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E-raamat: Primer on Complex Systems: With Applications to Astrophysical and Laboratory Plasmas

  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Physics 943
  • Ilmumisaeg: 08-Mar-2018
  • Kirjastus: Springer
  • Keel: eng
  • ISBN-13: 9789402412291
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  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Physics 943
  • Ilmumisaeg: 08-Mar-2018
  • Kirjastus: Springer
  • Keel: eng
  • ISBN-13: 9789402412291

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The purpose of this book is to illustrate the fundamental concepts of complexity and complex behavior and the best methods to characterize this behavior by means of their applications to some current research topics from within the fields of fusion, earth and solar plasmas. In this sense, it is a departure from the many books already available that discuss general features of complexity.

The book is divided in two parts. In the first part the most important properties and features of complex systems are introduced, discussed and illustrated. The second part discusses several instances of possible complex phenomena in magnetized plasmas and some of the analysis tools that were introduced in the first part are used to characterize the dynamics in these systems. A list of problems is proposed at the end of each chapter.

This book is intended for graduate and post-graduate students with a solid college background in mathematics and classical physics, who intend to work in the field of plasma physics and, in particular, plasma turbulence. It will also be of interest to senior scientists who have so far approached these systems and problems from a different perspective and want a new fresh angle.

Part I Characterization of Complex Systems
1 Primer on Complex Systems
3(38)
1.1 Introduction
3(9)
1.1.1 What Is a Complex System?
3(2)
1.1.2 Examples of Complex Systems
5(2)
1.1.3 Complex Systems in Plasma Science
7(3)
1.1.4 Complexity Science
10(2)
1.2 Key Concepts in the Study of Complex Systems
12(13)
1.2.1 Defining Characteristics
13(1)
1.2.2 Basic Ingredients
14(7)
1.2.3 Main Emergent Features
21(4)
1.3 Self-organized Criticality
25(9)
1.3.1 The Running Sandpile
26(2)
1.3.2 Criticality in the SOC State
28(2)
1.3.3 Memory in the SOC State
30(2)
1.3.4 Transport in the SOC State
32(2)
1.4 Overview of the First Part of This Book
34(1)
Appendix 1 Fixed Points of a Dynamical System
35(1)
Problems
36(1)
References
37(4)
2 Statistics
41(62)
2.1 Introduction
41(1)
2.2 The Probability Density Function
42(9)
2.2.1 Definition
42(1)
2.2.2 Cumulative Distribution Function
43(1)
2.2.3 Survival Function
44(1)
2.2.4 Characteristic Function
45(2)
2.2.5 Expected Values
47(1)
2.2.6 Moments
47(1)
2.2.7 Cumulants
48(3)
2.3 Significance of Specific Pdfs
51(19)
2.3.1 Gaussian and Levy Pdfs: Additive Processes
52(5)
2.3.2 Log-Normal and Log-Stable Pdfs: Multiplicative Processes
57(4)
2.3.3 Weibull, Gumbel and Frechet Pdfs: Extreme Value Pdfs
61(3)
2.3.4 Exponential and Related Pdfs: Poisson Processes
64(6)
2.4 Techniques for the Practical Estimation of Pdfs
70(11)
2.4.1 Constant Bin Size Method
71(2)
2.4.2 Constant Bin Content Method
73(5)
2.4.3 Survival/Cumulative Distribution Function Method
78(3)
2.5 Techniques to Compare Experimentally Obtained Pdfs with Analytical Forms
81(9)
2.5.1 Maximum Likelihood Estimators
81(4)
2.5.2 Pearson's Goodness-of-Fit Test
85(4)
2.5.3 Minimum Chi-Square Parameter Estimation
89(1)
2.6 Case Study: The Running Sandpile
90(4)
2.7 Final Considerations
