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This book is devoted to the mathematical modelling of electromagnetic materials. Electromagnetism in matter is developed with particular emphasis on material effects, which are ascribed to memory in time and nonlocality. Within the mathematical modelling, thermodynamics of continuous media plays a central role in that it places significant restrictions on the constitutive equations. Further, as shown in connection with uniqueness, existence and stability, variational settings, and wave propagation, a correct formulation of the pertinent problems is based on the knowledge of the thermodynamic restrictions for the material. The book is divided into four parts. Part I (chapters 1 to 4) reviews the basic concepts of electromagnetism, starting from the integral form of Maxwell’s equations and then addressing attention to the physical motivation for materials with memory. Part II (chapers 5 to 9) deals with thermodynamics of systems with memory and applications to evolution and initial/boundary-value problems. It contains developments and results which are unusual in textbooks on electromagnetism and arise from the research literature, mainly post-1960s. Part III (chapters 10 to 12) outlines some topics of materials modelling — nonlinearity, nonlocality, superconductivity, and magnetic hysteresis — which are of great interest both in mathematics and in applications.

This book concerns the physics of plasma at high density, which is compressed so strongly that the effects of interparticle interactions, nonideality, govern its behavior. The interest in this non-traditional plasma has emerged during the last few years when states of matter with high concentration of energy, constituting the basis of the modern technologies and facilities, became accessible for impulse experiments. The greatest part of the Universe matter is in this exotic state. In this book, the methods of strongly coupled plasma generation and diagnostics are considered. The experimental results on thermodynamic, kinetic, and optical properties are given, and the main theoretical models of the strongly coupled plasma state are discussed. Particular attention is given to fast developing modern directions of strongly coupled plasma physics, such as metallization of dielectrics and dielectrization of metals, nonneutral plasma, complex (dusty) plasma, and its crystallization.

Modelling of heterogeneous processes, such as electrochemical reactions, extraction, or ion-exchange, usually requires solving the transport problem associated with the process. Since the processes at the phase boundary are described by scalar quantities and transport quantities are vectors or tensors, the coupling of them can take place only via conservation of mass, charge, or momentum. In this book transport of ionic species is addressed in a versatile manner, emphasizing the mutual coupling of fluxes in particular. Treatment is based on the formalism of irreversible thermodynamics, i.e., on linear (ionic) phenomenological equations, from which the most frequently used Nernst-Planck equation is derived. Limitations and assumptions made are discussed in detail. The Nernst-Planck equation is applied to selected problems at the electrodes and in membranes. Mathematical derivations are presented so that the reader can learn the methodology of solving transport problems. Each chapter contains a large number of exercises.

This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs — dating from the 19th century and extended considerably over the following 100 years — is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-20th Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.

This book explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the ‘principle theory’ approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein's treatment of the relativistic behaviour of rigid bodies and clocks in motion in the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. This book both examines and extends these arguments (which support a more ‘constructive’ approach to relativistic effects in Einstein's terminology), after giving a careful analysis of key features of the pre-history of relativity theory. It argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, the book tries to show that the dynamical interpretation of special relativity defended in the book is consistent with the role this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.

Intermolecular interactions stem from the electric properties of atoms. Being the cause of molecular aggregation, intermolecular forces are at the roots of chemistry and are the fabric of the world. They are responsible for the structure and properties of all condensed bodies — the human body, the food we eat, the clothes we wear, the drugs we take, the paper on which this book is printed. In the last forty years or so, theoretical and experimental research in this area has struggled to establish correlations between the structure of the constituent molecules, the structure of the resulting condensed phase, and the observable properties of any material. As in all scientific enterprise, the steps to follow are analysis, classification, and prediction, while the final goal is control; which in this case means the deliberate design of materials with specified properties. This last step requires a synthesis and substantial command of the three preceding steps. This book provides a brief but accurate summary of all the basic ideas, theories, methods, and conspicuous results of structure analysis and molecular modelling of the condensed phases of organic compounds: quantum chemistry, the intermolecular potential, force field and molecular dynamics methods, structural correlation, and thermodynamics. The book also exposes the present status of studies in the analysis, categorisation, prediction, and control, at a molecular level, of intermolecular interactions in liquids, solutions, mesophases, and crystals. The main focus here is on the links between energies, structures, and chemical or physical properties.

In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.

Lord Kelvin was one of the greatest physicists of the Victorian era. Widely known for the development of the Kelvin scale of temperature measurement, Kelvin's interests ranged across thermodynamics, the age of the Earth, the laying of the first transatlantic telegraph cable, not to mention inventions such as an improved maritime compass and a sounding device, which allowed depths to be taken both quickly and while the ship was moving. He was an academic engaged in fundamental research, while also working with industry and technological advances. He corresponded and collaborated with other eminent men of science such as Stokes, Joule, Maxwell, and Helmholtz; was raised to the peerage as a result of his contributions to science, and finally buried in Westminster Abbey next to Newton. This book contains a collection of chapters covering the life and wide-ranging scientific contributions made by William Thomson, Lord Kelvin (1824-1907).

Does the brain create the mind, or is some external entity involved? In addressing this hard problem of consciousness, we face a central human challenge: what do we really know and how do we know it? Tentative answers in this book follow from a synthesis of profound ideas, borrowed from philosophy, religion, politics, economics, neuroscience, physics, mathematics, and cosmology, the knowledge structures supporting our meager grasp of reality. This search for new links in the web of human knowledge extends in many directions: the shadows of our thought processes revealed by brain imagining, brains treated as complex adaptive systems that reveal fractal-like behavior in the brain's nested hierarchy, resonant interactions facilitating functional connections in brain tissue, probability and entropy as measures of human ignorance, fundamental limits on human knowledge, and the central role played by information in both brains and physical systems. The author discusses the possibility of deep connections between relativity, quantum mechanics, thermodynamics, and consciousness; all entities involved with fundamental information barriers. This study elaborates on possible new links in this nested web of human knowledge that may tell us something new about the nature and origins of consciousness. In the end, does the brain create the mind? Or is the mind already out there?

This book argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, this book demonstrates how to build a metaphysics compatible with current fundamental physics (“ontic structural realism”), which, when combined with metaphysics of the special sciences (“rainforest realism”), can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously, this book argues, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. The text assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the books' metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism versus empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds.