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The General Theory of Homogenization
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.
Children Today
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Her Last Breath
A gripping new detective series set in Brighton for readers who enjoy Peter James' Roy Grace series. When a young woman is attacked and left fighting to survive in hospital, the police are pulled into a race against time to save her life. But just 24 hours later, she dies and a deadly tattoo is discovered on her body. And when another young woman disappears, Detective Francis Sullivan and his team fear a serial killer walks the streets of Brighton. His team identify a suspect, Alex Mullins, son of Francis's lover, Marni. Can Francis forget their shared past and save the next victim before it is too late?
From Hyperbolic Systems to Kinetic Theory
This fascinating book, penned by Luc Tartar of America’s Carnegie Mellon University, starts from the premise that equations of state are not always effective in continuum mechanics. Tartar relies on H-measures, a tool created for homogenization, to explain some of the weaknesses in the theory. These include looking at the subject from the point of view of quantum mechanics. Here, there are no "particles", so the Boltzmann equation and the second principle, can’t apply.
Nonlinear Partial Differential Equations
The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications. These proceedings present a selection of the latest exciting results by world leading researchers.
From Particle Systems to Partial Differential Equations
This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations X, which was held at the University of Minho, Braga, Portugal, from 2022. It includes papers on mathematical problems motivated by various applications in physics, engineering, economics, chemistry, and biology.
