Critical phenomena in natural sciences: chaos, fractals, selforganization, and disorder : concepts and tools
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
2004
|
| Edition: | Second edition |
| Series: | Springer series in synergetics
Springer complexity |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 528 Seiten Illustrationen, Diagramme |
| ISBN: | 9783540308829 3540407545 |
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| 245 | 1 | 0 | |a Critical phenomena in natural sciences |b chaos, fractals, selforganization, and disorder : concepts and tools |c Didier Sornette |
| 250 | |a Second edition | ||
| 264 | 1 | |a Berlin |b Springer |c 2004 | |
| 300 | |a XXII, 528 Seiten |b Illustrationen, Diagramme | ||
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| _version_ | 1804130241950515200 |
|---|---|
| adam_text | CONTENTS
1.
USEFUL
NOTIONS
OF
PROBABILITY
THEORY
.....................
1
1.1
WHAT
IS
PROBABILITY?
..................................
1
1.1.1
FIRSTINTUITIVENOTIONS
..........................
1
1.1.2
OBJECTIVE
VERSUS
SUBJECTIVE
PROBABILITY
...........
2
1.2
BAYESIANVIEWPOINT...................................
6
1.2.1
INTRODUCTION...................................
6
1.2.2
BAYES THEOREM................................
7
1.2.3
BAYESIAN
EXPLANATION
FOR
CHANGE
OF
BELIEF.........
9
1.2.4
BAYESIAN
PROBABILITY
AND
THE
DUTCH
BOOK
.........
10
1.3
PROBABILITY
DENSITY
FUNCTION............................
12
1.4
MEASURESOFCENTRALTENDENCY
..........................
13
1.5
MEASUREOFVARIATIONSFROMCENTRALTENDENCY.............
14
1.6
MOMENTSANDCHARACTERISTICFUNCTION....................
15
1.7
CUMULANTS............................................
16
1.8
MAXIMUM
OF
RANDOM
VARIABLES
AND
EXTREME
VALUE
THEORY.
18
1.8.1
MAXIMUM
VALUE
AMONG
N
RANDOM
VARIABLES
.....
19
1.8.2
STABLEEXTREMEVALUEDISTRIBUTIONS...............
23
1.8.3
FIRST
HEURISTIC
DERIVATION
OFTHESTABLEGUMBELDISTRIBUTION................
25
1.8.4
SECOND
HEURISTIC
DERIVATION
OFTHESTABLEGUMBELDISTRIBUTION................
26
1.8.5
PRACTICAL
USE
AND
EXPRESSION
OF
THE
COEFFICIENTS
OFTHEGUMBELDISTRIBUTION......................
28
1.8.6
THE
GNEDENKO-PICKANDS-BALKEMA-DE
HAAN
THEO
REM
ANDTHEPDFOFPEAKS-OVER-THRESHOLD
.............
29
2.
SUMS
OF
RANDOM
VARIABLES,
RANDOM
WALKS
AND
THE
CENTRAL
LIMIT
THEOREM
...........................
33
2.1
THERANDOMWALKPROBLEM
............................
33
2.1.1
AVERAGEDRIFT..................................
34
2.1.2
DIFFUSIONLAW..................................
35
2.1.3
BROWNIAN
MOTION
AS
SOLUTION
OF
A
STOCHASTIC
ODE
.
35
2.1.4
FRACTALSTRUCTURE
..............................
37
XVI
CONTENTS
2.1.5
SELF-AFFINITY
...................................
39
2.2
MASTER
AND
DIFFUSION
(FOKKER-PLANCK)
EQUATIONS
..........
41
2.2.1
SIMPLEFORMULATION.............................
41
2.2.2
GENERALFOKKER-PLANCKEQUATION.................
43
2.2.3
ITOVERSUSSTRATONOVICH
.........................
44
2.2.4
EXTRACTING
MODEL
EQUATIONS
FROM
EXPERIMENTAL
DATA
47
2.3
THECENTRALLIMITTHEOREM
............................
48
2.3.1
CONVOLUTION
...................................
48
2.3.2
STATEMENT.....................................
50
2.3.3
CONDITIONS
....................................
50
2.3.4
COLLECTIVEPHENOMENON
.........................
51
2.3.5
RENORMALIZATIONGROUPDERIVATION
...............
52
2.3.6
RECURSION
RELATION
AND
PERTURBATIVE
ANALYSIS......
55
3.
