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Stauffer D., Aharony A. — Introduction to percolation theory
Stauffer D., Aharony A. — Introduction to percolation theory



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Название: Introduction to percolation theory

Авторы: Stauffer D., Aharony A.

Аннотация:

Percolation theory deals with clustering, criticality, diffusion, fractals, phase transitions and disordered systems. It provides a quantitative model for understanding these phenomena, and therefore provides a theoretical, statistical background to many physical and natural science disciplines. The scope of this book covers the basic theory for the graduate while it also reaches into the specialized fields of disordered systems and renormalization groups. Readers are expected to be able to handle some fundamental mathematical procedures such as integration and differentiation of single variable functions, probability and statistics. They will also find it useful if they have some computer programming experience for example in Fortran. While percolation is treated as being a fundamentally physical concept, its relevance to various natural and living systems is addressed. Much of the book deals with systems lying close to the critical point phase transition point, where the subject is at its most interesting and sensitive. This book should be of value to all those who deal with systems which exhibit critical points and phase transition behaviour.


Язык: en

Рубрика: Математика/Математическая Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 91

Добавлена в каталог: 25.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A table of exponents appears      52
A table of thresholds appears      17
Accessible perimeter      127
Aggregation      127
Alexander — Orbach rule      123
Amplitudes      43
Animals      24
Anomalous diffusion      112
Ant in a labyrinth      11
Ant species (blind, myopic, etc.)      116
Backbone      91
Bethe lattice      26
Biased walk      127
Bins      49
Blind ant      116
Bond percolation      16
Bootstrap percolation      32
Branched polymers      4
Broken symmetry      8
Cayley tree see Bethe lattice      26
Characteristic time      6
Chemical path      7
Classification of labels      160
Cluster (definition)      1
Cluster numbers      20
Collapsing data      44
Compressibility      23
Computer experiments      152
Conductivity      89
Connectivity length      60
Continuum models      108
Corrections      62
Corrections to scaling      155
Correlated percolation      143
Correlation function      59
correlation length      10
Counting of clusters      157
Critical exponents      31
Critical phenomena      4
Critical point      7
Critical slowing down      8
Crossover      13
Crossover length      64
Cumulant      99
Curie point      138
Curie — Weiss law      38
dangling bonds      90
Data collapse      44
Dead ends      90
Density of states      126
Density profiles      64
Dictatorship      60
Diffusion      10
Diffusion front      130
Dilution      139
Directed percolation      122
dispersion relation      125
Distribution function of conductances      99
Distribution function of currents      100
Distribution function of hitting probabilities      127
Distribution function of random walks      122
Double-logarithmic plot      11
Droplet model      140
Effective fractal dimensionality      63
Effective medium approximation      34
Effective threshold      52
Elastic networks      111
Elementary excitations      142
Equal rights      117
Error bars      155
Exact cluster numbers      23
Exchange energy      135
Extrapolation      44
Ferromagnet      138
Field (magnetic)      138
Field theories      171
Finite-size scaling      70
Fisher droplet model      33
Fixed point      76
Flory approximant      170
Flow of renormalization      81
Fluctuations      74
Fluids      138
Forest fires      5
Fortran program      160
Fractal dimensionality      9
Fractal models      103
Fractals      9
Fracton dimensionality      123
Fractons      125
Gamma function      36
Gap      99
Gaussian      84
Gelation      4
Ghost spin      144
Graphite paper      90
Growth      134
Heisenberg ferromagnets      148
Hull      127
Hyperscaling      67
Ideal gas      141
Incipient infinite cluster      65
Invasion percolation      133
Ising ferromagnest      138
Kinetics      146
Kirchhoff rule      93
Label of labels      158
Lacunarity      99
Lattice animals      24
Lattice gas      138
Lattice gauge theory      146
Lattices (square, triangular, etc.)      15
Least-squares fit      154
Links-nodes-blobs picture      95
Local fractal dimension      63
localization      125
Loops      32
Mandelbrot — Given curve      105
Master equation      116
Maximum of scaling function      42
Mean cluster size      21
Minimal path      7
moment      38
Monte Carlo      47
Monte Carlo renormalization      83
Multifractal      99
Myopic ant      116
Next-nearest neighbours      18
Nucleation      140
Oil reservoirs      8
One-dimensional percolation      19
Opalescence      23
Order of ramification      105
Order parameter      138
Pade approximants      45
Percolation (definition)      4
Percolator for coffee      17
Perimeter      25
Periodic boundary condition      50
Phase transition      8
Phonons      125
Polymer chains      169
Porosity      8
Porous rocks      8
Position space renormalization      70
Power laws      31
Pressure      96
Quantum percolation      126
Quenched dilution      139
Radius of gyration      59
Random numbers      47
Random resistor networks      89
Random walk      11
Ratio method      44
Real space renormalization      70
Recursive fractals      103
Recycling of labels      163
Red bonds      96
Renormalization      70
Resistance      93
resistors      89
Root Mean Square (RMS)      11
Scaling of cluster numbers      41
Scaling of cluster radii      63
Scaling of distances for diffusion      118
Scaling of finite sizes      70
Scaling of functions      63
Scaling theorv      4
Self-affine      132
Self-avoiding walks      169
Self-organized criticality      135
Self-similarity      82
Series      44
Sierpinski carpet      103
Sierpinski gasket      105
Similarity      75
Singly-connected bonds      87
Singular part      39
Site percolation      16
Site-bond percolation      18
Sound velocity      125
Spanning probability      72
Spectral dimension      123
Spin waves      126
Spontaneous magnetization      138
Statistical error      155
Stiffness constant      126
Strength of infinite cluster      28
Striptease      51
Superconductors      93
Superlocalization      126
surface      26
susceptibility      139
Swendsen — Wang algorithm      145
Swiss-cheese model      109
Systematic error      153
Temperature      137
Termites      122
Threshold      6
Triangular lattice on computers      157
Unionism      64
Universality      51
Upper critical dimensionality      169
Van der Waals equation      23
Vector computer      168
Vibrational excitations      125
Viscous fingering      96
Width of threshold distribution      74
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