Elegant Simulations: From Simple Oscillators To Many-body Systems PDF Download
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Author: Julien Clinton Sprott
Publisher: World Scientific
ISBN: 9811263582
Category : Science
Languages : en
Pages : 325
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Book Description
A recent development is the discovery that simple systems of equations can have chaotic solutions in which small changes in initial conditions have a large effect on the outcome, rendering the corresponding experiments effectively irreproducible and unpredictable. An earlier book in this sequence, Elegant Chaos: Algebraically Simple Chaotic Flows provided several hundred examples of such systems, nearly all of which are purely mathematical without any obvious connection with actual physical processes and with very limited discussion and analysis.In this book, we focus on a much smaller subset of such models, chosen because they simulate some common or important physical phenomenon, usually involving the motion of a limited number of point-like particles, and we discuss these models in much greater detail. As with the earlier book, the chosen models are the mathematically simplest formulations that exhibit the phenomena of interest, and thus they are what we consider 'elegant.'Elegant models, stripped of unnecessary detail while maximizing clarity, beauty, and simplicity, occupy common ground bordering both real-world modeling and aesthetic mathematical analyses. A computational search led one of us (JCS) to the same set of differential equations previously used by the other (WGH) to connect the classical dynamics of Newton and Hamilton to macroscopic thermodynamics. This joint book displays and explores dozens of such relatively simple models meeting the criteria of elegance, taste, and beauty in structure, style, and consequence.This book should be of interest to students and researchers who enjoy simulating and studying complex particle motions with unusual dynamical behaviors. The book assumes only an elementary knowledge of calculus. The systems are initial-value iterated maps and ordinary differential equations but they must be solved numerically. Thus for readers a formal differential equations course is not at all necessary, of little value and limited use.
Author: Julien Clinton Sprott
Publisher: World Scientific
ISBN: 9811263582
Category : Science
Languages : en
Pages : 325
Get Book Here
Book Description
A recent development is the discovery that simple systems of equations can have chaotic solutions in which small changes in initial conditions have a large effect on the outcome, rendering the corresponding experiments effectively irreproducible and unpredictable. An earlier book in this sequence, Elegant Chaos: Algebraically Simple Chaotic Flows provided several hundred examples of such systems, nearly all of which are purely mathematical without any obvious connection with actual physical processes and with very limited discussion and analysis.In this book, we focus on a much smaller subset of such models, chosen because they simulate some common or important physical phenomenon, usually involving the motion of a limited number of point-like particles, and we discuss these models in much greater detail. As with the earlier book, the chosen models are the mathematically simplest formulations that exhibit the phenomena of interest, and thus they are what we consider 'elegant.'Elegant models, stripped of unnecessary detail while maximizing clarity, beauty, and simplicity, occupy common ground bordering both real-world modeling and aesthetic mathematical analyses. A computational search led one of us (JCS) to the same set of differential equations previously used by the other (WGH) to connect the classical dynamics of Newton and Hamilton to macroscopic thermodynamics. This joint book displays and explores dozens of such relatively simple models meeting the criteria of elegance, taste, and beauty in structure, style, and consequence.This book should be of interest to students and researchers who enjoy simulating and studying complex particle motions with unusual dynamical behaviors. The book assumes only an elementary knowledge of calculus. The systems are initial-value iterated maps and ordinary differential equations but they must be solved numerically. Thus for readers a formal differential equations course is not at all necessary, of little value and limited use.
Author: Karl Johan Åström
Publisher: Princeton University Press
ISBN: 069121347X
Category : Technology & Engineering
Languages : en
Pages : 523
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Book Description
The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory
Author: Julien Clinton Sprott
Publisher: World Scientific
ISBN: 9814468673
Category : Mathematics
Languages : en
Pages : 302
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Book Description
This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.
Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Author: Alexander Altland
Publisher: Cambridge University Press
ISBN: 0521769752
Category : Science
Languages : en
Pages : 785
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Book Description
This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
Author: Carol L. Hoover
Publisher: Addison-Wesley Professional
ISBN: 0321685636
Category : Computers
Languages : en
Pages : 591
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Book Description
Effective decisions are crucial to the success of any software project, but to make better decisions you need a better decision-making process. In Evaluating Project Decisions, leading project management experts introduce an innovative decision model that helps you tailor your decision-making process to systematically evaluate all of your decisions and avoid the bad choices that lead to project failure. Using a real-world, case study approach, the authors show how to evaluate software project problems and situations more effectively, thoughtfully assess your alternatives, and improve the decisions you make. Drawing on their own extensive research and experience, the authors bridge software engineering theory and practice, offering guidance that is both well-grounded and actionable. They present dozens of detailed examples from both successful and unsuccessful projects, illustrating what to do and what not to do. Evaluating Project Decisions will help you to analyze your options and ultimately make better decisions at every stage in your project, including: Requirements–Elicitation, description, verification, validation, negotiation, contracting, and management over the software life cycle Estimates–Conceptual solution design, decomposition, resource and overhead allocation, estimate construction, and change management Planning–Defining objectives, policies, and scope; planning tasks, milestones, schedules, budgets, staff and other resources; and managing projects against plans Product–Proper product definition, development process management, QA, configuration management, delivery, installation, training, and field service Process–Defining, selecting, understanding, teaching, and measuring processes; evaluating process performance; and process improvement or optimization In addition, you will see how to evaluate decisions related to risk, people, stakeholder expectations, and global development. Simply put, you’ll use what you learn here on every project, in any industry, whatever your goals, and for projects of any duration, size, or type.
Author: W.G. Hoover
Publisher: Elsevier
ISBN: 0444596593
Category : Science
Languages : en
Pages : 330
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Book Description
Computational Statistical Mechanics describes the use of fast computers to simulate the equilibrium and nonequilibrium properties of gases, liquids, and solids at, and away from equilibrium. The underlying theory is developed from basic principles and illustrated by applying it to the simplest possible examples. Thermodynamics, based on the ideal gas thermometer, is related to Gibb's statistical mechanics through the use of Nosé-Hoover heat reservoirs. These reservoirs use integral feedback to control temperature. The same approach is carried through to the simulation and analysis of nonequilibrium mass, momentum, and energy flows. Such a unified approach makes possible consistent mechanical definitions of temperature, stress, and heat flux which lead to a microscopic demonstration of the Second Law of Thermodynamics directly from mechanics. The intimate connection linking Lyapunov-unstable microscopic motions to macroscopic dissipative flows through multifractal phase-space structures is illustrated with many examples from the recent literature. The book is well-suited for undergraduate courses in advanced thermodynamics, statistical mechanic and transport theory, and graduate courses in physics and chemistry.
Author: Alan Garfinkel
Publisher: Springer
ISBN: 3319597310
Category : Mathematics
Languages : en
Pages : 456
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Book Description
This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
Author: William Graham Hoover
Publisher: World Scientific
ISBN: 9814477184
Category : Mathematics
Languages : en
Pages : 315
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Book Description
This book takes readers through all the steps necessary for solving hard problems in continuum mechanics with smooth particle methods. Pedagogical problems clarify the generation of initial conditions, the treatment of boundary conditions, the integration of the equations of motion, and the analysis of the results. Particular attention is paid to the parallel computing necessary for large problems and to the graphic displays, including debugging software, required for the efficient completion of computational projects.The book is self-contained, with summaries of classical particle mechanics and continuum mechanics for both fluids and solids, computer languages, the stability of numerical methods, Lyapunov spectra, and message-passing parallel computing. The main difficulties faced by meshless particle methods are discussed and the means of overcoming them are illustrated with worked examples.
Author: Claire Ridgway
Publisher: Createspace Independent Pub
ISBN: 9781478295914
Category : Reference
Languages : en
Pages : 202
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Book Description
Learn how to succeed in indie publishing. With interviews from 34 of the hottest names in self-publishing, "Interviews with Indie Authors" contains a unique view into the world of the indie writer. Each bestselling author shares how they ensure their books are a hit, and what led them to indie publishing in the first place. You will also find out what they think the future of indie publishing will bring. Their first hand experience is invaluable for anyone planning to succeed with their own books. Whatever your background, you will learn from these incredible interviews. With diverse genres such as thrillers, young adult fiction, the paranormal, romance, comedy, fantasy, horror, science fiction, mystery and even non-fiction, whatever you are writing about, this book has it covered. Contains interviews with indie authors such as: Michael McCloskey, Nick Russell, Connie Suttle, Michael Prescott, Terri Reid, Hugh Howey, Scott Nicholson, Kristen Ashley, Aaron Patterson, Carol Davis Luce, Claire Ridgway, Alexa Grace, Marie Force, Shadonna Richards, Colleen Hoover, Barbara Freethy, Joseph Lallo, Rebecca Forster, Caryn Moya Block, Denise Grover Swank, Mainak Dhar, Imogen Rose, CJ Lyons, Bella Andre, Maria Murnane, Theresa Ragan, Russell Blake, Linda Welch, Debra Holland, J. Thorn, James Somers, Karen Cantwell, Tracey Garvis Graves and Elena Greene Learn how to succeed in indie publishing with this book.