LARGE
DEVIATIONS
.........................................
59
3.1
CUMULANTEXPANSION...................................
59
3.2
LARGEDEVIATIONTHEOREM
..............................
60
3.2.1
QUANTIFICATION
OF
THE
DEVIATION
FROMTHECENTRALLIMITTHEOREM
.................
61
3.2.2
HEURISTIC
DERIVATION
OFTHELARGEDEVIATIONTHEOREM(3.9).............
61
3.2.3
EXAMPLE:THEBINOMIALLAW
.....................
63
3.2.4
NON-IDENTICALLY
DISTRIBUTED
RANDOM
VARIABLES
.....
64
3.3
LARGE
DEVIATIONS
WITH
CONSTRAINTS
ANDTHEBOLTZMANNFORMALISM
..........................
66
3.3.1
FREQUENCIES
CONDITIONED
BYLARGEDEVIATIONS
......
66
3.3.2
PARTITIONFUNCTIONFORMALISM
...................
68
3.3.3
LARGEDEVIATIONSINTHEDICEGAME...............
70
3.3.4
MODEL
CONSTRUCTION
FROM
LARGE
DEVIATIONS
........
73
3.3.5
LARGE
DEVIATIONS
IN
THE
GUTENBERG-RICHTER
LAW
ANDTHEGAMMALAW
...........................
76
3.4
EXTREMEDEVIATIONS....................................
78
3.4.1
THE DEMOCRATIC RESULT
.......................
78
3.4.2
APPLICATION
TO
THE
MULTIPLICATION
OF
RANDOM
VARIABLES:
AMECHANISMFORSTRETCHEDEXPONENTIALS
..........
80
3.4.3
APPLICATION
TO
TURBULENCE
AND
TO
FRAGMENTATION
...
83
3.5
LARGE
DEVIATIONS
IN
THE
SUM
OF
VARIABLES
WITHPOWERLAWDISTRIBUTIONS...........................
87
3.5.1
GENERAL
CASE
WITH
EXPONENT
µ
2
...............
87
3.5.2
BORDERLINE
CASE
WITH
EXPONENT
µ
=2.............
90
CONTENTS
XVII
4.
POWER
LAW
DISTRIBUTIONS
.................................
93
4.1
STABLE
LAWS:
GAUSSIAN
AND
L´EVYLAWS
...................
93
4.1.1
DEFINITION
.....................................
93
4.1.2
THE
GAUSSIAN
PROBABILITY
DENSITY
FUNCTION........
93
4.1.3
THELOG-NORMALLAW...........................
94
4.1.4
THE
L´EVYLAWS
................................
96
4.1.5
TRUNCATED
L´EVYLAWS...........................101
4.2
POWERLAWS...........................................
104
4.2.1
HOW
DOES
ONE
TAME
WILD
DISTRIBUTIONS?
.......
105
4.2.2
MULTIFRACTALAPPROACH
..........................
110
4.3
ANOMALOUS
DIFFUSION
OF
CONTAMINANTS
INTHEEARTH SCRUSTANDTHEATMOSPHERE.................
112
4.3.1
GENERALINTUITIVEDERIVATION
.....................113
4.3.2
MORE
DETAILED
MODEL
OF
TRACER
DIFFUSION
IN
THE
CRUST113
4.3.3
ANOMALOUSDIFFUSIONINAFLUID
..................115
4.4
INTUITIVE
CALCULATION
TOOLS
FORPOWERLAWDISTRIBUTIONS
............................116
4.5
FOX
FUNCTION,
MITTAG-LEFFLER
FUNCTION
AND
L´EVYDISTRIBUTIONS.................................118
5.
FRACTALS
AND
MULTIFRACTALS
................................
123
5.1
FRACTALS..............................................
123
5.1.1
INTRODUCTION...................................
123
5.1.2
A
FIRST
CANONICAL
EXAMPLE:
THE
TRIADIC
CANTOR
SET
.
124
5.1.3
HOWLONGISTHECOASTOFBRITAIN?................
125
5.1.4
THEHAUSDORFFDIMENSION
.......................127
5.1.5
EXAMPLESOFNATURALFRACTALS
....................127
5.2
MULTIFRACTALS..........................................
141
5.2.1
DEFINITION
.....................................
141
5.2.2
CORRECTION
METHOD
FOR
FINITE
SIZE
EFFECTS
ANDIRREGULARGEOMETRIES........................
