Author: Ada Altieri Publisher: Springer Nature ISBN: 3030236005 Category : Science Languages : en Pages : 220
Book Description
The work described in this book originates from a major effort to develop a fundamental theory of the glass and the jamming transitions. The first chapters guide the reader through the phenomenology of supercooled liquids and structural glasses and provide the tools to analyze the most frequently used models able to predict the complex behavior of such systems. A fundamental outcome is a detailed theoretical derivation of an effective thermodynamic potential, along with the study of anomalous vibrational properties of sphere systems. The interested reader can find in these pages a clear and deep analysis of mean-field models as well as the description of advanced beyond-mean-field perturbative expansions. To investigate important second-order phase transitions in lattice models, the last part of the book proposes an innovative theoretical approach, based on a multi-layer construction. The different methods developed in this thesis shed new light on important connections among constraint satisfaction problems, jamming and critical phenomena in complex systems, and lay part of the groundwork for a complete theory of amorphous solids.
Author: Ada Altieri Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
The detailed description of disordered and glassy systems represents an open problem in statistical physics and condensed matter. As yet, there is no single, well-established theory allowing to understand such systems. The research presented in this thesis is related in particular to the study of glassy materials in the low-temperature regime. More precisely, considering systems formed by athermal particles subject to repulsive short-range interactions, upon progressively increasing the density, a so-called jamming transition can be detected. It entails a freezing of the degrees of freedom and hence a huge increase of the material rigidity.We shall study this problem in view of a formal analogy between sphere models and the perceptron, a theoretical model undergoing a jamming transition and frustration phenomena typical of disordered systems. Being a mean-field model, it allows to obtain exact analytical results, which are generalizable to more complex high-dimensional settings.The main aim is to reconstruct the vibrational spectrum and all the relevant properties of a specific phase of the perceptron, corresponding to the hard-sphere regime.In this framework, we will derive the effective potential as a function of the gaps between and forces among the particles, and we will show that it is dominated by a non-trivial logarithmic interaction near the jamming point. This interaction in turn will clarify the relations existing between the relevant variables of the system, in the critical jamming region and beyond.Understanding the jamming transition and the perceptron properties will allow us to make progress in several related fields. First, this study could lay part of the groundwork towards a complete theory of amorphous systems, in both infinite and finite dimensions. Furthermore, the perceptron model seems to a have a close connection with the so-called Von Neumann problems. Indeed, biological and ecological systems often develop pseudo-critical properties and give rise to general mechanisms of resource-consumption optimisation.Is the identification of a broken symmetry regime possible? What would it yield in terms of the spectrum of the energy fluctuations?These are just a few questions we shall attempt to answer in this context.However, the mean-field approximation can sometimes provide wrong or misleading information, especially in studying certain phase transitions and determining the exact lower and upper critical dimensions. To have a broad perspective and correctly deal with finite-dimensional systems, in the second part of the thesis we will discuss obtaining a systematic perturbative expansion which can be applied to any model, as long as defined on a lattice or a bipartite graph.Our motivation is in particular due to the possibility of studying relevant second-order phase transitions which exist on the Bethe lattice -- a lattice with a locally tree-like structure and fixed connectivity for each node -- but which are qualitatively different or absent in the corresponding fully-connected version.
Author: Patrick Charbonneau Publisher: World Scientific ISBN: 9811273936 Category : Science Languages : en Pages : 740
Book Description
About sixty years ago, the anomalous magnetic response of certain magnetic alloys drew the attention of theoretical physicists. It soon became clear that understanding these systems, now called spin glasses, would give rise to a new branch of statistical physics. As physical materials, spin glasses were found to be as useless as they were exotic. They have nevertheless been recognized as paradigmatic examples of complex systems with applications to problems as diverse as neural networks, amorphous solids, biological molecules, social and economic interactions, information theory and constraint satisfaction problems.This book presents an encyclopaedic overview of the broad range of these applications. More than 30 contributions are compiled, written by many of the leading researchers who have contributed to these developments over the last few decades. Some timely and cutting-edge applications are also discussed. This collection serves well as an introduction and summary of disordered and glassy systems for advanced undergraduates, graduate students and practitioners interested in the topic.
