Book Description
Everyone knows the small-world phenomenon: soon after meeting a stranger, we are surprised to discover that we have a mutual friend, or we are connected through a short chain of acquaintances. In his book, Duncan Watts uses this intriguing phenomenon--colloquially called "six degrees of separation"--as a prelude to a more general exploration: under what conditions can a small world arise in any kind of network?
The networks of this story are everywhere: the brain is a network of neurons; organisations are people networks; the global economy is a network of national economies, which are networks of markets, which are in turn networks of interacting producers and consumers. Food webs, ecosystems, and the Internet can all be represented as networks, as can strategies for solving a problem, topics in a conversation, and even words in a language. Many of these networks, the author claims, will turn out to be small worlds.
How do such networks matter? Simply put, local actions can have global consequences, and the relationship between local and global dynamics depends critically on the network's structure. Watts illustrates the subtleties of this relationship using a variety of simple models---the spread of infectious disease through a structured population; the evolution of cooperation in game theory; the computational capacity of cellular automata; and the sychronisation of coupled phase-oscillators.
Watts's novel approach is relevant to many problems that deal with network connectivity and complex systems' behaviour in general: How do diseases (or rumours) spread through social networks? How does cooperation evolve in large groups? How do cascading failures propagate through large power grids, or financial systems? What is the most efficient architecture for an organisation, or for a communications network? This fascinating exploration will be fruitful in a remarkable variety of fields, including physics and mathematics, as well as sociology, economics, and biology.
Customer Reviews:
All the details you need to know to understand Watts' and Strogatz' famous article.......2007-03-12
The book basically gives all the details needed to understand Watts and Strogatz famous Nature article 'Collective Dynamics of Complex Networks' in 1998. I think that it is basically Watts PhD-thesis and as such it is of course nicely written, but nothing for the laymen who is rather referred to Watts other, more story-telling book 'Six Degrees', Barabasi's book 'Linked', or to another book that I would recommend most, namely the one by Mark Buchanan titled 'Small Worlds'. Mark is a skillful scientific writer and his book has a broader scope that makes it more interesting than each of the two monographs that are a bit more focused on the scientists own contribution.
Not enough contents to be a good book.......2005-07-08
Networks are since a couple of years object of intense research in several different disciplines. One reason therefore is certainly the outstanding article by Watts and Strogatz, Collective dynamics of small world networks, Nature, 393:440--442, 1998. Unfortunatelly, this book can not continue the high level of this article. Actually, it does not really provide much more information than the article itself. I would suggest to read the article cited above and either decide for another book or to look directly in the literature and read the origninal articles.
To summarize, this book is not terribly weak, but one can clearly sees that it swims on the current 'complex networks' wave without providing enough justification for its existence. Of course, if you do not have access to the original literature and just what to have a general overview of complex networks and what be done with them, you may consider buying this book.
Good, but some typos.......2005-06-02
Mathematical level: Moderate; there's no calculus, and little high level math, but the book is quite mathematical in tone, and some of the arguments may be difficult to follow without a good "math sense". There are MANY equations and graphs.
Good points: Watts covers an area that will interest those who deal with mathematical models of social networks e.g. models of disease-spread, especially HIV. It might, however, cover other things that can spread through networks as well. He presents analysis of graphs (or networks) that are neither random nor highly structured; and begins to examine ways that the degree of structure v. randomness can be measured.
Bad points: There are more than the usual number of typos. The models presented are a "first step", only.
Inspiring.......2001-07-24
The author believes that human thought might be a small world, in the sense that one could reach any idea if he/she finds the right associations and "short-cut"s. The small-world theory is indeed one of those short cuts itself. It links many different domains and uncovers some interesting common behavior.
The theory is developed in a scientific manner with extensive numerical support. Rich literature reviews and many open questions make this book a good research reference. Complex observations are generally followed by qualitative explanations. However, some of the simpler derivations are not fully clear. I believe that adding a few lines here and there can turn this book into a textbook.
The book spans many different areas of science and a deep understanding of the related results may require some background. However, each chapter ends with a brief summary, allowing the reader to move forward if he/she finds the chapter difficult. In summary, as the author puts it, the book is simply the "end of the beginning" in an exciting new field.
