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

ISBN-13: 9781493979295 / Angielski / Miękka / 2018 / 280 str.

Andrei A. Snarskii; Igor V. Bezsudnov; Vladimir A. Sevryukov

Opis

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.

Spis treści

Introduction.

Part I.

1 Introduction. 1 Types of macroscopically disordered media. 2 Classification of physical properties. Physical analogies.

2 The methods of description of the macroscopically disordered media. 1 Effective kinetic coefficients, or what do we measure. 2 Correlation length and self averaging.

3 Effective conductivity of macroscopically disordered systems. 1 Double sided estimates of effective kinetic coefficients. 2 Approximations of Maxwell, Garnet and Bruggeman. 3 Periodically located inclusions. 4 Plain-layered systems.

4 Elements of geometrical theory of percolation. 1 Percolation problem. 2 Basic foundations of geometric percolation.

5 Effective conductivity in geometrical percolation theory. 1 Analogy with phenomenological theory of second order phase transition. Scaling and critical exponents.  2 Effective conductivity as an order parameter. Phenomenological description.  3 Calculation of critical indices. 4 Hyerarchical model of percolational structure. 5 Examples of applications of percolation theory.

6 Selfdual media. 1 Locally isotropic media. 2 Locally anisotropic media.

7 Continual percolation problem.  1 Types of continual percolation problems. 2 Media of  Swiss-Cheese models.

8 The systems with exponentially broad spectrum of local properties. 1 Set up of the problem and approximate calculation of effective. 2 Correlation length and pre-exponential factor.

9 Finite scaling. 1 Properties of the percolation systems with dimensions lesser than their correlation length. 2 Finite-size scaling for self-dual media.

10 Conductivity of percolation layer. 1 Effective conductivity of the percolation systems in the cases when some sizes are lesser and the other are greater than correlation length. Definition of the problem. 2 Solution technique.

Part II.

11 AC conductivity. 1 ЕМТ-approximation. 2 The method of percolation theory.

12 Galvano-magnetic properties of macroscopically disordered media.  1 Introduction. 2Layered medium in the magnetic field. 3 Dual media in the magnetic field. 4.Strongly inhomogeneous media in vicinity of the threshold of percolation, two-dimensional case. 5 Strong disorder, 3-dimensional case.

13 Flicker noise (1/f-noise). 1 Flicker-noise in inhomogeneous media. 2 Flicker-noise in inhomogeneous media- EMT approximation. 3 Flicker-noise in percolation systems. 4 Anomalously high rate of flicker- noise in percolation systems. 5 Flicker-noise in exponentially broad spectrum of the resistors.

14 Higher current moments. 1. Definitions. 2 Critical exponents of the higher current moments.

15 Thermoelectric properties. 1 ЕМТ-approximation. 2 Thermo-electric properties of the self-dual media.  3 Critical range of number density– behavior of  in the vicinity of percolation. 4 Isomorphism.

16 Effective elastic properties. 1 Basic notions of Elasticity Theory. 2 Effective modulae in the vicinity of percolation threshold.

17 Non-linear properties of composites. 1 Types of non-linearity. 2 The case of weak non-linearity. 3 The case of strong non-linearity.

18 Effective properties of ferromagnetic composites. 1 Non-linearity and hysteresis in ferromagnets.  2 Hysteresis-less case. 3 Ferromagnetic composites with a non-zero hysteresis loop.

19 Temperature coefficient of resistance and the third harmonic generation in the vicinity of the percolation. 1 Themperature coefficient of resistance. 2 The third harmonic generation.

20 Instability and chaos in the macroscopically disordered media with weak dissipation. 1 Dual media. 2 Ladder filter.

21 Percolation-like description of the Abrikosov vortex. 1 The pinning of the  Abrikosov vortexes. 2 The case of the wide pinning force distribution.

22 Anderson localization in the percolation structure. 1 Anderson localization. 2 Transition metal-Anderson dielectric in percolation structure.

23 Conclusion.

O autorze

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.

Blurb

This book 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.

Aimed at researchers and advanced students, it 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.