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Author: Francis Comets
Publisher: Springer
ISBN: 3319504878
Category : Mathematics
Languages : en
Pages : 210
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Book Description
Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
Author: Francis Comets
Publisher: Springer
ISBN: 3319504878
Category : Mathematics
Languages : en
Pages : 210
Get Book Here
Book Description
Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
Author: Bikas K. Chakrabarti
Publisher: Elsevier
ISBN: 008046047X
Category : Technology & Engineering
Languages : en
Pages : 368
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Book Description
With the mapping of the partition function graphs of the n-vector magnetic model in the n to 0 limit as the self-avoiding walks, the conformational statistics of linear polymers was clearly understood in early seventies. Various models of disordered solids, percolation model in particular, were also established by late seventies. Subsequently, investigations on the statistics of linear polymers or of self-avoiding walks in, say, porous medium or disordered lattices were started in early eighties. Inspite of the brilliant ideas forwarded and extensive studies made for the next two decades, the problem is not yet completely solved in its generality. This intriguing and important problem has remained since a topic of vigorous and active research. This book intends to offer the readers a first hand and extensive review of the various aspects of the problem, written by the experts in the respective fields. We hope, the contents of the book will provide a valuable guide for researchers in statistical physics of polymers and will surely induce further research and advances towards a complete understanding of the problem. First book on statistics of polymers in random media. Contents straight away from research labs. Chapters written by foremost experts in the respective fields. Theories, experiments and computer simulations extensively discussed. Includes latest developments in understanding related important topics like DNA unzipping, Travelling salesman problem, etc. Comprehensive index for quick search for keywords.
Author: Alain-Sol Sznitman
Publisher: Springer Science & Business Media
ISBN: 3662112817
Category : Mathematics
Languages : en
Pages : 366
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Book Description
This book provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. It also includes an overview of known results and connections with other areas of random media, taking a highly original and personal approach throughout.
Author: PROF SATYA N.. SCHEHR MAJUMDAR (PROF GREGORY.)
Publisher: Oxford University Press
ISBN: 0198797338
Category : Mathematics
Languages : en
Pages : 257
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Book Description
Rare events such as earthquakes, tsunamis, and floods fortunately do not occur every day, but when they do, their effects are devastating. Such rare events are particularly important in understanding and characterizing global warming and climate changes. In addition to natural catastrophes, rare events such as big financial crashes also play a significant role in the economy. In the absence of predictive models, the best way forward is to analyse the statistics of these extreme events and draw conclusions about the probability of their occurrences.Extreme value statistics (EVS) and the statistics of records in a random sequence are examples of a truly interdisciplinary topic, spanning from statistics and mathematics on one side to physics of disordered systems on the other. They have tremendous importance and practical applications in a wide variety of fields, such as climate science, finance, spin-glasses, and random matrices.Statistics and mathematical literature have explored the subject of the classical theory of EVS. However, more recently, EVS started to play a very important role in statistical physics, in particular in disordered systems. This has led to a plethora of activities, both in the statistical physics and in the mathematics communities over the last few decades. This book develops the theory of rare events, both for the classical uncorrelated as well as for correlated sequences, in terms of simple models and examples. Statistics of Extremes and Records in Random Sequences is a pedagogical book with examples illustrating the basic tools and techniques that are essential to a student starting to work in this interesting and rapidly developing field.
Author: Frank Hollander
Publisher: Springer Science & Business Media
ISBN: 364200332X
Category : Mathematics
Languages : en
Pages : 271
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Book Description
Polymer chains that interact with themselves and/or their environment display a range of physical and chemical phenomena. This text focuses on the mathematical description of some of these phenomena, offering a mathematical panorama of polymer chains.
Author: A.- L. Barabási
Publisher: Cambridge University Press
ISBN: 9780521483186
Category : Mathematics
Languages : en
Pages : 392
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Book Description
This book brings together two of the most exciting and widely studied subjects in modern physics: namely fractals and surfaces. To the community interested in the study of surfaces and interfaces, it brings the concept of fractals. To the community interested in the exciting field of fractals and their application, it demonstrates how these concepts may be used in the study of surfaces. The authors cover, in simple terms, the various methods and theories developed over the past ten years to study surface growth. They describe how one can use fractal concepts successfully to describe and predict the morphology resulting from various growth processes. Consequently, this book will appeal to physicists working in condensed matter physics and statistical mechanics, with an interest in fractals and their application. The first chapter of this important new text is available on the Cambridge Worldwide Web server: http://www.cup.cam.ac.uk/onlinepubs/Textbooks/textbookstop.html
Author: Alejandro F. Ramírez
Publisher: Springer
ISBN: 149390339X
Category : Mathematics
Languages : en
Pages : 178
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Book Description
This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical understanding of phenomena describing systems in highly inhomogeneous and disordered media, including the KPZ universality class (describing the evolution of interfaces in two dimensions), random walks in random environment and percolative systems. PASI fosters a collaboration between North American and Latin American researchers and students. The conference that inspired this volume took place in January 2012 in both Santiago de Chile and Buenos Aires. Researchers and graduate students will find timely research in probability theory, statistical physics and related disciplines.
Author: Carles Casacuberta
Publisher: Birkhäuser
ISBN: 3034882688
Category : Mathematics
Languages : en
Pages : 611
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Book Description
This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabré, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. Föllmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Simó, B. Tóth, E. van den Ban, M.-F. Vignéras, O. Viro.
Author:
Publisher: Elsevier
ISBN: 0080538770
Category : Science
Languages : en
Pages : 209
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Book Description
The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies.Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations.The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.
Author: Gunilla Sundström
Publisher: CRC Press
ISBN: 1317126017
Category : Technology & Engineering
Languages : en
Pages : 211
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Book Description
The recent financial crisis has made it paramount for the financial services industry to find new perspectives to look at their industry and, most importantly, to gain a better understanding of how the global financial system can be made less vulnerable and more resilient. The primary objective of this book is to illustrate how the safety science of Resilience Engineering can help to gain a better understanding of what the financial services system is and how to improve governance and control of financial services systems by leveraging some of its key concepts. Resilience is the intrinsic ability of a system to adjust its functioning prior to, during, or following changes and disturbances, so that it can sustain required operations under both expected and unexpected conditions. This definition is focused on the ability to function, rather than just to be impervious to failure, and thereby bridges the traditional conflict between productivity and safety. The core concept of the book is that the behaviour of the financial services system is the result of the tight couplings among the humans, organizations and technologies that are necessary to provide complex financial functions such as the transfer of economic resources. It is a consequence of this perspective that the risks associated with these systems cannot be understood without considering the nature of these tight couplings. Adopting this perspective, the book is designed to provide some answers to the following key questions about the financial crisis: - What actually happened? - Why and how did it happen? - Could something similar happen again? How can we see that in time and how can we control it? - How can sustainable recovery of the global financial system be established? How can its resilience be improved?