143
5.2.3
ORIGIN
OF
MULTIFRACTALITY
AND
SOME
EXACT
RESULTS...
145
5.2.4
GENERALIZATION
OF
MULTIFRACTALITY:
INFINITELY
DIVISIBLE
CASCADES
.....................
146
5.3
SCALEINVARIANCE.......................................
148
5.3.1
DEFINITION
.....................................
148
5.3.2
RELATION
WITH
DIMENSIONAL
ANALYSIS...............
150
5.4
THEMULTIFRACTALRANDOMWALK
.........................153
5.4.1
A
FIRST
STEP:
THE
FRACTIONAL
BROWNIAN
MOTION
.....
153
5.4.2
DEFINITION
AND
PROPERTIES
OFTHEMULTIFRACTALRANDOMWALK.................154
5.5
COMPLEX
FRACTAL
DIMENSIONS
ANDDISCRETESCALEINVARIANCE
...........................
156
5.5.1
DEFINITION
OF
DISCRETE
SCALE
INVARIANCE
............
156
5.5.2
LOG-PERIODICITY
AND
COMPLEX
EXPONENTS
..........
157
XVIII
CONTENTS
5.5.3
IMPORTANCE
AND
USEFULNESS
OFDISCRETESCALEINVARIANCE......................
159
5.5.4
SCENARII
LEADING
TO
DISCRETE
SCALE
INVARIANCE
......
160
6.
RANK-ORDERING
STATISTICS
AND
HEAVY
TAILS
................
163
6.1
PROBABILITY
DISTRIBUTIONS
...............................
163
6.2
DEFINITIONOFRANKORDERINGSTATISTICS....................
164
6.3
NORMALANDLOG-NORMALDISTRIBUTIONS
...................
166
6.4
THEEXPONENTIALDISTRIBUTION...........................167
6.5
POWERLAWDISTRIBUTIONS
...............................
170
6.5.1
MAXIMUMLIKELIHOODESTIMATION.................
170
6.5.2
QUANTILESOFLARGEEVENTS
.......................
173
6.5.3
POWER
LAWS
WITH
A
GLOBAL
CONSTRAINT:
FRACTALPLATETECTONICS ........................174
6.6
THEGAMMALAW......................................
179
6.7
THESTRETCHEDEXPONENTIALDISTRIBUTION..................
180
6.8
MAXIMUM
LIKELIHOOD
AND
OTHER
ESTIMATORS
OFSTRETCHEDEXPONENTIALDISTRIBUTIONS
...................
181
6.8.1
INTRODUCTION...................................
182
6.8.2
TWO-PARAMETER
STRETCHED
EXPONENTIAL
DISTRIBUTION
185
6.8.3
THREE-PARAMETER
WEIBULL
DISTRIBUTION
............
194
6.8.4
GENERALIZEDWEIBULLDISTRIBUTIONS
................196
7.
STATISTICAL
MECHANICS:
PROBABILISTIC
POINT
OF
VIEW
AND
THE
CONCEPT
OF
TEMPERATURE
.......................
199
7.1
STATISTICAL
DERIVATION
OF
THE
CONCEPT
OF
TEMPERATURE.......
200
7.2
STATISTICALTHERMODYNAMICS
............................202
7.3
STATISTICAL
MECHANICS
AS
PROBABILITY
THEORY
WITHCONSTRAINTS
......................................
203
7.3.1
GENERALFORMULATION............................
203
7.3.2
FIRSTLAWOFTHERMODYNAMICS
...................206
7.3.3
THERMODYNAMICPOTENTIALS
......................207
7.4
DOES
THE
CONCEPT
OF
TEMPERATURE
APPLY
TONON-THERMALSYSTEMS?...............................208
7.4.1
FORMULATIONOFTHEPROBLEM
.....................
208
7.4.2
AGENERALMODELINGSTRATEGY....................
210
7.4.3
DISCRIMINATINGTESTS............................
211
7.4.4
STATIONARY
DISTRIBUTION
WITH
EXTERNAL
NOISE
.......
213
7.4.5
EFFECTIVE
TEMPERATURE
GENERATED
BYCHAOTICDYNAMICS...........................
214
7.4.6
PRINCIPLE
OF
LEAST
ACTION
FOR
OUT-OF-EQUILIBRIUM
SYSTEMS..................
218
7.4.7
SUPERSTATISTICS
.................................
219
CONTENTS
XIX
8.
