Review of random media homogenization using effective medium theories." Thesis, Virginia Tech, 1992. http://hdl.handle.net/10919/40659.

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<p>Calculation of propagation constants in particulate matter is an important aspect of wave propagation analysis in engineering disciplines such as satellite comnlunication, geophysical exploration, radio astronomy and material science. It is important to understand why different propagation constants produced by different theories are not applicable to a particular problem. Homogenization of the random media using effective medium theories yields the effective propagation constants by effacing the particulate, microscopic nature of the medium. The Maxwell-Gamet and Bruggeman effective medium

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Byström, Johan. "Some mathematical and engineering aspects of the homogenization theory." Doctoral thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-16820.

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This thesis is devoted to some problems connected to the theory of homogenization of partial differential operators. The thesis consists of an elementary introduction and five different parts, A-E. In the introduction we give an elementary presentation of the basic ideas in the homogenization theory. Moreover, the introduction also serves as an overview of the field and points out where the results contained in this thesis fit in. The first part, Part A, consists of two papers with a complementary appendix and deals some purely theoretical parts of homogenization theory. Part B consists of one

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Engström, Jonas. "Some developments of the homogenization theory and related questions /." Luleå, 2005. http://epubl.luth.se/1402-1544/2005/15.

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Books on the topic "Homogenization Theorem"

1

Cioranescu, D. Homogenization of reticulated structures. Springer, 1999.

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2

M, Stuart A., ed. Multiscale methods: Averaging and homogenization. Springer, 2008.

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Jikov, V. V. Homogenization of Differential Operators and Integral Functionals. Springer Berlin Heidelberg, 1994.

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4

Bensoussan, Alain. Asymptotic analysis for periodic structures. American Mathematical Society, 2011.

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1952-, Kawohl Bernhard, Cellina Arrigo 1941-, and Ornelas A, eds. Optimal shape design: Lectures given at the joint C.I.M/C.I.M.E. summer school held in Tróia, Portugal, June 1-6, 1998 / c B. Kawohl ... [et al.] ; editors, A. Cellina and A. Ornelas. Springer, 2000.

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Nev.) International Conference on Scientific Computing and Applications (8th 2012 Las Vegas. Recent advances in scientific computing and applications: Eigth International Conference on Scientific Computing and Applications, April 1-4, 2012, University of Nevada, Las Vegas, Nevada. Edited by Li, Jichun, editor of compilation, Yang, Hongtao, 1962- editor of compilation, and Machorro, Eric A. (Eric Alexander), 1969- editor of compilation. American Mathematical Society, 2013.

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7

Rosenbaum, Ute, and Doina Cioranescu Jeannine Saint Jean Paulin. Homogenization of Reticulated Structures. Springer New York, 2011.

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8

Awrejcewicz, Jan, Igor V. Andrianov, and Vladyslav Danishevskyy. Linear and Nonlinear Waves in Microstructured Solids: Homogenization and Asymptotic Approaches. Taylor & Francis Group, 2021.

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Linear and Nonlinear Waves in Microstructured Solids: Homogenization and Asymptotic Approaches. Taylor & Francis Group, 2021.

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Awrejcewicz, Jan, Igor V. Andrianov, and Vladyslav Danishevskyy. Linear and Nonlinear Waves in Microstructured Solids: Homogenization and Asymptotic Approaches. Taylor & Francis Group, 2021.

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Book chapters on the topic "Homogenization Theorem"

1

Gulisashvili, Archil, and Josef Teichmann. "The Gärtner-Ellis Theorem, Homogenization, and Affine Processes." In Large Deviations and Asymptotic Methods in Finance. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-11605-1_11.

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Birrell, Jeremiah, and Jan Wehr. "A Homogenization Theorem for Langevin Systems with an Application to Hamiltonian Dynamics." In Sojourns in Probability Theory and Statistical Physics - I. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0294-1_4.

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Alicandro, Roberto, Nadia Ansini, Andrea Braides, Andrey Piatnitski, and Antonio Tribuzio. "Periodic Homogenization." In A Variational Theory of Convolution-Type Functionals. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0685-7_6.

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Alicandro, Roberto, Nadia Ansini, Andrea Braides, Andrey Piatnitski, and Antonio Tribuzio. "Stochastic Homogenization." In A Variational Theory of Convolution-Type Functionals. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0685-7_8.

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Gilbert, Robert P., Ana Vasilic, and Sandra Ilic. "Homogenization Theories and Inverse Problems." In Bone Quantitative Ultrasound. Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0017-8_9.

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Manevitch, Leonid I., Victor G. Oshmyan, and Igor V. Andrianov. "Definitions, assumptions and theorems in homogenization problems." In Foundations of Engineering Mechanics. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-44571-5_2.

