Homogenization in perforated domains with rapidly pulsing perforations

Cioranescu, Doina; Piatnitski, Andrey

doi:10.1051/cocv:2003023

Cited by 9 publications

(8 citation statements)

References 6 publications

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“…The papers [2,3] consider the sieve problem in the framework of Γ -convergence, focusing on the limiting behaviour of energy functionals. Besides the previous references dealing with stationary models, we quote the papers [10,11,16,22] where homogenization of domains with pulsating or evolving cavities is considered; however, the holes in these papers appear in the bulk of the domain.…”

Section: The Novelty With Respect To the Stationary Casementioning

confidence: 99%

Permeability of interfaces with alternating pores in parabolic problems

Andreucci

Bellaveglia

2012

Asymptotic Analysis

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We study a parabolic problem set in a domain divided by a perforated interface. The pores alternate between an open and a closed state, periodically in time. We consider the asymptotics of the solution for vanishingly small size of the pores and time period. The interface condition prevailing in the limit is a linear relation between the flux (on either side) and the jump of the limiting solution across the interface. More exactly this behaviour only takes place when the relative sizes of the relevant geometrical and temporal parameters are connected by suitable relations.With respect to the stationary version of this problem, which is known in the literature, we demonstrate the appearance of a new admissible asymptotic standard. More in general, we describe the precise interplay between the geometrical and temporal parameters leading to the quoted interface condition.This work represents a preliminary mathematical investigation of a model of selective transport of chemical species through biological membranes.

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Section: The Novelty With Respect To the Stationary Casementioning

confidence: 99%

Permeability of interfaces with alternating pores in parabolic problems

Andreucci

Bellaveglia

2012

Asymptotic Analysis

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“…In this work both fluid and solid domains are connected subsets. In [9] the homogenization of a perforated media with time-oscillating perforation is studied.…”

Section: Prefacementioning

confidence: 99%

“…The idea is now to linearize (9). The Gâteaux derivative of the functional G ε,k is given by (see [8] p. 83)…”

Section: Description Of the Modelsmentioning

confidence: 99%

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Homogenization of Elastic Media with Gaseous Inclusions

Baffico¹,

Grandmont²,

Maday³

et al. 2008

Multiscale Model. Simul.

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We study the asymptotic behavior of a system modeling a composite material made of an elastic periodically perforated support, with period ε > 0, and a perfect gas placed in each of these perforations, as ε goes to zero. The model we use is linear corresponding to deformations around a reference configuration. We apply both two-scale asymptotic expansion and two-scale convergence methods in order to identify the limit behaviors as ε goes to 0. We state that in the limit, we get a two-scale linear elasticity-like boundary value problem. From this problem, we identify the corresponding homogenized and periodic cell equations which allows us to find the first corrector term. The analysis is performed both in the case of an incompressible and compressible material. We derive some mechanical properties of the limit materials by studying the homogenized coefficients. Finally, we numerically calculate the homogenized coefficients in the incompressible case, for different types of elastic materials.

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“…For example, [21] considered traveling speeds for coefficients oscillating in t/ε 2 scale, while [2,24] looked at the homogenization of parabolic equations in bounded domains when, among other cases, the coefficients oscillate as t/ε, and [3,15,16] …”

Section: Introductionmentioning

confidence: 99%

A homogenization approach to flashing ratchets

Perthame

Souganidis

2010

Nonlinear Differ. Equ. Appl.

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Abstract. The paper continues the program of the authors to develop a mathematical framework to understand and characterize the notion of "asymmetric" potentials, which has been introduced to explain how molecular motors work, considering flashing ratchets, i.e., molecules diffusing in a potential with periodic switches. The mathematical model is a Fokker-Planck equation with a space-time periodic potential and diffusion of order of magnitude compatible with the period of the potential. After performing a homogenization analysis of the problem the "asymmetric" potentials are characterized by the property that the solution, which models the molecule density, concentrates on one end of the domain. Finally explicit examples are presented exhibiting that the concentration phenomena (motor effect) takes place are presented. The proof uses techniques from the theory of viscosity solutions for the HamiltonJacobi equation which, in the homogenization limit, defines the effective hamiltonian. Mathematics Subject Classification (2000). 35B25, 35B27, 49L25, 92C05.

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Homogenization in perforated domains with rapidly pulsing perforations

Cited by 9 publications

References 6 publications

Permeability of interfaces with alternating pores in parabolic problems

Permeability of interfaces with alternating pores in parabolic problems

Homogenization of Elastic Media with Gaseous Inclusions

A homogenization approach to flashing ratchets

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