LONG-RANGE
CORRELATIONS
.................................
223
8.1
CRITERIONFORTHERELEVANCEOFCORRELATIONS................
223
8.2
STATISTICALINTERPRETATION
...............................
226
8.3
AN
APPLICATION:
SUPER-DIFFUSION
IN
A
LAYERED
FLUID
WITHRANDOMVELOCITIES
................................
228
8.4
ADVANCEDRESULTSONCORRELATIONS
.......................229
8.4.1
CORRELATIONANDDEPENDENCE.....................229
8.4.2
STATISTICAL
TIME
REVERSAL
SYMMETRY
..............
231
8.4.3
FRACTIONAL
DERIVATION
AND
LONG-TIME
CORRELATIONS
.
236
9.
PHASE
TRANSITIONS:
CRITICAL
PHENOMENA
AND
FIRST-ORDER
TRANSITIONS
...............................
241
9.1
DEFINITION
............................................241
9.2
SPINMODELSATTHEIRCRITICALPOINTS.....................
242
9.2.1
DEFINITIONOFTHESPINMODEL.....................
242
9.2.2
CRITICALBEHAVIOR...............................245
9.2.3
LONG-RANGE
CORRELATIONS
OF
SPIN
MODELS
ATTHEIRCRITICALPOINTS..........................
246
9.3
FIRST-ORDERVERSUSCRITICALTRANSITIONS...................248
9.3.1
DEFINITIONANDBASICPROPERTIES
..................248
9.3.2
DYNAMICAL
LANDAU-GINZBURG
FORMULATION.........
250
9.3.3
THE
SCALING
HYPOTHESIS:
DYNAMICAL
LENGTH
SCALES
FORORDERING...................................253
10.
TRANSITIONS,
BIFURCATIONS
AND
PRECURSORS
..................
255
10.1
SUPERCRITICAL BIFURCATION
.............................
256
10.2
CRITICALPRECURSORYFLUCTUATIONS.........................258
10.3
SUBCRITICAL BIFURCATION
...............................
262
10.4
SCALINGANDPRECURSORSNEARSPINODALS
...................
264
1
0
.5
SE
LE
C
TIO
NO
FA
NATTR
A
C
TO
RINTHEABS
E
NC
E
OFAPOTENTIAL
.........................................
265
11.
THE
RENORMALIZATION
GROUP
..............................
267
11.1
GENERALFRAMEWORK
...................................267
11.2
AN
EXPLICIT
EXAMPLE:
SPINS
ON
A
HIERARCHICAL
NETWORK
.....
269
11.2.1
RENORMALIZATION
GROUP
CALCULATION...............
269
11.2.2
FIXED
POINTS,
STABLE
PHASES
AND
CRITICAL
POINTS
....
273
11.2.3
SINGULARITIES
AND
CRITICAL
EXPONENTS
..............
275
11.2.4
COMPLEX
EXPONENTS
ANDLOG-PERIODICCORRECTIONSTOSCALING...........276
11.2.5
WEIERSTRASS-TYPE
FUNCTIONS
FROM
DISCRETE
RENORMALIZATION
GROUP
EQUATIONS
...
279
11.3
CRITICALITY
AND
THE
RENORMALIZATION
GROUP
ONEUCLIDEANSYSTEMS..................................283
XX
CONTENTS
11.4
A
NOVEL
APPLICATION
TO
THE
CONSTRUCTION
OFFUNCTIONALAPPROXIMANTS
............................287
11.4.1
GENERALCONCEPTS
..............................287
11.4.2
SELF-SIMILARAPPROXIMANTS.......................
288
11.5
TOWARDSAHIERARCHICALVIEWOFTHEWORLD
................
291
12.
THE
PERCOLATION
MODEL
...................................
293
12.1
PERCOLATIONASAMODELOFCRACKING
......................293
12.2
EFFECTIVE
MEDIUM
THEORY
AND
PERCOLATION
................
296
12.3
RENORMALIZATION
GROUP
APPROACH
TO
PERCOLATION
ANDGENERALIZATIONS....................................298
12.3.1
CELL-TO-SITETRANSFORMATION......................
299
12.3.2
A
WORD
OF
CAUTION
ON
REAL
SPACE
RENORMALIZATION
GROUP
TECHNIQUES
..
301
12.3.3
THE
PERCOLATION
MODEL
ONTHEHIERARCHICALDIAMONDLATTICE..............
