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Physics - Theoretical, Mathematical & Computational Physics | The General Theory of Homogenization - A Personalized Introduction

The General Theory of Homogenization

A Personalized Introduction

Tartar, Luc

2010, XXII, 471p.

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Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly.

For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.

Content Level » Research

Keywords » H-measures - compactness - continuum mechanics - differential equation - homogenization - partial differential equations - physics

Related subjects » Classical Continuum Physics - Dynamical Systems & Differential Equations - Mechanics - Theoretical, Mathematical & Computational Physics

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