Fractals, scaling and growth far from equilibrium:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Edition: | 1. paperback ed. |
| Series: | Cambridge nonlinear science series
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 674 S. Ill., graph. Darst. |
| ISBN: | 9780521452533 9780521189811 |
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MARC
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| 245 | 1 | 0 | |a Fractals, scaling and growth far from equilibrium |c Paul meakin |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2011 | |
| 300 | |a XIV, 674 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804145603791290368 |
|---|---|
| adam_text | Contents
Preface
xiii
«lunuri
Pattern Formation Far From Equilibrium
ι
її
Power Laws and Scaling
4
1-2
The Logistic Map
16
13
The Variety of Patterns in Nature
22
1.3.1
Euclidean Patterns
24
1-3-2
Cellular Patterns
27
-3-3 Spiral and Helix Patterns
31
1-3-4
Labyrinthine Patterns
32
135
Fluid Convection Patterns
34
1-4
Moving-Boundary Processes
36
14.1
Solidification
37
1-4-2
Growth from Solution
39
• -4-3
Solidification of Impure Materials
42
1-4-4
Viscous Fingering
44
1-4-5
Pattern Selection
45
1-4-6
Anisotropy and Growth Velocity
46
1-4-7
Laplacian Growth
49
1-4-8
Instabilities
49
14.9
Characteristic Lengths
$0
■4-ю
Beyond Linear-Stability Analysis
51
•5
Solution of Interface Equations of Motion
52
vn
viii Contents
ι.
5.
ι
Numerical Solution of the
Non-
Local Equations
52
1.5.2
Local Models
53
1.6
Complex and Disorderly Patterns
57
1.6.1
Aggregates
59
1.6.2
Polymers
60
ι η
Scaling Symmetry
61
1.8
Notation
62
1.9
Monte Carlo Methods
62
1.10
Additional Information
64
Chapter
2
Fractals and Scaling
65
2.1
Self-Similar Fractals
65
2.1.1
Statistical Self-Similarity
69
2.1.2
Lacunarity
70
2.1.3
Determination of the Fractal Dimensionality
74
2.1.4
^e Devil s Staircase
81
2.2
Simple Rules Sj
2.3
Finite-Size Effects and Crossovers S5
2.4
Power Law Distributions
100
2.5
Scaling
/04
2.5.1
Corrections to Scaling
m
2.5.2
Multiscaling
¡12
2.6
Fractal Trees and Inhomogeneous Fractals
113
2.7
Self-Affine Fractals
119
2.7.1
Generation of Self-Affine Surfaces
124
2.7.2
The Geometry and Growth of Rough Surfaces 1
30
2.7.3
Characterization of Self-Affine Rough Surfaces
135
2.7.4
Finite-Size Effects and Crossovers
152
2.7.5
Status
153
2.7.6
Long Range Persistence
155
2.8
Multifractals
160
2.9
Universality
165
2.10
Additional Information
166
Chapter
3
Growth Models
168
3.1
Cluster Growth and Cluster Surfaces
169
3.2
Lattice Animals
172
3.3
Random Walks
/75
Contents
ЇХ
3.3.1
Self-Avoiding Random Walks
174
3.3.2
Indefinitely Growing Walks Ij6
3.3.3
The Diffusion-Limited Growth Walk
177
3.3.4
Random Walks on Random Substrates
181
3.3.5
Active Random Walk Models
182
3.4
Cluster Growth Models
183
3.4.1
The Eden Model 1
84
3.4.2
Ballistic Aggregation
187
3.4.3
The Diffusion-Limited Aggregation Model
í8ç
3.4.4
The Dielectric Breakdown Model
193
3.4.5
The Scaling Structure of
DLA
í
98
3.4.6
Other Aspects of
DLA
2
ro
3.4.7
Diffusion-Limited Annihilation
211
3.5
Percolation and Invasion Percolation
214
3.5.1
Growth Models for Percolation
229
3.5.2
Invasion Percolation
231
3.5.3
Diffusion Fronts and the Effect of Gradients
234
3.5.4
Directed Percolation
239
3.5.5
The Screened Growth Model
242
3.5.6
Faceted Growth Models
243
3.6
Packing Models
246
3.7
Growth Models Related to
DLA
250
3.7.1
Homogeneous Perturbations
253
3.7.2
Inhomogeneous Perturbations
2ζ6
3-7-3
Attractive Interaction Model
269
3.7.4
Growth on Fibers and Surfaces
272
3.7.5
Simplified
DLA
Models
279
3.8
Noise Reduction and Deterministic Models
285
3.8.1
Lattice Structure Effects
29
1
3.9
Models with Quenched Disorder
295
3.9.1
Growth in High-Dimensionality Spaces
297
3.10
Theoretical Methods
299
3.10.1
Mean Field Theories
302
3.10.2
Wedge Growth Theories
306
3.10.3
Real-Space Renormalization Theories
316
3.10.4
Other Approaches
3/9
311
Additional Information
32
j
Contents
Chapter
4
Experimental Studies
326
4-і
4.1.1
4.1.2
4.1.3
4.1.4
4-1-5
4.1.6
4.1.7
4-2
4.2.1
4.2.2
4.2.3
4.2.4
4-3
4-4
4-5
4-5-1
4-5-2
4-5-3
4-5-4
4.6
4-7
Chapter
5
5-і
5.1.1
5.1.2
5-1-3
5-1-4
5-1-5
5-2
5-2.1
5.2.2
5-2-3
5-2-4
5-2-5
5-2-6
DLA
Processes
327
Electrochemical Deposition
328
Fluid-Fluid Displacement Experiments
342
Thin Films and Interfaces
348
Dissolution. Melting and Erosion of Porous Media
356
Solidification and Crystallization 360
Dielectric Breakdown
363
Growth Probability Distributions
364
Dense Branching Morphology
366
Electrochemical Deposition 36c
Thin Films
375
Fluid-Fluid Displacement
377
Spherulites
380
Percolation
381
Invasion Percolation
384
Displacement in Complex Fluids
388
Polymer Solutions
389
Colloidal Systems
389
Foams
393
Fractal Systems
394
Other 2-Dimensional Patterns
397
