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.
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.
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.
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.