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Tail estimates for homogenization theorems in random media

Daniel Boivin (2009)

ESAIM: Probability and Statistics

Consider a random environment in d given by i.i.d. conductances. In this work, we obtain tail estimates for the fluctuations about the mean for the following characteristics of the environment: the effective conductance between opposite faces of a cube, the diffusion matrices of periodized environments and the spectral gap of the random walk in a finite cube.

Tangential fields in optical diffraction problems

Krček, Jiří, Vlček, Jaroslav, Žídek, Arnošt (2013)

Programs and Algorithms of Numerical Mathematics

Optical diffraction for periodical interface belongs to relatively fewer exploited application of boundary integral equations method. Our contribution presents the formulation of diffraction problem based on vector tangential fields, for which the periodical Green function of Helmholtz equation is of key importance. There are discussed properties of obtained boundary operators with singular kernel and a numerical implementation is proposed.

T-coercivity for scalar interface problems between dielectrics and metamaterials

Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of Rd, with d = 2,3. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or coercive...

T-coercivity for scalar interface problems between dielectrics and metamaterials

Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of Rd, with d = 2,3. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or coercive...

Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity

Pavel Krejčí, Jürgen Sprekels (1998)

Applications of Mathematics

In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress σ contains, in addition to elastic, viscous and thermic contributions, a plastic component σ p of the form σ p ( x , t ) = 𝒫 [ ε , θ ( x , t ) ] ( x , t ) . Here ε and θ are the fields of strain and absolute temperature, respectively, and { 𝒫 [ · , θ ] } θ > 0 denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum...

Teoremi di confronto tra diverse nozioni di movimento secondo la curvatura media

Giovanni Bellettini, Maurizio Paolini (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota presentiamo alcuni teoremi di confronto tra il movimento secondo la curvatura media ottenuto con il metodo delle minime barriere di De Giorgi e i movimenti definiti con i metodi di Evans-Spruck, Chen-Giga-Goto, Giga-Goto-Ishii-Sato.

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