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E-raamat: Transport Processes in Macroscopically Disordered Media: From Mean Field Theory to Percolation

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 02-Sep-2016
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781441982919
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Transport Processes in Macroscopically Disordered Media: From Mean Field Theory to PercolationSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 02-Sep-2016
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781441982919
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Based on the authors’ research, this volume is an original take on the modern theory of inhomogeneous media. It shows the reader how to use component distribution data to find the effective properties of composites, and covers many other aspects of the topic.

Transport Processes in Macroscopically Disordered Media: From Mean Field Theory to Percolation reflects on recent advances in the understanding of percolation systems to present a wide range of transport phenomena in inhomogeneous disordered systems. Further developments in the theory of macroscopically inhomogeneous media are also addressed. These developments include galvano-electric, thermoelectric, elastic properties, 1/f noise and higher current momenta, Anderson localization, and harmonic generation in composites in the vicinity of the percolation threshold. The book describes how one can find effective characteristics, such as conductivity, dielectric permittivity, magnetic permeability, with knowledge of the distribution of different components constituting an inhomogeneous medium. Considered are a wide range of recent studies dedicated to the elucidation of physical properties of macroscopically disordered systems. This book contains a straightforward set of useful tools which will allow the reader to derive the basic physical properties of complicated systems together with their corresponding qualitative characteristics and functional dependencies.
Part I Methods
1 Introduction
3(4)
1.1 Types of Macroscopically Disordered Media
3(2)
1.2 Classification of Physical Properties. Physical Analogies
5(2)
References
6(1)
2 The Methods of Description of Random Media
7(8)
2.1 Effective Kinetic Coefficients, or What Do We Measure
7(4)
2.2 Correlation Length and Self-averaging
11(4)
References
12(3)
3 Effective Conductivity of Macroscopically Disordered Media
15(26)
3.1 Double-Sided Estimates of the Effective Kinetic Coefficients
15(3)
3.2 Approximations of Maxwell, Garnett, and Bruggeman
18(10)
3.3 Periodically Located Inclusions
28(5)
3.4 Plain-Layered Systems
33(8)
References
38(3)
4 Elements of Geometrical Theory of Percolation
41(6)
4.1 Percolation Problem
41(2)
4.2 Basic Concepts of Geometric Percolation
43(4)
References
45(2)
5 Effective Conductivity of Percolation Media
47(30)
5.1 Analogy with the Phenomenological Theory of Second-Order Phase Transitions. Scaling and Critical Exponents
47(4)
5.2 Effective Conductivity as an Order Parameter. Phenomenological Description
51(5)
5.3 Calculation of Critical Indices
56(7)
5.4 Hierarchical Model of Percolation Structure
63(9)
5.5 Examples of Applications of Percolation Theory
72(5)
References
73(4)
6 Self-dual Media
77(18)
6.1 Locally Isotropic Media
77(9)
6.2 Locally Anisotropic Media
86(9)
References
93(2)
7 Continual Percolation Problem
95(8)
7.1 Types of Continual Percolation Problems
95(2)
7.2 Swiss Cheese Media
97(6)
References
101(2)
8 Media with Exponentially Broad Spectrum of Local Properties
103(10)
8.1 Formulation of the Problem and Approximate Calculation of the Effective Conductivity
103(2)
8.2 Correlation Length and Pre-exponential Factor
105(8)
References
110(3)
9 Finite Scaling
113(10)
9.1 Properties of Percolation Systems with Dimensions Lesser Than Their Correlation Length
113(6)
9.2 Finite-Size Scaling for Self-dual Media
119(4)
References
122(1)
10 Conductivity of Percolation Layer
123(8)
10.1 Effective Conductivity of the Percolation Systems in the Cases with Some Sizes Are Lesser and the Other Greater Than Percolation Length. Definition of the Problem
123(2)
10.2 Solution Technique
125(6)
References
128(3)
Part II Processes
11 AC Conductivity
131(10)
11.1 EMT-Approximation
131(2)
11.2 The Method of Percolation Theory
133(8)
References
139(2)
12 Galvanomagnetic Properties of Macroscopically Disordered Media
141(20)
12.1 Introduction
141(3)
12.2 Layered Media in the Magnetic Field
144(1)
12.3 Dual Media in the Magnetic Field
145(3)
12.4 Strongly Inhomogeneous Media in the Vicinity of the Percolation Threshold, Two-Dimensional Case
148(6)
12.5 Strong Disorder, Three-Dimensional Case
154(7)
References
158(3)
13 Flicker-Noise (1/f-Noise)
161(20)
13.1 Flicker-Noise in Inhomogeneous Media
161(3)
13.2 Flicker-Noise in Inhomogeneous Media---EMT-Approximation
164(1)
13.3 Flicker-Noise in Percolation Systems
165(5)
13.4 Abnormally High Rate of Flicker-Noise in Self-dual Media
170(2)
13.5 Flicker-Noise in the Systems with Exponentially Broad Spectrum of the Resistances
172(5)
13.6 Flicker-Noise for Fluctuation of Phase Concentration
177(4)
References
178(3)
14 Higher Current Moments
181(8)
14.1 Definitions
181(1)
14.2 Critical Exponents of the Higher Current Moments
182(7)
References
186(3)
15 Thermoelectric Properties
189(18)
15.1 EMT-Approximation
189(3)
15.2 Thermoelectric Properties of the Self-dual Media
192(3)
15.3 Critical Region of Concentration---Behavior of αe in the Vicinity of Percolation
195(3)
15.4 Isomorphism
198(9)
References
204(3)
16 Effective Elastic Properties
207(12)
16.1 Basic Concepts of Elasticity Theory
207(2)
16.2 Effective Module in the Vicinity of Percolation Threshold
209(10)
References
216(3)
17 Nonlinear Properties of Composites
219(20)
17.1 Types of Nonlinearity
219(1)
17.2 The Case of Weak Nonlinearity
220(6)
17.3 The Case of Strong Nonlinearity
226(13)
References
236(3)
18 Effective Properties of Ferromagnetic Composites
239(8)
18.1 Nonlinearity and Hysteresis in Ferromagnets
239(1)
18.2 Hysteresis-Less Case
240(2)
18.3 Ferromagnetic Composites with a Nonzero Hysteresis Loop
242(5)
References
245(2)
19 Temperature Coefficient of Resistance and Third Harmonic Generation Close to Percolation Threshold
247(6)
19.1 Temperature Coefficient of Resistance
247(1)
19.2 Third Harmonic Generation
248(5)
References
251(2)
20 Instability and Chaos in the Macroscopically Inhomogeneous Media with Weak Dissipation
253(12)
20.1 Dual Media
253(6)
20.2 Ladder Filter
259(6)
References
263(2)
21 Percolation-Similar Description of Abrikosov Vortex
265(10)
21.1 The Pinning of the Abrikosov Vortexes
266(1)
21.2 The Case of the Wide Pinning Force Distribution
267(8)
References
272(3)
22 Anderson Localization in the Percolation Structure
275(4)
22.1 Anderson Localization
275(1)
22.2 Anderson Metal-Insulator Transition in Percolation Structure
276(3)
References
278(1)
23 Conclusion
279
References
280
Professor Andrew Snarskii obtained his physics undergraduate and Master Science degrees from Chernivtsi State University in 1972. In 1976 he received PhD also from Chernivtsi State University. He received degree of doctor of science (habilitation degree) from Kiev Institute of Physics in 1991. His fields of research include thermoelectricity, physical processes in percolation structures, deterministic chaos, fractals, theory of complex networks. Now he is a full tenured Professor of Kiev Polytechnic University.





