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Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from PoincarĂ©'s theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity!

- Series:
**Lecture Notes of the Unione Matematica Italiana 6** - Author:
**Luc Tartar (auth.)** - Year:
**2008** - Publisher:
**Springer-Verlag Berlin Heidelberg** - Language:
**English** - ISBN:
**3540775617,978-3-540-77561-4**

- File size:
**3 919 984** - Format:
**pdf**

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This monograph is intended to provide a comprehensive description of the relaÂ tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain i...

Explore a Kinetic Approach to the Description of Nucleation - An Alternative to the Classical Nucleation TheoryKinetic Theory of Nucleationpresents an alternative to the classical theory of nucleation in gases and liquids--the kinetic nucleation theory of...

The last several decades have demonstrated dramatic technological changes that influence work conditions in all applied domains, including manufacturing, transportation, and human-computer interactions. These changes require new approaches to the study of...

This book introduces physics students and teachers to the historical development of the kinetic theory of gases, by providing a collection of the most important contributions by Clausius, Maxwell and Boltzmann, with introductory surveys explaining their s...

Systems Modelling: Theory and Practice brings together some of the leading minds in the fields of Systems Modelling and Operational Research, to produce a book which addresses issues that are of both practical importance and theoretical significance. Th...

Oxidative Stress in Aging: From Model Systems to Human Diseases discusses the role of free radicals in aging in different animal models, as well as the relevance of free radicals on age-related diseases and pathological conditions in humans (following an ...

This volume collects the papers presented at the first international conference dedicated to spatial and temporal reasoning in geographic space, entitled "GIS: from space to territory - theories and methods of spatio-temporal reasoning". Within the Nation...

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This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, all...

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At a time when postmodernism seems to have achieved a dominant position in cultural and critical theory, the contributors to this volume present a much needed corrective to the misleading images of modernism which have dominated recent debate. Theorizing...

This second book by Coach Thibaudeau focuses more on the science of strength as well as the various methods you can use to boost your strength and power. Agreat tool for athletes of all kinds! Also includes information on electromyostimulation, chains,...

Tracing the developing modernist aesthetic in the thought and writings of James Joyce, Dorothy Richardson and Virginia Woolf, Deborah Parsons considers the cultural, social and personal influences upon the three writers. Exploring the connections between ...

This book constitutes the thoroughly refereed post-proceedings of the 6th International Conference on Theory and Applications of Satisfiability Testing, SAT 2003, held in Santa Margherita Ligure, Italy, in May 2003.The 33 revised full papers presented tog...

Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, other topics). Exercises thr...