Andrei A. Snarskii,
Igor V. Bezsudnov,
Vladimir A. Sevryukov,
Alexander Morozovskiy,
Joseph Malinsky
e.a.
Springer New York
2015e druk, 2016
9781441982902
Transport Processes in Macroscopically Disordered Media
From Mean Field Theory to Percolation
Specificaties
Gebonden, 310 blz.
|
Engels
Springer New York |
2015e druk, 2016
ISBN13: 9781441982902
Rubricering
Levertijd ongeveer 8 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9781441982902
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:310
Uitgever:Springer New York
Druk:2015
Inhoudsopgave
<p>Introduction. </p>
<p>Part I. </p>
<p>1 Introduction. 1 Types of macroscopically disordered media. 2 Classification of physical properties. Physical analogies.</p>
<p>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.</p>
<p>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.</p>
4 Elements of geometrical theory of percolation. 1 Percolation problem. 2 Basic foundations of geometric percolation. <p></p>
<p>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.</p>
<p>6 Selfdual media. 1 Locally isotropic media. 2 Locally anisotropic media.</p>
<p>7 Continual percolation problem. 1 Types of continual percolation problems. 2 Media of Swiss-Cheese models.</p>
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.<p></p>
<p>9 Finite scaling. 1 Properties of the percolation systems with dimensions lesser than their correlation length. 2 Finite-size scaling for self-dual media.</p>
<p>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.</p>
<p>Part II.</p>
<p>11 AC conductivity. 1 ЕМТ-approximation. 2 The method of percolation theory.</p>
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.<p></p>
<p>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. </p>
<p>14 Higher current moments. 1. Definitions. 2 Critical exponents of the higher current moments.</p>
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.<p></p>
<p>16 Effective elastic properties. 1 Basic notions of Elasticity Theory. 2 Effective modulae in the vicinity of percolation threshold. </p>
<p>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.</p>
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. <p></p>
<p>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. </p>
<p>20 Instability and chaos in the macroscopically disordered media with weak dissipation. 1 Dual media. 2 Ladder filter.</p>
<p>21 Percolation-like description of the Abrikosov vortex. 1 The pinning of the Abrikosov vortexes. 2 The case of the wide pinning force distribution. </p>
<p>22 Anderson localization in the percolation structure. 1 Anderson localization. 2 Transition metal-Anderson dielectric in percolation structure. </p>
23 Conclusion.<p></p>
<p>Part I. </p>
<p>1 Introduction. 1 Types of macroscopically disordered media. 2 Classification of physical properties. Physical analogies.</p>
<p>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.</p>
<p>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.</p>
4 Elements of geometrical theory of percolation. 1 Percolation problem. 2 Basic foundations of geometric percolation. <p></p>
<p>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.</p>
<p>6 Selfdual media. 1 Locally isotropic media. 2 Locally anisotropic media.</p>
<p>7 Continual percolation problem. 1 Types of continual percolation problems. 2 Media of Swiss-Cheese models.</p>
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.<p></p>
<p>9 Finite scaling. 1 Properties of the percolation systems with dimensions lesser than their correlation length. 2 Finite-size scaling for self-dual media.</p>
<p>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.</p>
<p>Part II.</p>
<p>11 AC conductivity. 1 ЕМТ-approximation. 2 The method of percolation theory.</p>
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.<p></p>
<p>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. </p>
<p>14 Higher current moments. 1. Definitions. 2 Critical exponents of the higher current moments.</p>
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.<p></p>
<p>16 Effective elastic properties. 1 Basic notions of Elasticity Theory. 2 Effective modulae in the vicinity of percolation threshold. </p>
<p>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.</p>
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. <p></p>
<p>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. </p>
<p>20 Instability and chaos in the macroscopically disordered media with weak dissipation. 1 Dual media. 2 Ladder filter.</p>
<p>21 Percolation-like description of the Abrikosov vortex. 1 The pinning of the Abrikosov vortexes. 2 The case of the wide pinning force distribution. </p>
<p>22 Anderson localization in the percolation structure. 1 Anderson localization. 2 Transition metal-Anderson dielectric in percolation structure. </p>
23 Conclusion.<p></p>