Carlo Cercignani Knihy

The book explores the two branches of statistical mechanics: equilibrium and nonequilibrium systems. It highlights the well-defined Gibbs's ensembles for understanding equilibrium properties and discusses the less understood realm of nonequilibrium phenomena, particularly focusing on dilute gases. The Boltzmann equation, established in 1872, serves as a foundational tool for kinetic theory, applicable to various fields such as electron transport, neutron transport, and radiative transfer. Recent advancements in both areas are also examined, reflecting significant progress in the last three decades.

Focusing on the principles of kinetic theory, this book explores its methods and applications specifically in the context of rarefied gas dynamics. It delves into the fundamental concepts that govern the behavior of gases at low densities, providing a comprehensive understanding of the subject. Through detailed explanations and examples, it aims to bridge theoretical insights with practical applications, making it a valuable resource for researchers and students in the field of fluid dynamics and gas behavior.

This book originated from a 1988 summer school on mathematical physics, inspired by the late Marvin Shinbrot's vision for a comprehensive work on the Boltzmann equation. Despite initial ambitions, the authors adapted their approach to compile significant, often scattered results from the last two decades, aiming for clarity and rigor.

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning. Transport Phenomena and Kinetic Theory is an excellent self-study reference for graduate students, researchers, and practitioners working in pure and applied mathematics, mathematical physics, and engineering. The work may be used in courses or seminars on selected topics in transport phenomena or applications of the Boltzmann equation.

This volume is intended to coverthe presentstatus of the mathematicaltools used to deal with problems related to slow rare? ed ? ows. The meaning and usefulness of the subject, and the extent to which it is covered in the book, are discussed in some detail in the introduction. In short, I tried to present the basic concepts and the techniques used in probing mathematical questions and problems which arise when studying slow rare? ed ? ows in environmental sciences and micromachines. For the book to be up-to-date without being excessively large, it was necessary to omit some topics, which are treated elsewhere, as indicated in the introd- tion and, whenever the need arises, in the various chapters of this volume. Their omission does not alter the aim of the book, to provide an understanding of the essential mathematical tools required to deal with slow rare? ed ? ows and give the background for a study of the original literature. Although I have tried to give a rather complete bibliographical coverage, the choice of the topics and of the references certainly re? ects a personal bias and I apologize in advance for any omission. I wish to thank Lorenzo Valdettaro, Antonella Abb` a, Silva Lorenzani and Paolo Barbante for their help with pictures and especially Professor Ching Shen for his permission to reproduce his pictures on microchannel ? ows.

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.

The book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th to 20th century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific revolution, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved; others are still at the level of likely but unproven conjectures. The main text of this biography is written almost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject.

Focusing on Ludwig Boltzmann's life, the book delves into his scientific and philosophical contributions, particularly his role in establishing the atomic structure of matter. It also explores his profound influence on modern physics. The narrative includes a detailed account of his tragic life, culminating in his suicide, providing insight into the personal struggles that accompanied his groundbreaking work.