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# đź“™ From Hyperbolic Systems to Kinetic Theory: A Personalized Quest by Luc Tartar (auth.) â€” free epub

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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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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...

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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...

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