Great scientific synthesis.......2000-07-12
The book takes a systematic look at the 'small world' graphs. These natural graphs have been discovered by graph theoretist as erly as 60's, but were not properly understood. The graphs are remarkable in their ability to cluster and scale lengths. There are fundumental connections between these graphs and complex systems, discrete dynamical systems, computation and information processing. Duncan has done a tremendous job in building experimetal and theoretical models trying to understand how these graphs come about and sustain themselves. Read this book.
Book Description
The new edition of this highly acclaimed textbook contains several major additions, including more than four hundred new exercises (with hints and answers). To match the mathematical preparation of current senior college and university entrants, the authors have included a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, induction, and the proof of necessary and sufficient conditions. Elsewhere, matrix decompositions, nearly-singular matrices and non-square sets of linear equations are treated in detail. The presentation of probability has been reorganized and greatly extended, and includes all physically important distributions. New topics covered in a separate statistics chapter include estimator efficiency, distributions of samples, t- and F- tests for comparing means and variances, applications of the chi-squared distribution, and maximum likelihood and least-squares fitting. In other chapters the following topics have been added: linear recurrence relations, curvature, envelopes, curve-sketching, and more refined numerical methods.
Customer Reviews:
Just one comment, this is a great book........2007-05-30
This is one of the best mathematical methods book, very readable.
It has very clear explainations, in each topic it's developing from basic intuitions until it reaches the genralized equations, several detailed examples help a reader checks his understanding and follows the authors.
The contents are very well-organized and self-contained, one can looks directly at the topic he wants to know. It's lucid and normally answer and teach a reader what he wants to do. All definitions make sense and a reader can accepts easily it's a smart thing to do math that way.
It also serves as a one-stop, if you feel confused when you're reading because your background knowledge is not strong enough, just search for the previous related topics, all brilliant explainations are waiting for you to grasp them, make you ready for what you need.
Any undergrads and beginning grad students in Physics will find this book is great. This is an excellent example how to write an approachable math methods book. Eventhough it has a thick over than 1,300 pages, but it never turns a reader away becuase of its thickness at all. Once one starts reading it, he'll enjoy and come back looking for another explaination.
One more great point is, this book contains a lot of real physical examples besides the math formulations, make a reader understands the topic deeply and sees a practical use.
Besides the book, I totally don't agree with a previous comment from a chemical physicist who gave this book just one star.
There are much better options........2007-04-24
This book is only good for someone who is very experienced in these areas of mathematics it discusses. It is not whatsoever for a student who wants to learn these things for the first time. It should be avoided at all costs to someone who does not already know how to do these mathematical operations. If you want to learn techniques of math for science, read Mary Boas's book (excellent) or Glen Fletcher.
If you are looking for an in depth analysis of these subjects after a course in mathematical methods and comfort in mathematics of physics undergraduate, then this book is comprehensive and good reference book. I still, however, find the book very lacking and regret buying it overall.
Average customer rating:
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Nonlinear Interactions: Analytical, Computational, and Experimental Methods
Ali H. Nayfeh
Manufacturer: Wiley-Interscience
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Nonlinear Oscillations (Wiley Classics Library)
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Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (Wiley Series in Nonlinear Science)
ASIN: 0471175919 |
Book Description
Nonlinear Interactions provides a coherent and unified treatment of analytical, computational, and experimental methods and concepts of modal interactions. This book is an obvious extension of Ali Nayfeh's well-known book Applied Nonlinear Dynamics (with Bala Balachandran). These methods are used to explore and unfold in a unified manner the fascinating complexities in nonlinear dynamical systems. The systems discussed are drawn from fluid mechanics and structural dynamics.
Nonlinear interactions between high-frequency and low-frequency modes are of great practical importance. Through the mechanisms discussed in this book, energy from high-frequency sources can be transferred to the low-frequency modes of supporting structures and foundations, and the result can be harmful large-amplitude oscillations that decrease their fatigue lives. On the other hand, these mechanisms can be exploited to transfer the energy from a system to a sacrificial subsystem and hence decrease considerably the vibrations of the main system and increase its fatigue life.
Book Description
This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world.
The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Bäcklund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painlevé test, the Bethe ansatz, the Yang-Baxter relation, chaos, fractals, complexity, etc.