94(1)
Appendix 1 The Fourier Transform
94(3)
Appendix 2 Numerical Generation of Series with Prescribed Statistics
97(2)
Problems
99(2)
References
101(2)
3 Scale Invariance
103(74)
3.1 Introduction
103(3)
3.2 Scale-Invariance in Space
106(14)
3.2.1 Fractals
107(4)
3.2.2 Multifractals
111(9)
3.3 Scale-Invariance in Time
120(25)
3.3.1 Self-Similar Time Random Processes
121(1)
3.3.2 Propagator of a Random Process
122(8)
3.3.3 Fractional Brownian Motion
130(3)
3.3.4 Fractional Levy Motion
133(2)
3.3.5 Stationarity and Self-Similarity
135(3)
3.3.6 Self-Similar Processes with Stationary Increments
138(2)
3.3.7 Multifractal Time Random Processes
140(5)
3.4 Techniques for the Practical Determination of Scale-Invariance
145(17)
3.4.1 Analysis of Non-stationary Processes
146(4)
3.4.2 Analysis of Stationary Processes
150(6)
3.4.3 Multifractal Analysis
156(6)
3.5 Case Study: The Running Sandpile
162(5)
3.6 Final Considerations
167(1)
Appendix 1 Numerical Generation of Fractional Noises
167(2)
Appendix 2 Detrended Fluctuation Analysis
169(2)
Appendix 3 Multifractal Analysis via Wavelets
171(1)
Problems
172(1)
References
173(4)
4 Memory
177(44)
4.1 Introduction
177(1)
4.2 Memory and Correlation
178(17)
4.2.1 The Autocorrelation Function
178(10)
4.2.2 The Power Spectrum
188(5)
4.2.3 The Autodifference Function
193(2)
4.3 Memory in Self-Similar Time Random Processes
195(3)
4.3.1 Fractional Brownian Motion
195(1)
4.3.2 Fractional Levy Motion
196(2)
4.4 Techniques for Detecting Memory in Stationary Time Series
198(15)
4.4.1 Methods Based on the Autocorrelation Function
199(1)
4.4.2 Methods Based on the Power Spectrum
200(2)
4.4.3 Methods Based on the Autodifference
202(1)
4.4.4 Hurst's Rescaled Range (R/S) Method
203(9)
4.4.5 Waiting Time Statistics
212(1)
4.5 Case Study: The Running Sandpile
213(5)
4.6 Final Considerations
218(1)
Problems
218(1)
References
219(2)
5 Fundamentals of Fractional Transport
221(58)
5.1 Introduction
221(2)
5.2 Diffusive Transport: Fundamentals
223(11)
5.2.1 The Continuous-Time Random Walk
223(7)
5.2.2 The Langevin Equation
230(4)
5.3 Scale Invariant Formulations of Transport
234(13)
5.3.1 Scale Invariant Continuous-Time Random Walks
234(7)
5.3.2 The Fractional Langevin Equation
241(2)
5.3.3 The Fractional Transport Equation
243(4)
5.4 Techniques for the Characterization of Fractional Transport
247(8)
5.4.1 Eulerian Methods
247(5)
5.4.2 Lagrangian Methods
252(3)
5.5 Case Study: The Running Sandpile
255(6)
5.5.1 fTe for the Directed Running Sandpile
260(1)
5.6 Final Considerations
261(3)
Appendix 1 The Laplace Transform
264(1)
Appendix 2 Riemann-Liouville Fractional Derivatives and Integrals
265(4)
Appendix 3 The Riesz-Feller Fractional Derivative
269(1)
Appendix 4 Discrete Approximations for Fractional Derivatives
270(3)
Problems
273(1)
References
274(5)
Part II Complex Dynamics in Magnetized Plasmas
6 Laboratory Fusion Plasmas: Dynamics of Near-Marginal Turbulent Radial Transport
279(34)
6.1 Introduction
279(1)
6.2 Nuclear Fusion Processes
280(4)
6.3 Primer on Magnetic Confinement Fusion
284(7)
6.3.1 Tokamaks
285(2)
6.3.2 Stellarators
287(1)
6.3.3 Main Transport Processes in Toroidal MCF Plasmas
288(3)
6.4 Are MCF Plasmas Complex Systems?
291(8)
6.4.1 Tokamak Transport Phenomenology
292(3)
6.4.2 Stellarator Confinement Phenomenology
295(1)
6.4.3 Self-organized Criticality and Toroidal MCF Plasmas
296(3)
6.5 Case Study: Analysis of Turbulent Fluctuations from the Edge of the W7-AS Stellarator
299(9)
6.5.1 Statistics
300(3)
6.5.2 Power Spectrum
303(1)
6.5.3 R/S Analysis
304(2)
6.5.4 Multifractal Analysis
