# Transport Phenomena and Kinetic Theory

## Applications to Gases, Semiconductors, Photons, and Biological Systems

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This volume aims to provide an overview of some recent developments of mathematical kinetic theory focused on its application in modelling complex systems in various ?elds of applied sciences. Mathematical kinetic theory is essentially based on the Boltzmann eq- tion, which describes the evolution, possibly far from equilibrium, of a class of particles modelled as point masses. The equation de?nes the evolution in time and space of the distribution function over the possible microscopic states of the test particle, classically position and velocity. The test particle is subject to pair collisions with the ?eld particles. The interested reader can ?nd in the book, Theory and Application of the Boltzmann Equation, by C. Cercignani, R. Illner, and M. Pulvirenti, Springer, Heidelberg, 1993, all necessary knowledge of the physics and mathematical topics related to this celebrated model of non-equilibrium statistical mech- ics. Another important model of mathematical kinetic theory is the Vlasov equation, where interactions between particles are not speci?cally collisions, but mean ?eld actions of the ?eld particles over the test particle. The model de?nes again an evolution equation for the one-particle distribution function over the microscopic state of the test particle. The two models brie?y mentioned above can be regarded as the fun- mental models of mathematical kinetic theory and the essential background o?ered from the kinetic theory for classical particles towards the modelling of large systems of several particles undergoing non classical interactions.
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Birkhäuser Boston; December 2007

284 pages; ISBN 9780817645540

Read online, or download in secure PDF format

Title: Transport Phenomena and Kinetic Theory

Author: Carlo Cercignani; Ester Gabetta

284 pages; ISBN 9780817645540

Read online, or download in secure PDF format

Title: Transport Phenomena and Kinetic Theory

Author: Carlo Cercignani; Ester Gabetta

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Subject categories

- Academic > Physics > Atomic physics > Statistical mechanics
- Academic > Physics > Atomic physics > Transport theory
- Academic > Physics > Physics; Abstracts; Periodicals
- Academic > Physics > Physics; Early works to 1800
- Technology > Engineering > Mechanical
- Mathematics > Applied
- Science > Thermodynamics
- Science > Mechanics
- Science > Chemistry

ISBNs

0817645543

9780817644895

9780817645540

### In the press

From the reviews:

"In this collection of articles by experts in the field the reader is given a rather comprehensive overview of many of the mathematical aspects and applications of the Boltzmann equation … . intended for scientists and engineers in the applied sciences, my own feeling is that investigators whose acquaintance with mathematics is at an advanced level are likely to be the main beneficiaries of this book. The presentation of the material is excellent, very well organized, and highly recommended to this audience." (L.S. García-Colín, Journal of Statistical Physics, Vol. 132, 2008)