By Rainer Klages, Günter Radons, Igor M. Sokolov
This multi-author reference paintings offers a different creation to the at present rising, hugely interdisciplinary box of these shipping strategies that can't be defined through the use of common equipment of statistical mechanics. It comprehensively summarizes themes starting from mathematical foundations of anomalous dynamics to the latest experiments during this box. In so doing, this monograph extracts and emphasizes universal ideas and strategies from many alternative disciplines whereas delivering up to date insurance of this new box of analysis, contemplating such different purposes as plasma physics, glassy fabric, mobilephone technological know-how, and socio-economic elements. The booklet should be of curiosity to either theorists and experimentalists in nonlinear dynamics, statistical physics and stochastic tactics. It additionally types an excellent start line for graduate scholars entering into this region. 18 chapters written through across the world famous specialists during this box supply in-depth introductions to basic facets of anomalous shipping.
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Extra info for Anomalous Transport: Foundations and Applications (Wiley 2008)
6) instead of Eq. 5) as an equally “natural” starting point (this was later done by Liouville in [76, p. 3, eq. 7) k for functions represented as exponential series f ( x ) ∼ ∑k ck exp(λk x ). 8) 0 as a sum of exponentials, Liouville [76, p. 7] then applied Eq. 1 Historical Introduction to Fractional Derivatives where the last equality follows by substituting yx = z in the integral. 10) a formula similar to, but not exactly equal to Eq. 5). Although Eq. 10) agrees with Eq. 5) for integer α it differs for noninteger α.
I became convinced (for the ﬁrst time) of the usefulness of fractional calculus. All the papers I read previously about the subject left me with an impression of a heavy and untransparent formalism, which did not give me an impetus for further study. ” Over the next few months Radu became increasingly interested in the fractional diffusion approach to plasma turbulence, and we had the opportunity to discuss the topic in considerable detail. During this time, I was thankful to Radu’s kindness, enthusiasm, and support.
P. J. Sigmar, “Neoclassical transport of impurities in tokamak plasmas”, Nucl. Fusion 21, 1079 (1981). 12 B. Ph. van Milligen, R. A. Carreras, “Probabilistic ﬁnite-size transport models for fusion: anomalous transport and scaling laws”, Phys. Plasmas 11, 2272 (2004). 13 R. Balescu, “Anomalous transport in turbulent plasmas and continuous time random walks”, Phys. Rev. E 51, 4807 (1995). 14 R. Balescu, Aspects of Anomalous Transport in Plasmas (IOP, Bristol, 2005). Part I Fractional Calculus and Stochastic Theory 15 Introduction to Part I The opening Part I of this book is devoted to Fractional calculus and stochastic theory.