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Blanc, Xavier, and Claude Le Bris. "Homogenization in Dimension 1." In Homogenization Theory for Multiscale Problems. Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-21833-0_2.

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Alberti, Giovanni, and Giuseppe Buttazzo. "Integral Representation of Functionals Defined on Sobolev Spaces." In Composite Media and Homogenization Theory. Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4684-6787-1_1.

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Khruslov, E. Ya. "Homogenized Models of Composite Media." In Composite Media and Homogenization Theory. Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4684-6787-1_10.

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Kikuchi, Noboru, and Katsuyuki Suzuki. "Structural Optimization of a Linearly Elastic Structure using the Homogenization Method." In Composite Media and Homogenization Theory. Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4684-6787-1_11.

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Conference papers on the topic "Homogenization Theorem"

1

Chen, Min, Abdelkader Hachemi, and Dieter Weichert. "Limit Loads for Structural Elements Made of Heterogeneous Materials." In ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78308.

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A numerical method is presented for determining the limit loads of periodically heterogeneous structures subjected to variable loads. The Melan’s lower-bound shakedown theorem was applied to representative volume elements. Combined with the homogenization technique, the homogenized material properties were determined through transformation from the mesoscopic to macroscopic admissible loading domains. For the numerical applications, solid non-conforming finite element discretization and large-scale nonlinear optimization, based on an interior-point-algorithm were used. The methodology is illus

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2

Dal Maso, G., and G. Dell'Antonio. "Composite Media & Homogenization Theory." In Second Workshop on Composite Media and Homogenization Theory. WORLD SCIENTIFIC, 1995. http://dx.doi.org/10.1142/9789814532075.

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Guiamatsia, Irene, and Jorn S. Hansen. "A Homogenization-Based Laminated Plate Theory." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-61763.

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A new approach to plate theory is presented which yields a straight-forward yet extremely accurate plate model. The approach yields precise and complete three-dimensional stress and strain states with minimal computational effort. This development is based on the assumption that the plate response characteristics can be represented in terms of far-field stress and strain solutions corresponding to constant, linear, quadratic, , nth degree bending states; such solutions, referred to as Fundamental State Solutions (FS), can be determined uniquely and are independent of boundary conditions. Defin

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Yu, Wenbin, and Tian Tang. "A New Micromechanics Model for Predicting Thermal Properties of Heterogeneous Materials." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15117.

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A new micromechanics model, namely, the variational asymptotic method for unit cell homogenization (VAMUCH), is extended to predict thermal properties of heterogeneous anisotropic materials. In comparison to existing micromechanics models, VAMUCH is unique in the following three aspects: (1) it invokes only essential assumptions within the concept of micromechanics and achieves the same accuracy as mathematical homogenization theories; (2) it calculates the complete set of properties simultaneously without applying any loads; and (3) the dimensionality of the problem is determined by the dimen

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Tsukerman, Igor, and Vadim Markel. "A nonasymptotic homogenization theory of electromagnetic metamaterials." In 2014 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2014. http://dx.doi.org/10.1109/iceaa.2014.6903848.

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Lukkassen, Dag, Annette Meidell, and Peter Wall. "On the role of homogenization in lubrication theory." In 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4904692.

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Vinogradov, Alexei P. "Scaling theory for homogenization of the Maxwell equations." In Far East and Pacific Rim Symposium on Smart Materials, Structures, and MEMS, edited by Alex Hariz, Vijay K. Varadan, and Olaf Reinhold. SPIE, 1997. http://dx.doi.org/10.1117/12.293534.

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Mont, A., A. Alu, A. Toscano, and F. Bilotti. "Homogenization of All-Dielectric Metasurfaces: Theory and Applications." In 2019 Thirteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials). IEEE, 2019. http://dx.doi.org/10.1109/metamaterials.2019.8900909.

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Auciello, Nicola M., and Massimo M. Auciello. "The homogenization theory in the analysis of masonry arches." In The 6th International Virtual Scientific Conference. Publishing Society, 2017. http://dx.doi.org/10.18638/ictic.2017.6.1.300.

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Jin Ma, Zhibin Liu, Bingshu Wang, and Xinhui Duan. "The study on spatial homogenization parameters based upon equivalence theory." In 2014 IEEE Workshop on Advanced Research and Technology in Industry Applications (WARTIA). IEEE, 2014. http://dx.doi.org/10.1109/wartia.2014.6976463.

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Reports on the topic "Homogenization Theorem"

1

Farzad Rahnema. High-Order Homogenization Method in Diffusion Theory for Reactor Core Simulation and Design Calculation. Office of Scientific and Technical Information (OSTI), 2003. http://dx.doi.org/10.2172/816337.

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Aidun, J. B., and F. L. Addessio. A cell model for homogenization of fiber-reinforced composites: General theory and nonlinear elasticity effects. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/130626.

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