Customer Reviews

Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools (Springer Series in Synergetics)

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As I am teaching the statistical mechanics part of a graduate class in mathematics,I was looking for a textbook on complex systems & statistical physics with derivations, intuitions, and some physical examples. I did not realize that I was looking too far --Sornette, with hom I correspond regularly, is well known for his contributions and his prolific output (actually some physicists make fun of the quantity of papers he writes). So his book did not come to mind. I once stumbled on a problem with the derivation of preferential attachments;he recommended his book, which I took with a grain a salt. After spending some time working the derivations on scalable laws, extreme value theory, renormalization groups in this book, I elected to use it as my textbook. There is no equivalent. I have a dozen such yellow manuals; this one is complete and ultimately clearest.
I do not know of a better textbook.

Sornette's book is quite an achievement both in quantity and
quality. The presentation remains informal and quite readable; it reads like a physics textbook, not a math textbook. The references are very extensive (a total of 832! altogether) and they are a very valuable component of the book. In fact much of the book is about the reference material. You might choose to read the book instead of the 832 references... I think this is
the point...

There's probably nothing wrong with this book besides the fact that it throws it all at you at a high degree of sophistication and in as terse a way as possible, it seems. It's a unique and beautiful achievement but because it is so dense with information and insight, it seems every word counts for ten and you'll want to read several chapters again and again. Also, even though there is a clear unifying theme from chapter to chapter, the book simply ends almost like in the middle of a sentence. After machinegunning out 392 pages of material at research level spanning quite a few scientific fields, there is absolutely no attempt to put it all together. It's up to you to do it and it almost seems like the author is indirectly suggesting you start reading it all over again to "get it"... So, for the second edition, perhaps the author will be bold and add ten pages of wrap up material at the end so that this will read less like an atlas. Apart from that, it's the best!

Didier Sornette who is potentialy nobelisable realises with this book a great present for everybody interested to the recent progresses toward the physics of critical phenomena.
Particularly, it shows the way that some seismologists follow toward the ultimate goal to predict the event of large earthquakes. If this task was impossible yesterday,Didier Sornette shows that it is now became realisable.

This book describes many mathematical techniques used to study complex systems and numerous applications. These techniques include random walks, large deviations, fractals, power laws and renormalization. A strength of the book is relating these techniques to each other and applications in several fields. The book assumes readers are comfortable with calculus and statistics. It thus complements introductory books such as Complexity: A Guided Tour and how nature works: the science of self-organized criticality.

The book includes an extensive bibliography, and provides a unifying survey of these references. Unfortunately, the index is skimpy making it difficult to quickly find particular topics when using the book as a reference. E.g., the discussions of 'coherent noise', 'finite-size scaling' an 'highly optimized tolerance' are not mentioned in the index. The text has numerous typos that would easily be found by a spell checker, giving the impression there may also be more substantive errors.