303
12.4
DIRECTEDPERCOLATION...................................304
12.4.1
DEFINITIONS
....................................
304
12.4.2
UNIVERSALITYCLASS..............................306
12.4.3
FIELD
THEORY:
STOCHASTIC
PARTIAL
DIFFERENTIAL
EQUA
TION
WITHMULTIPLICATIVENOISE........................
308
12.4.4
SELF-ORGANIZED
FORMULATION
OF
DIRECTED
PERCOLATION
ANDSCALINGLAWS...............................309
13.
RUPTURE
MODELS
..........................................
313
13.1
THEBRANCHINGMODEL
.................................
314
13.1.1
MEAN
FIELD
VERSION
OR
BRANCHING
ONTHEBETHELATTICE............................314
13.1.2
A
BRANCHING-AGGREGATION
MODEL
AUTOMATICALLY
FUNCTIONING
AT
ITS
CRITICAL
POINT
....
316
13.1.3
GENERALIZATION
OF
CRITICAL
BRANCHING
MODELS
.......
317
13.2
FIBER
BUNDLE
MODELS
AND
THE
EFFECTS
OFSTRESSREDISTRIBUTION
................................
318
13.2.1
ONE-DIMENSIONAL
SYSTEM
OFFIBERSASSOCIATEDINSERIES....................318
13.2.2
DEMOCRATIC
FIBER
BUNDLE
MODEL
(DANIELS,
1945)....
320
13.3
HIERARCHICALMODEL
....................................323
13.3.1
THE
SIMPLEST
HIERARCHICAL
MODEL
OF
RUPTURE
.......
323
13.3.2
QUASI-STATIC
HIERARCHICAL
FIBER
RUPTURE
MODEL.....
326
13.3.3
HIERARCHICAL
FIBER
RUPTURE
MODEL
WITHTIME-DEPENDENCE..........................
328
13.4
QUASI-STATICMODELSINEUCLIDEANSPACES
.................
330
13.5
A
DYNAMICAL
MODEL
OF
RUPTURE
WITHOUT
ELASTO-DYNAMICS:
THE THERMALFUSEMODEL
.............................335
CONTENTS
XXI
13.6
TIME-TO-FAILUREANDRUPTURECRITICALITY..................
339
13.6.1
CRITICALTIME-TO-FAILUREANALYSIS.................
339
13.6.2
TIME-TO-FAILURE
BEHAVIOR
INTHEDIETERICHFRICTIONLAW
....................
343
14.
MECHANISMS
FOR
POWER
LAWS
..............................
345
14.1
TEMPORAL
COPERNICAN
PRINCIPLE
AND
µ
=1
UNIVERSAL
DISTRIBUTION
OF
RESIDUAL
LIFETIMES
.....
346
14.2
CHANGEOFVARIABLE
....................................
348
14.2.1
POWER
LAW
CHANGE
OF
VARIABLE
CLOSE
TO
THE
ORIGIN
.
348
14.2.2
COMBINATIONOFEXPONENTIALS
....................354
14.3
MAXIMIZATION
OF
THE
GENERALIZED
TSALLIS
ENTROPY
..........
356
14.4
SUPERPOSITIONOFDISTRIBUTIONS...........................
359
14.4.1
POWERLAWDISTRIBUTIONOFWIDTHS................
359
14.4.2
SUM
OF
STRETCHED
EXPONENTIALS
(CHAP.
3)..........
362
14.4.3
DOUBLE
PARETO
DISTRIBUTION
BY
SUPERPOSITION
OFLOG-NORMALPDF S
............................
362
14.5
RANDOM
WALKS:
DISTRIBUTION
OF
RETURN
TIMES
TO
THE
ORIGIN.
363
14.5.1
DERIVATION.....................................364
14.5.2
APPLICATIONS...................................
365
14.6
SWEEPING
OF
A
CONTROL
PARAMETER
TOWARDS
AN
INSTABILITY....
367
14.7
GROWTHWITHPREFERENTIALATTACHMENT....................370
14.8
MULTIPLICATIVENOISEWITHCONSTRAINTS....................
373
14.8.1
DEFINITIONOFTHEPROCESS
........................
373
14.8.2
THE
KESTEN
MULTIPLICATIVE
STOCHASTIC
PROCESS
......
374
14.8.3
RANDOMWALKANALOGY
.........................
375
14.8.4
EXACT
DERIVATION,
GENERALIZATION
AND
APPLICATIONS..