306(2)
6.6 Conclusions
308(1)
References
309(4)
7 Space Plasmas: Complex Dynamics of the Active Sun
313(26)
7.1 Introduction
313(1)
7.2 Our Own Star: The Sun
313(6)
7.2.1 Structure of the Sun
314(3)
7.2.2 The Active Magnetic Sun
317(2)
7.3 Is Our Sun a Complex System?
319(5)
7.3.1 The Tachocline: A Case of Self-Organization
320(1)
7.3.2 Scale-Invariance of Solar Flare Data
321(1)
7.3.3 Lu-Hamilton SOC Flaring Model
322(2)
7.4 Case Study: Analysis of the SOHO-LASCO CME Database (1996--2016)
324(11)
7.4.1 Waiting-Time Statistics
326(1)
7.4.2 Linear Speed Analysis
326(3)
7.4.3 Ejected Mass Analysis
329(4)
7.4.4 Ejected Energy Analysis
333(2)
7.5 Conclusions
335(1)
References
335(4)
8 Planetary Plasmas: Complex Dynamics in the Magnetosphere of the Earth
339(42)
8.1 Introduction
339(1)
8.2 The Magnetosphere of the Earth
340(12)
8.2.1 The Geomagnetic Field
341(1)
8.2.2 Structure of the Magnetosphere of the Earth
342(5)
8.2.3 Dynamics of the Magnetosphere of the Earth
347(5)
8.3 Is the Magnetosphere of the Earth a Complex System?
352(4)
8.3.1 Chang's SOC Substorming Model
353(3)
8.3.2 Evidence of Critical Dynamics in the Magnetotail
356(1)
8.4 Case Study: Magnetospheric and Solar Wind Indices
356(22)
8.4.1 Analysis of the Dst Index (1957--2008)
357(6)
8.4.2 Analysis of the AE Index (1990--2008)
363(6)
8.4.3 Analysis of the Scalar Bin the Solar Wind (1963--2017)
369(5)
8.4.4 Analysis of the Proton Density in the Solar Wind (1963--2017)
374(4)
8.5 Conclusions
378(1)
References
378(3)
9 Laboratory Plasmas: Dynamics of Transport Across Sheared Flows
381(20)
9.1 Introduction
381(1)
9.2 Stable Sheared Flows
382(6)
9.2.1 Differential Rotation and Magnetic Fields
383(1)
9.2.2 Turbulence Suppression by Sheared Flows
384(2)
9.2.3 Zonal Flows in Tokamaks
386(2)
9.3 Non-diffusive Transport Across Sheared Flows
388(3)
9.4 Case Study: Transport Across Self-Consistent Zonal Flows in Ion-Temperature-Gradient (ITG) Tokamak Turbulence
391(8)
9.4.1 Radial Propagator Analysis
395(2)
9.4.2 Other Considerations
397(2)
9.5 Conclusions
399(1)
References
399(2)
Index 401
Raul Sanchez is a full professor of Physics at the Universidad Carlos III de Madrid, SPAIN. He served as Vice-chancellor for Undergraduate Studies of this university from 2011 to 2015. Previously, he spent almost a decade at the Fusion Energy Division of the Oak Ridge National Laboratory (Tennessee, USA), first as a post-doctoral fellow (1998-99) and later as a senior staff scientist (2005-2011). During his more than twenty five years in research, he has authored more than a hundred refereed publications in the fields of nuclear fusion, plasma physics, turbulence, computational physics and complex systems. He was the recipient of the Spanish Miguel Catalán Science Award in 2009 for scientists younger than forty.

David Newman is a full professor of Physics at the University of Alaska at Fairbanks, and the Director of the Center for Complex Studies there. He held the prestigious Eugene Wigner Fellowship at the Fusion Energy Division of the Oak Ridge National Laboratory (Tennessee, USA), where he was a staff scientist from 1993 to1998. During his more than thirty years in research, he has authored more than 150 publications in peer-reviewed journals in the fields of complex systems, turbulence, plasma physics, nuclear fusion and electric power networks. He was the recipient of the US Presidential Early Career Award for Scientists and Engineers and the US Department of Energy Young Scientist Award in 1997. He was selected as a Fellow of the American Physical Society in 2011.