Author: Corrado Rainone Publisher: Springer ISBN: 3319604236 Category : Science Languages : en Pages : 219
Book Description
This thesis presents a theoretical analysis of the behavior of glasses under external perturbations, i.e. compression and shear straining. Written in a pedagogical style, it explains every facet of the problem in detail, including many crucial steps that cannot be found in the existing literature—making it particularly useful for students and as an introduction to the subject of glassy physics. In glassy systems the behavior under external compression and shear-strain is quite peculiar. Many complex phenomena are observed and grasping them fully would be a major step toward a complete theory of the glass transition. This thesis makes important advances in this direction, analyzing the behavior of glassy states in painstaking detail and reproducing it in the framework of a recently developed mean field theory for glasses that has proven extremely successful for jamming, demonstrating its predictive power in the context of metastable glassy states obtained through nonequilibrium protocols.
Author: Freeman John Dyson Publisher: World Scientific ISBN: 9814759090 Category : Science Languages : en Pages : 386
Book Description
"Freeman Dyson has designed nuclear reactors and bomb-powered spacecraft; he has studied the origins of life and the possibilities for the long-term future; he showed quantum mechanics to be consistent with electrodynamics and started cosmological eschatology; he has won international recognition for his work in science and for his work in reconciling science to religion; he has advised generals and congressional committees. An STS (Science, Technology, Society) curriculum or discussion group that engages topics such as nuclear policies, genetic technologies, environmental sustainability, the role of religion in a scientific society, and a hard look towards the future, would count itself privileged to include Professor Dyson as a class participant and mentor. In this book, STS topics are not discussed as objectified abstractions, but through personal stories. The reader is invited to observe Dyson's influence on a generation of young people as they wrestle with issues of science, technology, society, life in general and our place in the universe. The book is filled with personal anecdotes, student questions and responses, honest doubts and passions"--
Author: Kurt Binder Publisher: World Scientific ISBN: 9814350176 Category : Science Languages : en Pages : 562
Book Description
This book gives a pedagogical introduction to the physics of amorphous solids and related disordered condensed matter systems. Important concepts from statistical mechanics such as percolation, random walks, fractals and spin glasses are explained. Using these concepts, the common aspects of these systems are emphasized, and the current understanding of the glass transition and the structure of glasses are concisely reviewed. This second edition includes new material on emerging topics in the field of disordered systems such as gels, driven systems, dynamical heterogeneities, growing length scales etc. as well as an update of the literature in this rapidly developing field.
Author: Andrea J. Liu Publisher: CRC Press ISBN: 1482268175 Category : Science Languages : en Pages : 568
Book Description
The subject of jamming and rheology is a broad and interdisciplinary one that is generating increasing interest. This book deals with one of the oldest unsolved problems in condensed matter physics - that of the nature of glass transition in supercooled liquids. Jamming and Rheology is a collection of reprinted articles from several fields, ran
Author: Alberto Fernandez-Nieves Publisher: John Wiley & Sons ISBN: 111922053X Category : Technology & Engineering Languages : en Pages : 872
Book Description
This book presents a compilation of self-contained chapters covering a wide range of topics within the broad field of soft condensed matter. Each chapter starts with basic definitions to bring the reader up-to-date on the topic at hand, describing how to use fluid flows to generate soft materials of high value either for applications or for basic research. Coverage includes topics related to colloidal suspensions and soft materials and how they differ in behavior, along with a roadmap for researchers on how to use soft materials to study relevant physics questions related to geometrical frustration.
Author: Giorgio Parisi Publisher: Cambridge University Press ISBN: 1108126103 Category : Science Languages : en Pages : 341
Book Description
This pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical physics, before reviewing the key elements of the thermodynamic theory of liquids and the dynamical properties of liquids and glasses. The central feature of the mean field theory of disordered systems, the existence of a large multiplicity of metastable states, is then introduced. The replica method is then covered, before the final chapters describe important, advanced topics such as Gardner transitions, complexity, packing spheres in large dimensions, the jamming transition, and the rheology of glass. Presenting the theory in a clear and pedagogical style, this is an excellent resource for researchers and graduate students working in condensed matter physics and statistical mechanics.
Author: Ada Altieri
Author: Ada Altieri
Author: Patrick Charbonneau
Author: Corrado Rainone
Author: Freeman John Dyson
Author: Kurt Binder
Author: Bertrand Duplantier
Author: Andrea J. Liu
Author: Alberto Fernandez-Nieves
Author: Giorgio Parisi