378
14.9
THE COHERENT-NOISE MECHANISM.......................381
14.10
AVALANCHESIN
HYSTERETIC
LOOPSAND
FIRST-ORDERTRANSITIONS
WITHRANDOMNESS......................................
386
14.11
HIGHLYOPTIMIZEDTOLERANT (HOT)SYSTEMS.............389
14.11.1
MECHANISM
FOR
THE
POWER
LAW
DISTRIBUTION
OF
FIRE
SIZES
.........................................
390
14.11.2
CONSTRAINEDOPTIMIZATIONWITHLIMITEDDEVIATIONS
(COLD).......................................393
14.11.3
HOTVERSUSPERCOLATION.........................393
15.
SELF-ORGANIZED
CRITICALITY
.................................
395
15.1
WHATISSELF-ORGANIZEDCRITICALITY?......................395
15.1.1
INTRODUCTION...................................
395
15.1.2
DEFINITION
.....................................
397
15.2
SANDPILEMODELS.......................................398
15.2.1
GENERALITIES....................................
398
15.2.2
THEABELIANSANDPILE...........................
398
15.3
THRESHOLDDYNAMICS...................................
402
XXII
CONTENTS
15.3.1
GENERALIZATION
.................................402
15.3.2
ILLUSTRATION
OF
SELF-ORGANIZED
CRITICALITY
WITHINTHEEARTH SCRUST........................
404
15.4
SCENARIOSFORSELF-ORGANIZEDCRITICALITY...................406
15.4.1
GENERALITIES....................................
406
15.4.2
NONLINEAR
FEEDBACK
OF
THE
ORDER
PARAMETER
ONTOTHE CONTROLPARAMETER ....................
407
15.4.3
GENERICSCALEINVARIANCE
........................
409
15.4.4
MAPPINGONTOACRITICALPOINT
...................
414
15.4.5
MAPPINGTOCONTACTPROCESSES
...................422
15.4.6
CRITICALDESYNCHRONIZATION.......................
424
15.4.7
EXTREMALDYNAMICS.............................427
15.4.8
DYNAMICAL
SYSTEM
THEORY
OF
SELF-ORGANIZED
CRITI
CALITY
.........................................435
15.5
TESTS
OF
SELF-ORGANIZED
CRITICALITY
IN
COMPLEX
SYSTEMS:
THEEXAMPLEOFTHEEARTH SCRUST........................
438
16.
INTRODUCTION
TO
THE
PHYSICS
OF
RANDOM
SYSTEMS
..........
441
16.1
GENERALITIES...........................................441
16.2
THERANDOMENERGYMODEL.............................
445
16.3
NON-SELF-AVERAGINGPROPERTIES
..........................449
16.3.1
DEFINITIONS
....................................
449
16.3.2
FRAGMENTATIONMODELS
..........................451
17.
RANDOMNESS
AND
LONG-RANGE
LAPLACIAN
INTERACTIONS
......
457
17.1
L´EVY
DISTRIBUTIONS
FROM
RANDOM
DISTRIBUTIONS
OF
SOURCES
WITHLONG-RANGEINTERACTIONS...........................
457
17.1.1
HOLTSMARK S
GRAVITATIONAL
FORCE
DISTRIBUTION
......
457
17.1.2
GENERALIZATION
TO
OTHER
FIELDS
(ELECTRIC,ELASTIC,HYDRODYNAMICS)................
461
17.2
LONG-RANGE
FIELD
FLUCTUATIONS
DUE
TO
IRREGULAR
ARRAYS
OF
SOURCES
AT
BOUNDARIES
...............................
463
17.2.1
PROBLEMANDMAINRESULTS
......................463
17.2.2
CALCULATIONMETHODS............................
464
17.2.3
APPLICATIONS...................................
471
REFERENCES
....................................................
477
INDEX
.........................................................