Dr. Igor V. Bezsudnov graduated from Moscow Institute of Electronics and Mathematics in 1985. Since then he always worked in research and development departments of different companies. In 2012 he received Ph.D in physics from Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine. His fields of research include the behaviour of inhomogeneous media near the percolation threshold, phenomenon of self-organized criticality, thermoelectric properties of disordered media, computer numerical modelling of complex media. Now his affiliation is vice director of NPP Nauka-Service, Moscow, chef of R&D.

Mr. Vladimir A. Sevryukov graduated from Bauman Moscow State Technical University in 1983. His work has always been connected with the development and application of advanced technologies and scientific achievements. Fields of research and interest includes percolation systems and their transport properties, computer modelling of highly disordered media. Currently he is the director of NPP Nauka-Service,Moscow.





Dr. Alexander Morozovskiy graduated from Kiev Polytechnic University in 1982. He worked as researcher in Kiev Institute of Metal Physics. He received his PhD from Kiev Institute of Metal Physics in 1988. His area of research includes theory of percolation, superconductivity, market microstructure, credit risk, econophysics. Currently he is working at Citibank.





Professor Joseph Malinsky obtained his physics undergraduate and (advanced) Master of Science degrees from Kiev State University in 1973. In 1985 he has received Ph.D in physics from the Graduate Center of CUNY under the supervision of Professor Joseph L.Birman. His fields of research include areas of Condensed Matter Physics, Biophysics, Mathematical Biology etc. His affiliations include CCNY, BCC, Graduate Center of City University of NY (physics program), Mount Sinai Medical School (Departments of Biophysics and Biomathematics). Now he is a full tenured Professor.
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