Asymptotic Analysis of Periodic Structures
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This article is published in Journal of Applied Mechanics.The article was published on 1979-06-01 and is currently open access. It has received 5038 citations till now. The article focuses on the topics: Asymptotic analysis.read more
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Topology optimization of microstructures of cellular materials and composites for macrostructures
TL;DR: In this article, a topology optimization algorithm for the optimal design of cellular materials and composites with periodic microstructures is presented. And a bi-directional evolutionary structural optimization approach is developed to achieve a clear and optimized topology for the material microstructure.
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Error estimate and unfolding for periodic homogenization
TL;DR: In this article, the error estimate in problems of periodic homogenization is obtained using the results of Theorem 2.3, which states that the periodic defect of a harmonic function belonging to a cell is written with the help of the norms of its traces diff erences on the opposite faces of the cell.
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Univalent σ-Harmonic Mappings
TL;DR: In this article, the authors prove sufficient conditions for the injectivity of σ-harmonic mappings and local bounds in BMO on the logarithm of the Jacobian determinant of such mappings.
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An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows
Marco Avellaneda,Andrew J. Majda +1 more
TL;DR: In this article, necessary and sufficient conditions on the velocity statistics for mean field behavior in advection-diffusion by a steady incompressible velocity field are developed, and a rigorous Stieltjes integral representation for effective diffusivity in turbulent transport is derived.
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An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
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Théorie des distributions
TL;DR: The merite as discussed by the authors is a date marque une date dans le progres des mathematiques and de la physique en levant l'ambiguite que constituait le succes des methodes de calcul symbolique aupres des physiciens and l'inacceptabilite de leurs formules au regard de la rigueur mathematiques.