525
|
| any_adam_object | 1 |
| author | Sornette, Didier 1957- |
| author_GND | (DE-588)171887921 |
| author_facet | Sornette, Didier 1957- |
| author_role | aut |
| author_sort | Sornette, Didier 1957- |
| author_variant | d s ds |
| building | Verbundindex |
| bvnumber | BV017428788 |
| callnumber-first | Q - Science |
| callnumber-label | QC173 |
| callnumber-raw | QC173.4.C74 |
| callnumber-search | QC173.4.C74 |
| callnumber-sort | QC 3173.4 C74 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 3900 |
| ctrlnum | (OCoLC)52819765 (DE-599)BVBBV017428788 |
| dewey-full | 530.4/74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/74 |
| dewey-search | 530.4/74 |
| dewey-sort | 3530.4 274 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV017428788 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:17:55Z |
| institution | BVB |
| isbn | 9783540308829 3540407545 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010501660 |
| oclc_num | 52819765 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-19 DE-BY-UBM DE-83 DE-11 DE-384 |
| owner_facet | DE-703 DE-20 DE-19 DE-BY-UBM DE-83 DE-11 DE-384 |
| physical | XXII, 528 Seiten Illustrationen, Diagramme |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in synergetics Springer complexity |
| spelling | Sornette, Didier 1957- Verfasser (DE-588)171887921 aut Critical phenomena in natural sciences chaos, fractals, selforganization, and disorder : concepts and tools Didier Sornette Second edition Berlin Springer 2004 XXII, 528 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Springer series in synergetics Springer complexity Teoria de campos e ondas larpcal Critical phenomena (Physics) Fraktal (DE-588)4123220-3 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Naturwissenschaften (DE-588)4041421-8 gnd rswk-swf Selbstorganisation (DE-588)4126830-1 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Kritisches Phänomen (DE-588)4165788-3 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Kritisches Phänomen (DE-588)4165788-3 s Chaos (DE-588)4191419-3 s DE-604 Selbstorganisation (DE-588)4126830-1 s Fraktal (DE-588)4123220-3 s Naturwissenschaften (DE-588)4041421-8 s Chaotisches System (DE-588)4316104-2 s Wahrscheinlichkeit (DE-588)4137007-7 s 1\p DE-604 Statistische Physik (DE-588)4057000-9 s 2\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010501660&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sornette, Didier 1957- Critical phenomena in natural sciences chaos, fractals, selforganization, and disorder : concepts and tools Teoria de campos e ondas larpcal Critical phenomena (Physics) Fraktal (DE-588)4123220-3 gnd Chaotisches System (DE-588)4316104-2 gnd Naturwissenschaften (DE-588)4041421-8 gnd Selbstorganisation (DE-588)4126830-1 gnd Chaos (DE-588)4191419-3 gnd Statistische Physik (DE-588)4057000-9 gnd Kritisches Phänomen (DE-588)4165788-3 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd |
| subject_GND | (DE-588)4123220-3 (DE-588)4316104-2 (DE-588)4041421-8 (DE-588)4126830-1 (DE-588)4191419-3 (DE-588)4057000-9 (DE-588)4165788-3 (DE-588)4137007-7 |
| title | Critical phenomena in natural sciences chaos, fractals, selforganization, and disorder : concepts and tools |
| title_auth | Critical phenomena in natural sciences chaos, fractals, selforganization, and disorder : concepts and tools |
| title_exact_search | Critical phenomena in natural sciences chaos, fractals, selforganization, and disorder : concepts and tools |
| title_full | Critical phenomena in natural sciences chaos, fractals, selforganization, and disorder : concepts and tools Didier Sornette |
| title_fullStr | Critical phenomena in natural sciences chaos, fractals, selforganization, and disorder : concepts and tools Didier Sornette |
| title_full_unstemmed | Critical phenomena in natural sciences chaos, fractals, selforganization, and disorder : concepts and tools Didier Sornette |
| title_short | Critical phenomena in natural sciences |
| title_sort | critical phenomena in natural sciences chaos fractals selforganization and disorder concepts and tools |
| title_sub | chaos, fractals, selforganization, and disorder : concepts and tools |
| topic | Teoria de campos e ondas larpcal Critical phenomena (Physics) Fraktal (DE-588)4123220-3 gnd Chaotisches System (DE-588)4316104-2 gnd Naturwissenschaften (DE-588)4041421-8 gnd Selbstorganisation (DE-588)4126830-1 gnd Chaos (DE-588)4191419-3 gnd Statistische Physik (DE-588)4057000-9 gnd Kritisches Phänomen (DE-588)4165788-3 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd |
| topic_facet | Teoria de campos e ondas Critical phenomena (Physics) Fraktal Chaotisches System Naturwissenschaften Selbstorganisation Chaos Statistische Physik Kritisches Phänomen Wahrscheinlichkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010501660&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sornettedidier criticalphenomenainnaturalscienceschaosfractalsselforganizationanddisorderconceptsandtools |