A Dynamical Perspective on the ɸ4 Model

2019-02-26 Science

Author : Panayotis G. Kevrekidis
Release : 2019-02-26
Genre : Science
Kind : eBook
Book Rating : 398/5 ( reviews)

GET EBOOK

Book Synopsis A Dynamical Perspective on the ɸ4 Model by : Panayotis G. Kevrekidis

Download or read book A Dynamical Perspective on the ɸ4 Model written by Panayotis G. Kevrekidis. This book was released on 2019-02-26. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the \phi^4 model has been the basis for a broad array of developments in the physics and mathematics of nonlinear waves. From kinks to breathers, from continuum media to discrete lattices, from collisions of solitary waves to spectral properties, and from deterministic to stochastic models of \phi^4 (and \phi^6, \phi^8, \phi^12 variants more recently), this dynamical model has served as an excellent test bed for formulating and testing the ideas of nonlinear science and solitary waves.

A Dynamical Perspective on the ɸ4 Model

2019 SCIENCE

Author : Panayotis G. Kevrekidis
Release : 2019
Genre : SCIENCE
Kind : eBook
Book Rating : 402/5 ( reviews)

GET EBOOK

Book Synopsis A Dynamical Perspective on the ɸ4 Model by : Panayotis G. Kevrekidis

Download or read book A Dynamical Perspective on the ɸ4 Model written by Panayotis G. Kevrekidis. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a careful selection of the most important developments of the 4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the 4 model has been the basis for a broad array of developments in the physics and mathematics of nonlinear waves. From kinks to breathers, from continuum media to discrete lattices, from collisions of solitary waves to spectral properties, and from deterministic to stochastic models of 4 (and 6 ,8 ,12 variants more recently), this dynamical model has served as an excellent test bed for formulating and testing the ideas of nonlinear science and solitary waves. .

A Dynamical Approach to Random Matrix Theory

2017-08-30 Mathematics

Author : László Erdős
Release : 2017-08-30
Genre : Mathematics
Kind : eBook
Book Rating : 485/5 ( reviews)

GET EBOOK

Book Synopsis A Dynamical Approach to Random Matrix Theory by : László Erdős

Download or read book A Dynamical Approach to Random Matrix Theory written by László Erdős. This book was released on 2017-08-30. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Models of Science Dynamics

2012-01-24 Social Science

Author : Andrea Scharnhorst
Release : 2012-01-24
Genre : Social Science
Kind : eBook
Book Rating : 687/5 ( reviews)

GET EBOOK

Book Synopsis Models of Science Dynamics by : Andrea Scharnhorst

Download or read book Models of Science Dynamics written by Andrea Scharnhorst. This book was released on 2012-01-24. Available in PDF, EPUB and Kindle. Book excerpt: Models of Science Dynamics aims to capture the structure and evolution of science, the emerging arena in which scholars, science and the communication of science become themselves the basic objects of research. In order to capture the essence of phenomena as diverse as the structure of co-authorship networks or the evolution of citation diffusion patterns, such models can be represented by conceptual models based on historical and ethnographic observations, mathematical descriptions of measurable phenomena, or computational algorithms. Despite its evident importance, the mathematical modeling of science still lacks a unifying framework and a comprehensive study of the topic. This volume fills this gap, reviewing and describing major threads in the mathematical modeling of science dynamics for a wider academic and professional audience. The model classes presented cover stochastic and statistical models, system-dynamics approaches, agent-based simulations, population-dynamics models, and complex-network models. The book comprises an introduction and a foundational chapter that defines and operationalizes terminology used in the study of science, as well as a review chapter that discusses the history of mathematical approaches to modeling science from an algorithmic-historiography perspective. It concludes with a survey of remaining challenges for future science models and their relevance for science and science policy.

Mathematical Modeling of Earth's Dynamical Systems

2011-03-28 Science

Author : Rudy Slingerland
Release : 2011-03-28
Genre : Science
Kind : eBook
Book Rating : 114/5 ( reviews)

GET EBOOK

Book Synopsis Mathematical Modeling of Earth's Dynamical Systems by : Rudy Slingerland

Download or read book Mathematical Modeling of Earth's Dynamical Systems written by Rudy Slingerland. This book was released on 2011-03-28. Available in PDF, EPUB and Kindle. Book excerpt: A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

Popular eBooks

A Dynamical Perspective on the ɸ4 Model

A Dynamical Perspective on the ɸ4 Model

A Dynamical Approach to Random Matrix Theory

Mathematical Modeling of Earth's Dynamical Systems

You may also like...