Additional Information
400
The Growth of Surfaces and Interfaces
401
The Structure and Growth of Rough Surfaces
404
Basic Surface Growth Equations 405
Surface Diffusion
408
Universality Classes
411
Exponent Scaling Relationships
4
1
5
The Kuramoto-Sivashinsky Equation 417
Simple Models
418
Eden Growth Models
419
Ballistic Deposition Models
420
Solid-on-Solid Models 42s
The Polynuclear Growth Model
428
Directed Polymers
429
Langevin
Dynamics Simulations
432
Contents xi
5.2.7
Directed Percolation
433
5.3
Theoretically Motivated Models
434
5.3.1
Surface Growth with Weak Non-linearity
434
5.3.2
Correlated Noise
439
5.3.3
Non-Gaussian Noise
445
5.3.4
Growth on Rough Substrates
449
5.4
Models with Quenched Disorder
450
5.4л
Models and Simulation Results
452
5.4.2
Universality Classes
465
5.4.3
Exponent Scaling Relationships
469
5.5
Experiments
475
5.5.1
Fluid-Fluid Displacement Experiments
476
5.5.2
The Growth of Cell Colonies
483
5.5.3
Phase Boundaries and Grain Boundaries
484
5.5.4
Deposition Experiments
486
5.5.5
Erosion Experiments 510
5.5.6
Electrochemical Deposition
516
5.5.7
Corrosion and Oxidation
518
5.5.8
Some General Comments
519
5.6
Thin Film Growth Models
520
5.6.1
The Effects of Surface Diffusion
521
5.6.2
Step Edge Dynamics
546
5.6.3
Anomalous Scaling
547
5.6.4
Porous and Amorphous Films
549
5.6.5 Anisotropie
Surfaces
551
5.6.6
The Huygens Principle Model
552
5.7
Oblique Incidence and Shadowing Models
553
5.7.1
Oblique Incidence Ballistic Deposition Models
553
5.7.2
Ballistic Fans
561
5.7.3
Shadowing Models
562
5.8
Cluster Shapes and Faceted Growth
569
5.9
Additional Information
573
Appendix A Instabilities
574
A.i The Mullins-Sekerka Instability
574
A.2 The Saffman-Taylor Problem
580
xii
Contents
Appendix
В
Multifractals
5^5
Β. ι
Generation of Simple Multifractal Sets
¡86
В
2
Characterization of Multifractal Sets
59/
B.3 Applications to Non-Equilibrium Growth
597
B.3.1 Quenched and Annealed Averages
605
B.3.2 Mass Multifractals
606
References
608
Index
663
Plate section between pp.
242
and
243*
♦This plate section is available for download in color from
www.cambridge.org/9780521452533
|
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV037323594 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:22:05Z |
| institution | BVB |
| isbn | 9780521452533 9780521189811 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022477726 |
| oclc_num | 694547875 |
| open_access_boolean | |
| owner | DE-20 DE-83 DE-384 |
| owner_facet | DE-20 DE-83 DE-384 |
| physical | XIV, 674 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge nonlinear science series |
| series2 | Cambridge nonlinear science series |
| spelling | Meakin, Paul 1944- Verfasser (DE-588)1011675951 aut Fractals, scaling and growth far from equilibrium Paul meakin 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2011 XIV, 674 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge nonlinear science series 5 Nichtgleichgewicht (DE-588)4171730-2 gnd rswk-swf Skalierung (DE-588)4055202-0 gnd rswk-swf Musterbildung (DE-588)4137934-2 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Fraktal (DE-588)4123220-3 s Musterbildung (DE-588)4137934-2 s Nichtgleichgewicht (DE-588)4171730-2 s DE-604 Skalierung (DE-588)4055202-0 s Cambridge nonlinear science series 5 (DE-604)BV004573757 5 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022477726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meakin, Paul 1944- Fractals, scaling and growth far from equilibrium Cambridge nonlinear science series Nichtgleichgewicht (DE-588)4171730-2 gnd Skalierung (DE-588)4055202-0 gnd Musterbildung (DE-588)4137934-2 gnd Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4171730-2 (DE-588)4055202-0 (DE-588)4137934-2 (DE-588)4123220-3 |
| title | Fractals, scaling and growth far from equilibrium |
| title_auth | Fractals, scaling and growth far from equilibrium |
| title_exact_search | Fractals, scaling and growth far from equilibrium |
| title_full | Fractals, scaling and growth far from equilibrium Paul meakin |
| title_fullStr | Fractals, scaling and growth far from equilibrium Paul meakin |
| title_full_unstemmed | Fractals, scaling and growth far from equilibrium Paul meakin |
| title_short | Fractals, scaling and growth far from equilibrium |
| title_sort | fractals scaling and growth far from equilibrium |
| topic | Nichtgleichgewicht (DE-588)4171730-2 gnd Skalierung (DE-588)4055202-0 gnd Musterbildung (DE-588)4137934-2 gnd Fraktal (DE-588)4123220-3 gnd |
| topic_facet | Nichtgleichgewicht Skalierung Musterbildung Fraktal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022477726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004573757 |
| work_keys_str_mv | AT meakinpaul fractalsscalingandgrowthfarfromequilibrium |