Customer Reviews:
Some of this Material is Undergrad Level but the rest! WHEW!.......2004-11-23
Table of Contents follows:
Volume 2: Advanced/Graduate Level
1 Lax Representations in Classical Mechanics
2 Kronecker and Tensor Products
3 Nambu Mechanics
4 Gateaux and Frechet Derivatives
5 Stability and Bifurcations
6 Nonlinear Ordinary Difference Equations
7 Nonlinear Ordinary Differential Equations
8 Groups
9 Generalized Functions
10 Linear Partial Differential Equations
11 Nonlinear Partial Differential Equations
12 Group Theoretical Reductions
13 Backland Transformations
14 Soliton Equations
15 Lax Pairs for Partial Differential Equations
16 Hirota Technique
17 Painleve Test
18 Lie Algebras
19 Differential Forms
20 Lie Derivative
21 Metric Tensor Fields
22 Killing Vector Fields
23 Inequalities
24 Ising Model and Heisenberg Model
25 Number Theory
26 Combinatorial Problems
27 Fermi Operators
28 Bose Operators
29 Lax Representations and Bethe Ansatz
30 Gauge Transformations
31 Chaos, Fractals and Complexity
Average customer rating:
- good book
- Not a self contained book!
- Not for beginners
- Good introduction to level set methods
- This is The Introduction to Level-Set Method
|
Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (Cambridge ... on Applied and Computational Mathematics)
J. A. Sethian
Manufacturer: Cambridge University Press
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Level Set Methods and Dynamic Implicit Surfaces
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Numerical Geometry of Images: Theory, Algorithms, and Applications
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Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
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Handbook of Mathematical Models in Computer Vision
ASIN: 0521645573 |
Book Description
In this new edition of the successful book Level Set Methods, Professor Sethian incorporates the most recent advances in Fast Marching Methods, many of which appear here for the first time. Continuing the expository style of the first edition, this introductory volume presents cutting edge algorithms in these groundbreaking techniques and provides the reader with a wealth of application areas for further study. Fresh applications to computer-aided design and optimal control are explored and studies of computer vision, fluid mechanics, geometry, and semiconductor manufacture have been revised and updated. The text includes over thirty new chapters. It will be an invaluable reference for researchers and students.
Customer Reviews:
good book.......2006-03-15
Neither an introduction nor a recipe book for level sets. Contains dense information and requires supplemental material.
Not a self contained book!.......2003-10-12
I bought this book with the intent of understanding the level set method AND be able to implement it in code. The book fails on the later. He gives you some basic formulas/algorithms to start with, but they are not good enough for most problems. You need to get the references (and the references of those references) to obtain the actual algorithms people use to implement the level set method.
The first six chapters are good for giving you a nice qualitative understanding of the method and the issues of implementing the method. And the rest of the book claims to show you the more advanced techniques, but whenever the nitty gritty details are needed, he refers you to the references.
My advice: just get his references. If you are at a university, then you probably have free access to the online journals that contain his (and others) research articles. In fact, this book is basically a copy-paste of those articles! Literally!
Not for beginners.......2003-04-23
I am afraid that this book is not for beginners who want to have a clear mind of the level set method. You will have to go to the library quite often to dig out all the references the author mentioned. I would say this book is for experienced researchers only.
Good introduction to level set methods.......2001-06-07
I use these methods in the context of image analysis, for image segmentation essentially. The book is an inescapable introduction by one of the main inventors of these methods. It is easy to read and relatively complete. Be sure to get the second edition. The only slight problems are the remaining typos. There are quite a few, for a second edition, and they might throw off a beginner. You will need to read some introduction text on finite differences methods at least. The chapter in Numerical Recipes is enough.
This is The Introduction to Level-Set Method.......2000-04-27
This is a very good introduction to the very exciting technique, level-set method. The method is basically for front-tracking or interface motion. But its application turned out to be so wide that it is now applied to problems which does not seem relevant to front-tracking, such as computaional grid generation. This book explaines the basics of this powerful tool very clearly, and it is in fact easy to read. Although it was written by a mathematician, it is not very mathematical like some texts on finite-element method written by mathematicians (which are often formidable to engineers). I recommend this book to anyone in engineering. You might find a new application of this technique.
