Natures Patterns and the Fractional Calculus (häftad)
Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
213
Utgivningsdatum
2017-09-11
Förlag
De Gruyter
Illustratör/Fotograf
48 Schwarz-Weiß-und 8 farbige Abbildungen
Illustrationer
8 Illustrations, color; 48 Illustrations, black and white
Dimensioner
244 x 170 x 13 mm
Vikt
540 g
Antal komponenter
1
Komponenter
1469:Standard Color 6.69 x 9.61 in or 244 x 170 mm (Pinched Crown) Case Laminate on White w/Matte La
ISBN
9783110534115

Natures Patterns and the Fractional Calculus

Inbunden,  Engelska, 2017-09-11
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Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a systems functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a systems information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus
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Fler böcker av Bruce J West

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Bruce J. West, US Army Research Office, Cary, US

Innehållsförteckning

Table of Content: Chapter 1: Complexity Science 1.1 It started with physics 1.2 Complexity 1.3 Measures of size 1.4 Allometry heuristics 1.5 Overview Chapter 2: Empirical Allometry 2.1 Living networks 2.2 Physical networks 2.3 Natural history 2.4 Sociology 2.5 Summary Chapter 3 Statistics, Scaling and Simulation 3.1 Interpreting fluctuations 3.2 Phenomenological distributions 3.3 Are ARs universal? 3.4 Summary Chapter 4: Models & Derivations of ARs 4.1 Optimization principles 4.2 Scaling and allometry 4.3 Stochastic differential equations 4.4 Fokker-Planck equations 4.5 Summary Chapter 5: Complex and Strange Kinetics 5.1 Fractional thinking 5.2 Fractional rate equations 5.3 Fractional Poisson process 5.4 A closer look at complexity 5.5 Recapitulation 5.6 Appendix Chapter 6: Fractional Probability Calculus 6.1 Fractional Fokker-Planck equation 6.2 Fully fractional phase space equations 6.3 Entropy entails allometry 6.4 Statistics of allometry parameters 6.5 Discussion and conclusions 6.6 Epilogue