Recursos de colección
Caltech Authors (158.172 recursos)
Repository of works by Caltech published authors.
Type = Book
Repository of works by Caltech published authors.
Type = Book
Nebe, Gabriele; Rains, Eric M.; Sloane, Neil J. A.
[No abstract]
Low, Steven H.
The congestion control mechanism has been responsible for maintaining stability as the Internet scaled up by many orders of magnitude in size, speed, traffic volume, coverage, and complexity over the last three decades. In this book, we develop a coherent theory of congestion control from the ground up to help understand and design these algorithms. We model network traffic as fluids that flow from sources to destinations and model congestion control algorithms as feedback dynamical systems. We show that the model is well defined. We characterize its equilibrium points and prove their stability. We will use several real protocols for...
[No abtract]
Liepmann, H. W.; Narasimhan, R.
The last two decades have witnessed an intensifying
effort in learning how to manage flow turbulence: it has in
fact now become one of the most challenging and prized technological goals in fluid dynamics. The goal itself is of course not new. More than a hundred years ago, Reynolds already listed factors conducive to laminar and to turbulent flow (including among them curvature and acceleration). Furthermore, it is in retrospect clear that there were several early instances of successful turbulence management. Examples are the reduction in drag achieved with a ring-trip placed on the front of a sphere or the insertion of...
The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and...
Stuart, A. M.; Humphries, A. R.
This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the...
Gonzalez, Oscar; Stuart, Andrew M.
A concise account of various classic theories of fluids and solids, this book is for courses in continuum mechanics for graduate students and advanced undergraduates. Thoroughly class-tested in courses at Stanford University and the University of Warwick, it is suitable for both applied mathematicians and engineers. The only prerequisites are an introductory undergraduate knowledge of basic linear algebra and differential equations. Unlike most existing works at this level, this book covers both isothermal and thermal theories. The theories are derived in a unified manner from the fundamental balance laws of continuum mechanics. Intended both for classroom use and for self-study,...
Pavliotis, Grigorios A.; Stuart, Andrew M.
This introduction to multiscale methods gives readers a broad overview of the many uses and applications of the methods. The book begins by setting the theoretical foundations of the subject area, and moves on to develop a unified approach to the simplification of a wide range of problems which possess multiple scales, via perturbation expansions; differential equations and stochastic processes are studied in one unified framework. The book concludes with an overview of a range of theoretical tools used to justify the simplified models derived via the perturbation expansions.
The presentation of the material is particularly suited to the range of...
Law, Kody; Stuart, Andrew; Zygalakis, Konstantinos
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online.
The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material...
Peter, Isabelle S.; Davidson, Eric H.
In our time, the sheer volume of published experimental measurements, their scope and technical sophistication, compounded with a proliferation of diverse approaches, objectives, and model systems, has made it particularly difficult to see the conceptual forest for the trees. Yet all of the elegant and sophisticated though disparate and unconnected data sets with which we are confronted represent biological output of the same fundamental operating principles. Each experimental system provides a different window which offers a pathway to these principles. In this book we provide a conceptual framework that we hope will make accessible the principles by which the genomic...
Mead, Carver; Conway, Lynn
[No abstract]
Gavalas, George R.
Prompted by the need of non-petroleum-based fuels, coal research has reemerged to center stage after a lengthy dormant period. Pyrolysis research, in particular, has gained considerable momentum because of its close connection to combustion, hydropyrolysis and liquefaction. Spectroscopic and other instrumental techniques are currently producing prodigious information about coal structure and pyrolysis mechanisms, while modeling efforts are breaking new ground in sorting out chemical and physical phenomena to provide a fundamental although simplified description.
The continuing generation of experimental data will lead to revisions, in some cases drastic, of current structural and kinetic precepts. Yet, the postulates and assumptions of...