Average customer rating:
- Only great for complete novices
- Excellent teaching book
- One of the best books for CFD code developers
- I give it 5 stars
- A lot of excellent detail
|
Computational Methods for Fluid Dynamics
Joel H. Ferziger , and
Milovan Peric
Manufacturer: Springer
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An Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd Edition)
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Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics)
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Computational Fluid Dynamics
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Turbulent Flows
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Computational Fluid Dynamics
Accessories:
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Essentials of Mathematica: With Applications to Mathematics and Physics
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Basic Training in Mathematics: A Fitness Program for Science Students
ASIN: 3540420746 |
Book Description
In its 3rd revised and extended edition the book offers an overview of the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice. Included are advanced methods in computational fluid dynamics, like direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, free surface flows. The 3rd edition contains a new section dealing with grid quality and an extended description of discretization methods. The book shows common roots and basic principles for many different methods. The book also contains a great deal of practical advice for code developers and users; it is designed to be equally useful to beginners and experts.The issues of numerical accuracy, estimation and reduction of numerical errors are dealt with in detail, with many examples.
Customer Reviews:
Only great for complete novices.......2002-01-29
Peric's PhD thesis is one of my most precious possessions. I consider Ferziger to be one of THE greats in Large Eddy Simulation. So I had great hopes for this book. I was warned before I saw it that it contained nothing that I wouldn't already know, but even so it was a big disappointment. I could have written a better book myself and I don't have half the brain of either of the authors. I've looked at it three times and each time turned away in disgust.
This book will point a novice in the correct direction, unlike Roach's book, and unlike Patankar's in a post Rhie-Chow age, but it avoids like the plague any subject with even the slightest whiff of controversy. As any new technique is always controversial, the book was some 5 to 10 years out of date even before it hit the press. Further, it discusses each subject in a very superficial way. More depth is needed.
I want a book that will tell me what the advantages are and how to program the conjugate gradient method, algebraic multigrid, superbee, wall reflection terms for Reynolds Stress, multiphase flow, viscoelasticity, coalescence, the axis in cylindrical coordinates, grid generation, surface tension, adaptive grids, spectral elements etc. This book is no help with any of these.
I frequently get asked "What's a good book for Computational Fluid Dynamics?". I have to admit that there isn't one. The best that I know are the user manuals for the various commercial CFD packages.
To summarise, if programming CFD is a 100 step journey then this book will only take you the first 3 steps, but at least they're 3 steps in the right direction. After you've been programming CFD for a year you can probably toss the book out without any great loss.
Excellent teaching book.......2001-07-10
I found this book an excellent support in teaching and invaluable as an occasional reference in my practical work in industry. It is particularly gratifying to see that free surface flows are covered well. Best book I have seen so far in the field.
One of the best books for CFD code developers.......2001-05-24
This is the best book on CFD I' ve read. It is more useful to those who want to develop their own codes rather than CFD users: It mostly describes in deep detail (although in a concise manner) a single method used by the authors and developed by themselves and their colleagues. It is not intended to be a list of the vast number of CFD techniques developed so far.
Their method is state-of-the-art and they provide plenty of results to support it's quality. It is mostly directed towards incompressible flows. They provide a chapter that extends their method to compressible flows but they do not describe any special convection schemes for flows with shock waves. It can be applied to both structured and arbitrarily unstructured grids, although their approach to the discretization of the convection and diffusion terms is particularly useful in the case of arbitrarily unstrucured grids. State of the art subjects such as multigrid and error-driven grid refinement are also covered and integrated into their method.
I agree with a previous reviewer that they provide a very good coverage of solution methods for linear equation systems which arise in CFD. Most other books on CFD (all the ones that I have read) have a poor coverage of the subject and describe only old and inneficient methods. However even this book does not sufficiently describe conjugate-gradient type methods or Krylov subspace methods in general, but references are provided.
In conclusion, this book is not for beginners but for code developers who have some basic knowlwdge of CFD and a relatively good mathematical background.
I give it 5 stars.......2001-03-16
I agree with the reviewer that said this book is complimentary to an intro text such as Patankar. This is not a cook book for a first time coder. But it is a really great reference for the Finite Volume dilettante.
I really appreciate that all numerical results presented are thoroughly documented. That counts.
Really, really nice chapter on iterative solvers....
Good overall description on many other topics such as multi-grid methods, turbulence, grid geometry and PV coupling.
This book really helped me speed up my homegrown quite a bit.
They also have all kinds of stuff available by ftp....
