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This collection of essays deals with three clusters of problems in the philo sophy of science: scientific method, conceptual models, and ontological underpinnings. The disjointedness of topics is more apparent than real, since the whole book is concerned with the scientific knowledge of fact. Now, the aim of factual knowledge is the conceptual grasping of being, and this understanding is provided by theories of whatever there may be. If the theories are testable and specific, such as a theory of a particular chemical reaction, then they are often called 'theoretical models' and clas sed as scientific. If the theories are extremely general, like a theory of syn thesis and dissociation without any reference to a particular kind of stuff, then they may be called 'metaphysical' - as well as 'scientific' if they are consonant with science. Between these two extremes there is a whole gamut of kinds of factual theories. Thus the entire spectrum should be dominated by the scientific method, quite irrespective of the subject matter. This is the leitmotiv of the present book. The introductory chapter, on method in the philosophy of science, tackles the question 'Why don't scientists listen to their philosophers?'.
The book introduces tools with which models of quantum matter are built. The most important technique, the Bethe ansatz, is developed in detail to perform exact calculations of the physical properties of quantum matter.
To do research that really makes a difference -- the authors of this book argue -- social scientists need a diverse set of questions and methods, both qualitative and quantitative, in order to reflect the complexity of the world. Bringing together a consortium of voices across a variety of fields, Methods That Matter offers compelling and successful examples of mixed methods research that does just that. Discussing their own endeavors to combine quantitative and qualitative methodologies, the authors invite readers into a conversation about the best designs and practices of mixed methods to stimulate creative ideas and find new pathways of insight. The result is an engaging exploration of a promising approach to the social sciences. --
The discovery of a duality between Anti-de Sitter spaces (AdS) and Conformal Field Theories (CFT) has led to major advances in our understanding of quantum field theory and quantum gravity. String theory methods and AdS/CFT correspondence maps provide new ways to think about difficult condensed matter problems. String theory methods based on the AdS/CFT correspondence allow us to transform problems so they have weak interactions and can be solved more easily. They can also help map problems to different descriptions, for instance mapping the description of a fluid using the Navier-Stokes equations to the description of an event horizon of a black hole using Einstein's equations. This textbook covers the applications of string theory methods and the mathematics of AdS/CFT to areas of condensed matter physics. Bridging the gap between string theory and condensed matter, this is a valuable textbook for students and researchers in both fields.
The Monte Carlo method is now widely used and commonly accepted as an important and useful tool in solid state physics and related fields. It is broadly recognized that the technique of "computer simulation" is complementary to both analytical theory and experiment, and can significantly contribute to ad vancing the understanding of various scientific problems. Widespread applications of the Monte Carlo method to various fields of the statistical mechanics of condensed matter physics have already been reviewed in two previously published books, namely Monte Carlo Methods in Statistical Physics (Topics Curro Phys. , Vol. 7, 1st edn. 1979, 2ndedn. 1986) and Applications of the Monte Carlo Method in Statistical Physics (Topics Curro Phys. , Vol. 36, 1st edn. 1984, 2nd edn. 1987). Meanwhile the field has continued its rapid growth and expansion, and applications to new fields have appeared that were not treated at all in the above two books (e. g. studies of irreversible growth phenomena, cellular automata, interfaces, and quantum problems on lattices). Also, new methodic aspects have emerged, such as aspects of efficient use of vector com puters or parallel computers, more efficient analysis of simulated systems con figurations, and methods to reduce critical slowing down at i>hase transitions. Taken together with the extensive activity in certain traditional areas of research (simulation of classical and quantum fluids, of macromolecular materials, of spin glasses and quadrupolar glasses, etc.
This book presents the theory of soft matter to students at the advanced undergraduate or beginning graduate level. It provides a basic introduction to theoretical physics as applied to soft matter, explaining the concepts of symmetry, broken symmetry, and order parameters; phases and phase transitions; mean-field theory; and the mathematics of variational calculus and tensors. It is written in an informal, conversational style, which is accessible to students from a diverse range of backgrounds. The book begins with a simple “toy model” to demonstrate the physical significance of free energy. It then introduces two standard theories of phase transitions—the Ising model for ferromagnetism and van der Waals theory of gases and liquids—and uses them to illustrate principles of statistical mechanics. From those examples, it moves on to discuss order, disorder, and broken symmetry in many states of matter, and to explain the theoretical methods that are used to model the phenomena. It concludes with a chapter on liquid crystals, which brings together all of these physical and mathematical concepts. The book is accompanied online by a set of “interactive figures”—some allow readers to change parameters and see what happens to a graph, some allow readers to rotate a plot or other graphics in 3D, and some do both. These interactive figures help students to develop their intuition for the physical meaning of equations. This book will prepare advanced undergraduate or early graduate students to go into more advanced theoretical studies. It will also equip students going into experimental soft matter science to be fully conversant with the theoretical aspects and have effective collaborations with theorists.
This volume deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry.
The discovery of a duality between Anti-de Sitter spaces (AdS) and Conformal Field Theories (CFT) has led to major advances in our understanding of quantum field theory and quantum gravity. String theory methods and AdS/CFT correspondence maps provide new ways to think about difficult condensed matter problems. String theory methods based on the AdS/CFT correspondence allow us to transform problems so they have weak interactions and can be solved more easily. They can also help map problems to different descriptions, for instance mapping the description of a fluid using the Navier–Stokes equations to the description of an event horizon of a black hole using Einstein's equations. This textbook covers the applications of string theory methods and the mathematics of AdS/CFT to areas of condensed matter physics. Bridging the gap between string theory and condensed matter, this is a valuable textbook for students and researchers in both fields.