The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering, Botelho, Fabio Silva
Автор: Gockenbach Название: Understanding and Implementing the Finite Element Method ISBN: 0898716144 ISBN-13(EAN): 9780898716146 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 15048.00 р. Наличие на складе: Нет в наличии.
Описание: The finite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics. The book is practical in nature. It includes a carefully documented collection of MATLAB programs implementing the ideas presented. Readers will benefit from a detailed explanation of data structures and specific coding strategies and will learn how to write a finite element code from scratch. Students can use the MATLAB codes to experiment with the method and extend them in various ways.
Автор: Schiesser William E Название: Method Of Lines Analysis Of Turing Models ISBN: 9813226692 ISBN-13(EAN): 9789813226692 Издательство: World Scientific Publishing Рейтинг: Цена: 12197.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book is directed toward the numerical integration (solution) of a system of partial differential equations (PDEs) that describes a combination of chemical reaction and diffusion, that is, reaction-diffusion PDEs. The particular form of the PDEs corresponds to a system discussed by Alan Turing and is therefore termed a Turing model.
Specifically, Turing considered how a reaction-diffusion system can be formulated that does not have the usual smoothing properties of a diffusion (dispersion) system, and can, in fact, develop a spatial variation that might be interpreted as a form of morphogenesis, so he termed the chemicals as morphogens.
Turing alluded to the important impact computers would have in the study of a morphogenic PDE system, but at the time (1952), computers were still not readily available. Therefore, his paper is based on analytical methods. Although computers have since been applied to Turing models, computer-based analysis is still not facilitated by a discussion of numerical algorithms and a readily available system of computer routines.
The intent of this book is to provide a basic discussion of numerical methods and associated computer routines for reaction-diffusion systems of varying form. The presentation has a minimum of formal mathematics. Rather, the presentation is in terms of detailed examples, presented at an introductory level. This format should assist readers who are interested in developing computer-based analysis for reaction-diffusion PDE systems without having to first study numerical methods and computer programming (coding).
The numerical examples are discussed in terms of: (1) numerical integration of the PDEs to demonstrate the spatiotemporal features of the solutions and (2) a numerical eigenvalue analysis that corroborates the observed temporal variation of the solutions. The resulting temporal variation of the 2D and 3D plots demonstrates how the solutions evolve dynamically, including oscillatory long-term behavior.
In all of the examples, routines in R are presented and discussed in detail. The routines are available through this link so that the reader can execute the PDE models to reproduce the reported solutions, then experiment with the models, including extensions and application to alternative models.
Автор: David Yang Gao Название: Duality Principles in Nonconvex Systems ISBN: 1441948252 ISBN-13(EAN): 9781441948250 Издательство: Springer Рейтинг: Цена: 25149.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Weimin Han Название: A Posteriori Error Analysis Via Duality Theory ISBN: 144193636X ISBN-13(EAN): 9781441936363 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems.
Автор: Patrascu Название: The Universal Coefficient Theorem and Quantum Field Theory ISBN: 3319461427 ISBN-13(EAN): 9783319461427 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.
Автор: Constantin P. Bachas; Adel Bilal; Michael R. Dougl Название: Unity from Duality: Gravity, Gauge Theory and Strings ISBN: 3642055478 ISBN-13(EAN): 9783642055478 Издательство: Springer Рейтинг: Цена: 27950.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The contributions to this volume of the famous summer school in Les Houches cover the recent developments in supersymmetric string theory, the gauge theory/string theory correspondence and string duality. The book is a comprehensive introduction to the recent developments in string/M-theory and quantum gravity.
Автор: Jonas Probst Название: Applications of the Gauge/Gravity Duality ISBN: 3030067580 ISBN-13(EAN): 9783030067588 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Many open questions in Theoretical Physics pertain to strongly interacting quantum systems such as the quark-gluon plasma (QGP) produced in heavy-ion collisions or the strange-metal phase observed in many high-temperature superconductors. These systems are notoriously difficult to study using traditional methods such as perturbation theory, but the gauge/gravity duality offers a successful alternative approach, which maps strongly interacting quantum gauge theories to computationally tractable, classical gravity theories. This book begins with a pedagogical introduction to how the duality can be used to extract transport properties of quantum systems from their gravity dual. It then presents new results on hydrodynamic transport in strongly interacting quantum fluids, providing strong evidence that the Haack-Yarom identity between second-order transport coefficients holds for all fluids with a classical gravity dual and may be a universal feature of all strongly coupled quantum fluids such as the QGP. Newly derived Kubo formulae, expressing transport coefficients in terms of quantum correlators, hold independently of the duality. Lastly, the book discusses new results on magnetic impurities in strongly correlated metals, including the first dual gravity description of an inter-impurity coupling, crucial for the quantum criticality underlying the strange-metal phase.
Автор: Pierre Deymier; Keith Runge Название: Sound Topology, Duality, Coherence and Wave-Mixing ISBN: 3319623796 ISBN-13(EAN): 9783319623795 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book offers an essential introduction to the notions of sound wave topology, duality, coherence and wave-mixing, which constitute the emerging new science of sound.
Автор: Wan-Xie Zhong Название: Duality System in Applied Mechanics and Optimal Control ISBN: 1475779178 ISBN-13(EAN): 9781475779172 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Hamilton system methodology in analytical mechanics is used for eigenvalue problems, vibration theory, gyroscopic systems, structural mechanics, wave-guide, LQ control, Kalman filter, robust control etc.
Автор: Guram Bezhanishvili Название: Leo Esakia on Duality in Modal and Intuitionistic Logics ISBN: 9401788596 ISBN-13(EAN): 9789401788595 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Leo Esakia on Duality in Modal and Intuitionistic Logics
Автор: Sorin-Mihai Grad Название: Vector Optimization and Monotone Operators via Convex Duality ISBN: 3319361902 ISBN-13(EAN): 9783319361901 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed.
Автор: Rolf F?re; Daniel Primont Название: Multi-Output Production and Duality: Theory and Applications ISBN: 0792395182 ISBN-13(EAN): 9780792395188 Издательство: Springer Рейтинг: Цена: 23757.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text presents a complete summary of the major results in duality theory pioneered by Ronald W. Shephard. It provides a number of applications of duality theory to economic problems. These include efficiency measurement, index number theory and shadow pricing.
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