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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A general convergence result for a functional related to the theory of homogenization
TL;DR: In this paper, the convergence of the functional π (x,y) with support in a fixed compact set is studied and a convergence theorem is proved under the weaker assumption that π(x, y) remains in a bounded subset of the set, and the use of multiple scale expansions in homogenization is justified.
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Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review.
Xiaojian Wang,Shanqing Xu,Shiwei Zhou,Wei Xu,Martin Leary,Peter F. M. Choong,Ma Qian,Milan Brandt,Yi Min Xie +8 more
TL;DR: The state-of-the-art of topological design and manufacturing processes of various types of porous metals, in particular for titanium alloys, biodegradable metals and shape memory alloys are reviewed.
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Particles and fields in fluid turbulence
TL;DR: In this paper, the first analytical description of anomalous scaling laws in turbulent transport has been obtained and the underlying physical mechanism reveals the role of statistical integrals of motion in nonequilibrium systems.
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Averaging of functionals of the calculus of variations and elasticity theory
TL;DR: In this paper, the authors developed a duality method in the theory of averaging of nonlinear variational problems with stochastic Lagrangians and derived duality formulas that take account of the regularity problem.
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Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
TL;DR: (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations are considered.
References
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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.