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The Fokker-Planck Equation: Methods of Solution and Applications (Springer Series in Synergetics) (英語) ペーパーバック – 2013/10/4


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内容紹介

This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.


登録情報

  • ペーパーバック: 488ページ
  • 出版社: Springer; 2nd ed. 1996版 (1996/10)
  • 言語: 英語
  • ISBN-10: 354061530X
  • ISBN-13: 978-3540615309
  • 発売日: 2013/10/4
  • 商品パッケージの寸法: 17 x 2.8 x 24.2 cm
  • おすすめ度: この商品の最初のレビューを書き込んでください。
  • Amazon 売れ筋ランキング: 洋書 - 63,419位 (洋書の売れ筋ランキングを見る)
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7 人中、6人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち 2.0 Outrageous printing quality - I have been scammed - avoid it 2012/9/11
投稿者 J. R. G. Mendonca - (Amazon.com)
形式: ペーパーバック Amazonで購入
The book contents is OK. It is a classic reference in the field of stochastic processes and SDEs for natural scientists (engineers and financiers may find other titles more appealing), and it generally pays to have the title at hand.

The caveat in this review is the following: the printing and binding quality of the book being sold really suck. I mean, really. It comes with flimsy covers (of magazine-like quality) filmed with chep plastic that is going to detach soon, and the binding will crack for sure as the book starts to get used.

This Chinese quality standard comes from the fact that this kind of book is not printed in the usual sense anymore. It is produced "on demand:" when a customer orders it, it is printed (it seems that on a regular, $99 deskjet printer) and then bound by Amazon (by a third-party, of course) on agreement with Springer.

More and more, after having been scammed a few times by now (see my other review on Ma's "Statistical Mechanics" book), I will not buy technical books on paperback on Amazon anymore (except by Dover).
16 人中、15人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち 4.0 A good book on a difficult subject. 2004/3/15
投稿者 Ariel Gordon - (Amazon.com)
形式: ペーパーバック
I got the impression that there are very few good textbooks on the subject of random processes in continuous time and the Fokker-Planck equation, which are accessible for physicists. In this book the subject presented in a manner that I thought to be a good compromise between mathematical rigor and physical intuition. For example to the spirit of the book, white noise is introduced both from the point of view of a physicist (it has a very short correlation time etc) and from the point of view of a mathematician (as the "derivative" of a Wiener process). While I found the book not very friendly or easy to read, it was one of my main sources for self-learning this subject during my Ph. D. work. I found the book three years ago, own it for two years and keep learning from it until today. I recommend the book very much.
8 人中、7人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち 4.0 Rigorous book 2006/12/28
投稿者 Peyman Khorsand - (Amazon.com)
形式: ペーパーバック
This book is a classical reference in the subject of stochastic dynamics. It is a graduate level book written in clear and concise language. It covers all the basics about Langevin and Fokker-Planck equations (Chapters 3 and 4). In these chapters, Moyal expansion, Ito and Stratonovich interpretation of stochastic processes is presented carefully. Then they move on to study various methods of solving FP equation in the next 7 chapters. In the final chapter, FP equation and its application to Laser is discussed.

I recommend reading this book along with Gardiner's book (Handbook of Stochastic Methods) to anyone who wants to learn about stochastic dynamics seriously.
18 人中、5人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち 1.0 When a "Simple Laser Model" becomes too simple ... 2009/12/26
投稿者 Luitjens Popken - (Amazon.com)
形式: ペーパーバック
This book with Chapt. 12 on Statistical Properties of Laser Light is an example where the wish for general schemes creates selfmomentum that defeats the objective to describe real physics. The difficulties become serious when authors engage deeply in mathematical tools, here the Fokker-Planck equation, and impose methods onto systems for convenience, or to demonstrate an application - while compromising much on actual physics and the foundations. As a consequence, the missing integrity leaves readers behind in big uncertainty if obtained (formal) results represent, or do no longer represent (laser) physics.

The approach in the book to "treat the electrical field classically, i.e., neglect its operator character[istic], provided that a proper classical noise source is added [with a] strength ... so that it leads to the correct spontaneous emission rate" remains an ad hoc attempt ("semiclassical") without systematic investigation of the involved approximations and their validity that depends upon the scope of the intended laser investigation. A test for evidence would have been to indicate how higher approximations should be obtained and how they affect the results obtained from the "simple laser model".

Chapt. 12 starts from macroscopic considerations, i.e., an equation for the (complex) amplitude "b" of the field: db/dt = beta*d*b - beta*|b|^2 * b (on the right side the first and second parts represent the pumping and (nonlinear) collision effects, respectively). To introduce fluctuations of the field, a formal Langevin term n(t) is then added heuristically, which implies the "simple laser model". However, the delta-correlated Gaussian noise n(t) does not represent the real interactions; there is no true justification for simply adding this term. Finding a correct description of laser fluctuations requires studying the real physical mechanisms. One important source is the fluctuation in the pumping light itself. Therefore, the associated term ("beta*d") represents actually a random fluctuation. Consequently, we face a problem and a stochastic differential equation very much different from the artificial application of the Langevin equation, or the equivalent Fokker-Planck equation. Regrettably, the book does not attempt corresponding answers although crucial for integrity that would be a responsibility of the author, not the reader.

The book is not reader-friendly due to its difficult style of writing, apparently without a professional editing for clarity through better grammar. - The list of References is shockingly outdated (w/o exception all entries are older than 20 years). Note, the shown year of publication (1996) refers to a re-print, not to any revision of the 2nd edition which had been published years before, in 1989. It is very misleading, when the Synopsis to this book claims: "A supplement is included, containing a short review of new [!] material together with some recent [!] references."
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