This book deals with models and model-building in classical and quantum physics; it relies on logic and the philosophy of science as well as on modern mathematics. The reader will also find vistas into the history of ideas. The philosophical analysis is based on the separation of syntax and semantics, which is at the root of Kolmogorov's theory of probability; recursive functions and algorithmic complexity are used to discuss entropy and randomness. Basic concepts are discussed, together with concrete physical models for phase transitions, scaling, renormalization semigroups, and the irreversible approach to equilibrium. The book is intended for mathematicians, physicists and philosophers of science, both researchers and graduate students.

The book contains in-depth discussions in a rigorous manner of a host of interconnected issues and problems concerning the foundations of science. Some issues concern the substance of scientific subjects, such as the nature of spacetime and the problems in quantum mechanics, while other issues concern the methodology of science, such as the nature of theorization, idealization, as well as modeling. These discussions aim at clarifying the issues and problems, reviewing the proposed views and solutions, mapping out their logical spaces, and arguing for preferred views or solutions.

This book addresses several of the foundational problems in thermophysics, i. e. thermodynamics and statistical mechanics. It is an interdisciplinary work in that it examines the philosophical underpinning of scientific models and theories; it also refines the analysis of the problems at hand and delineates the place occupied by various scientific models in a generalized philosophical landscape. Hence, our philosophical - or theoretical - inquiry focuses sharply on the concept of models; and our empirical - or laboratory - evidence is sought in the model-building activities of scientists who have tried to confront the epistemological problems arising in the thermophysical sciences. Primarily for researchers and students in physics, philosophy of science, and mathematics, our book aims at informing the readers - with all the in dispensable technical details made readily available - about the nature of the foundational problems, how these problems are approached with the help of various mathematical models, and what the philosophical implications of such models and approaches involve. Some familiarity with elementary ther mophysics and/or with introductory-level philosophy of science may help, but neither is a prerequisite. The logical and mathematical background re quired for the book are introduced in the Appendices. Upon using the Subject Index, the readers may easily locate the concepts and theorems needed for understanding various parts of the book. The Citation Index lists the authors of the contributions we discuss in detail."

Spacecraft Attitude Control: A Linear Matrix Inequality Approach solves problems for spacecraft attitude control systems using convex optimization and, specifi cally, through a linear matrix inequality (LMI) approach. High-precision pointing and improved robustness in the face of external disturbances and other uncertainties are requirements for the current generation of spacecraft. This book presents an LMI approach to spacecraft attitude control and shows that all uncertainties in the maneuvering process can be solved numerically. It explains how a model-like state space can be developed through a mathematical presentation of attitude control systems, allowing the controller in question to be applied universally. The authors describe a wide variety of novel and robust controllers, applicable both to spacecraft attitude control and easily extendable to second-order systems. Spacecraft Attitude Control provides its readers with an accessible introduction to spacecraft attitude control and robust systems, giving an extensive survey of current research and helping researchers improve robust control performance.