Ageing and memory effects in anomalous diffusion processes:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2014
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20140219-1188463-0-6 Inhaltsverzeichnis |
| Beschreibung: | VI, 136 S. Ill., graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Schulz, Johannes H. P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ageing and memory effects in anomalous diffusion processes |c Johannes H. P. Schulz |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
SUMMARY III
1 STOCHASTIC MODELLING OF DIFFUSION PHENOMENA - A BRIEF HISTORY 1
1.1 THE RANDOM WALK S WALK TO FAME 1
1.2 PROBABILITY THEORY IN PHYSICS BEYOND ESTIMATION OF ERRORS 3
1.3 MOLECULES AND HEAT: PROBABLY RELATED 4
1.3.1 ALBERT EINSTEIN AND THE DIFFUSION EQUATION 8
1.3.2 MARIAN VON SMOLUCHOWSKI AND THE RANDOM WALK 10
1.3.3 JEAN BABTISTE PERRIN AND AVOGADRO S NUMBER 14
1.4 CRAFTING THE TOOLS OF STOCHASTIC MODELLING 15
1.4.1 THE WIENER PROCESS 16
1.4.2 THE LANGEVIN EQUATION 17
1.4.3 THE FOKKER-PLANCK EQUATION 21
1.5 GAUSSIAN WHITE NOISE: UNIVERSAL APPROACH FOR MODELLING FLUCTUATIONS
... 23
1.5.1 APPLICATIONS 23
1.5.2 FAST VERSUS SLOW VARIABLES 24
1.5.3 ATTRACTIVENESS MATTERS 25
1.6 ANOMALOUS DIFFUSION AND NOISE: NOT GAUSSIAN, NOT WHITE 30
2 PARADIGMS OF ANOMALOUS DIFFUSION 33
2.1 LEVY FLIGHTS 33
2.1.1 GENERALIZED CENTRAL LIMIT THEOREM AND STABLE RANDOM VARIABLES . .
34
2.1.2 A SCALING LIMIT FREE OF SCALES 37
2.1.3 FIRST PASSAGE STATISTICS, LEAP-OVER LENGTHS AND OTHER PROPERTIES
... 40
2.1.4 APPLICATIONS 42
2.2 CONTINUOUS TIME RANDOM WALKS 45
2.2.1 FLYING IN TIME 46
2.2.2 SUBORDINATION. 49
2.2.3 FINGERPRINT CHARACTERISTICS OF SCALE-FREE RELAXATION TIMES 50
2.2.4 MOTIVATION 51
2.2.5 APPLICATIONS 54
2.3 FRACTIONAL BROWNIAN MOTION 55
2.3.1 ASSESSING MEMORY 56
2.3.2 GAUSSIAN RANDOM WALKS 59
2.3.3 DEFINITION OF THE PROCESS 62
2.3.4 GENERALISATIONS AND APPLICATIONS 65
V
HTTP://D-NB.INFO/105018646X
CONTENTS
3 CORRELATED CONTINUOUS TIME RANDOM WALKS 69
3.1 MODEL DEFINITION 70
3.2 STATIONARITY 74
3.3 TIME SCALING ANALYSIS AND PROBABILITY DENSITY FUNCTION 77
3.4 COMPARISON WITH OTHER MODELS OF CORRELATED MOTIONS 81
4 AGEING RENEWAL THEORY 85
4.1 THE AGEING RENEWAL PROCESS 85
4.1.1 MOTIVATION 85
4.1.2 MODEL DEFINITION 87
4.1.3 LONG TIME SCALING LIMIT 89
4.1.4 AGEING PROBABILITY DISTRIBUTION 94
4.1.5 AGEING ENSEMBLE AVERAGES 100
4.1.6 CONDITIONAL ENSEMBLE AVERAGES 102
4.2 AGEING CONTINUOUS TIME RANDOM WALKS 103
4.2.1 FROM RENEWAL THEORY TO CONTINUOUS TIME RANDOM WALKS 103
4.2.2 POPULATION SPLITTING 104
4.2.3 ANALYSIS OF MEAN SQUARED DISPLACEMENTS 106
4.2.4 AGEING ENSEMBLE AND TIME AVERAGES 110
4.2.5 INTERPLAY OF AGEING AND INTERNAL RELAXATION 113
5 DISCUSSION AND OUTLOOK 121
LIST OF FIGURES 127
BIBLIOGRAPHY 129
VI
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| spelling | Schulz, Johannes H. P. Verfasser aut Ageing and memory effects in anomalous diffusion processes Johannes H. P. Schulz 2014 VI, 136 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2014 (DE-588)4113937-9 Hochschulschrift gnd-content Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20140219-1188463-0-6 http://mediatum.ub.tum.de/node?id=1188463 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20140219-1188463-0-6 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027170595&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schulz, Johannes H. P. Ageing and memory effects in anomalous diffusion processes |
| subject_GND | (DE-588)4113937-9 |
| title | Ageing and memory effects in anomalous diffusion processes |
| title_auth | Ageing and memory effects in anomalous diffusion processes |
| title_exact_search | Ageing and memory effects in anomalous diffusion processes |
| title_full | Ageing and memory effects in anomalous diffusion processes Johannes H. P. Schulz |
| title_fullStr | Ageing and memory effects in anomalous diffusion processes Johannes H. P. Schulz |
| title_full_unstemmed | Ageing and memory effects in anomalous diffusion processes Johannes H. P. Schulz |
| title_short | Ageing and memory effects in anomalous diffusion processes |
| title_sort | ageing and memory effects in anomalous diffusion processes |
| topic_facet | Hochschulschrift |
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