A lot of excellent detail.......1998-12-22
This is a very good book for learning the details of implementing the Finite Volume method in Computational Fluid Dynamics. I view it as very complimentary to S. V. Patankar's book, which is more general in nature. Both books are geared toward people who want to write computer programs to solve fluid transport problems (heat transfer, Navier-Stokes, etc.) Both tend to focus on numerical issues (as opposed to the physics of transport phenomena). But while Pantankar's book provides a very easy, approachable introduction that is thin on the details, Ferziger & Peric have written a book rich in details. For instance, they devote an entire chapter to solving linear systems of equations. They compare all of the commonly used methods and contrast their rates of convergence for various test cases. This level of detail is great if you already understand the big picture. I think it may be somewhat difficult for someone new to CFD to really understand the finite volume method from this book alone. I would recommend Patankar's book for a good intro and this book for the implementation details.
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Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications
Manufacturer: Springer
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ASIN: 3540417958 |
Book Description
This book focusses on the state of the art of Monte Carlo methods in radiation physics and particle transport simulation and applications, the latter involving in particular, the use and development of electron--gamma, neutron--gamma and hadronic codes. Besides the basic theory and the methods employed, special attention is paid to algorithm development for modeling, and the analysis of experiments and measurements in a variety of fields ranging from particle to medical physics.
Average customer rating:
- SPAM and sph, a superior route to continuum solutions
|
Smooth Particle Applied Mechanics: The State of the Art (Advanced Series in Nonlinear Dynamics) (Advanced Series in Nonlinear Dynamics)
William G. Hoover
Manufacturer: World Scientific Publishing Company
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ASIN: 9812700021 |
Customer Reviews:
SPAM and sph, a superior route to continuum solutions.......2007-01-15
This excellent monograph, prepared by Professor Hoover with the help of his wife Carol, contains all that a reader needs to understand, develop, and use smooth-particle techniques for computer simulations of continua. Applications to solid deformation and to fluid flow display a variety of useful techniques for avoiding the usual pitfalls with standard sph.
Average customer rating:
|
An Introduction to the Mathematical Theory of Waves (Student Mathematical Library, V. 3)
Roger Knobel
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Wave Motion (Texts in Applied Mathematics, No. 24)
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Mathematics of Wave Propagation
ASIN: 0821820397 |
Book Description
This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques.
The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.
The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow.
Average customer rating:
- Deeply insightful and utterly fascinating
- The Classic Text on Asymptotics
- A Classic Resource
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Advanced Mathematical Methods for Scientists and Engineers: Asymptotic
Carl M. Bender , and
Steven A. Orszag
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
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Mathematics and its History
ASIN: 0387989315 |
Book Description
This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions; over 600 problems, of varying levels of difficulty; and an appendix summarizing the properties of special functions.
Customer Reviews:
Deeply insightful and utterly fascinating.......2006-12-20
I had the privilege to explore this guide to the universe of asymptotics under Prof. Bender. I used to think, and still do (about 2 decades on), that this book is like the Rosetta Stone, and enables us to solve anything in applied mathematics.
A must have for anyone looking to understand the incredible universe we find ourselves in!
The Classic Text on Asymptotics.......2005-12-09
I am a mathematics professor, and asymptotic methods is my area of expertise. Bender and Orszag was the standard text on this topic in the early 1980s, and it remains by far the most thorough book on the subject. I had two courses from it in graduate school and have taught from it 3 times now. I have never found a mistake. The book is very well written; its only weakness is that its graphics reflect the technology of the 1970s. Nevertheless, I am teaching from it again next year, because it is in a class by itself.
There is one thing that individual readers and faculty users should be aware of. Some of the exercises, including a few marked as "intermediate," are incredibly difficult. My instructor made the mistake of assigning exercises without working them first. I am careful not to assign any exercises until after I have worked them.
A Classic Resource.......2005-10-07
I'll echo the sentiments of the other reviewers here. I have a well-worn and well-used copy of the first (1978) edition. Believe it or not, I actually had a chance to use these methods as recently as last month (September 2005). I would recommend, though, if you want to get the most out of this book, pick up a symbolic calculation program or calculator capable of doing symbolic math. I use the open-source programs Maxima and Axiom for this, but if you want to actually spend money, Amazon has some calculators that will handle this sort of thing.
Extremely useful.......2003-12-13
Great for anyone taking Partial differential equations, mathematical physics, and the related courses. Carl Bender is a master of the field as well as a great book writer, as well as Orszag. The only complaint is the type setting--a bit too small. But not a big problem
Excellent.......2003-10-19
This is an essential textbook for all applied mathematicians, physicists and research oriented engineers. It is very well written, and explains an enormous lot. It explains it all very well too. I've used chapter 3 and 6 in class, and they were full of insights and information that you cannot find in any other textbook.
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