Transport Phenomena and Kinetic Theory

1. Front Matter

   Pages i-xiii

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2. Analytic Aspects of the Boltzmann Equation

   1. Front Matter

      Pages 1-1

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   2. Rigorous results for conservation equations and trend to equilibrium in space-inhomogeneous kinetic theory

      • Carlo Cercignani

      Pages 3-17

   3. Results on optimal rate of convergence to equilibrium for spatially homogeneous Maxwellian gases

      • Ester Gabetta

      Pages 19-37

   4. Nonresonant velocity averaging and the Vlasov-Maxwell system

      • François Golse

      Pages 39-52

3. Modeling Applications, Inverse and Computational Problems in Quantum Kinetic Theory

   1. Front Matter

      Pages 53-53

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   2. Multiband quantum transport models for semiconductor devices

      • Luigi Barletti, Lucio Demeio, Giovanni Frosali

      Pages 55-89

   3. Optimization models for semiconductor dopant profiling

      • Martin Burger, Michael Hinze, Rene Pinnau

      Pages 91-115

   4. Inverse problems for semiconductors: models and methods

      • A. Leitão, P. A. Markowich, J. P. Zubelli

      Pages 117-149

   5. Deterministic kinetic solvers for charged particle transport in semiconductor devices

      • M. J. Cáceres, J. A. Carrillo, I. M. Gamba, A. Majorana, C. -W. Shu

      Pages 151-171

4. Miscellaneous Applications in Physics and Natural Sciences

   1. Front Matter

      Pages 173-173

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   2. Methods and tools of mathematical kinetic theory towards modelling complex biological systems

      • Nicola Bellomo, Abdelghani Bellouquid, Marcello Delitala

      Pages 175-193

   3. Kinetic modelling of late stages of phase separation

      • Guido Manzi, Rossana Marra

      Pages 195-214

   4. Ground states and dynamics of rotating Bose-Einstein condensates

      • Weizhu Bao

      Pages 215-255

   5. Two inverse problems in photon transport theory: evaluation of a time-dependent source and of a time-dependent cross section

      • Aldo Belleni-Morante

      Pages 257-271

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.

• Natur
• Profil
• Transport
• complex systems
• mathematics
• modeling
• modelling
• optimization
• physics
• science

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)

• Dipartimento di Matematica, Politecnico di Torino, Milano, Italy

  Carlo Cercignani

• Dipartimento di Matematica “F. Castorati”, Università degli Studi di Pavia, Pavia, Italy

  Ester Gabetta

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