Analytic approaches to stochastic many-particle systems: Scaling and renormalization in microbial communities and in chemical kinetics
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | Volltext Volltext Inhaltsverzeichnis |
| Physical Description: | X, 138 S. Ill., graph. Darst. |
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| 100 | 1 | |a Winkler, Anton |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analytic approaches to stochastic many-particle systems |b Scaling and renormalization in microbial communities and in chemical kinetics |c von Anton Winkler |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
ZUSAMMENFASSUNG V
ABSTRACT VII
1 INTRODUCTION 1
1.1 THREE-SPECIES CYCLIC DOMINANCE 2
1.2 REACTION-DIFFUSION PROCESSES AND RATE EQUATIONS 6
2 THREE-SPECIES CYCLIC DOMINANCE WITH MUTATIONS 1 1
2.1 DEFINITION OF THE MODEL AND THE DUAL PICTURE 12
2.2 T H E MEAN-FIELD EQUATION AND LARGE MUTATION RATES 14
2.3 THE LIMIT OF LOW MUTATION RATES 16
2.3.1 MUTATIONS TO THE PREDATOR 16
2.3.2 FIRST CORRECTION FOR MUTATIONS T O THE PREDATOR 17
2.3.3 MUTATIONS TO THE PREY 20
2.3.4 THE GENERAL CASE 21
2.4 THE LOW DENSITY LIMIT AND DETAILED BALANCE 23
2.4.1 EXACT SOLUTION T O THE STATIONARY STATE 25
2.4.2 PROOF OF DETAILED BALANCE 28
2.4.3 VIOLATION OF DETAILED BALANCE FOR ASYMMETRIC REACTION RATES 30
2.4.4 TIME SCALE SEPARATION AND RECOVERY OF DETAILED BALANCE 30
2.5 CONCLUSION 35
3 NPRG AND REACTION-DIFFUSION PROCESSES 3 7
3.1 T H E FOURIER TRANSFORM AND INTEGRATION CONVENTIONS 38
3-2 SECOND QUANTIZED REPRESENTATION OF REACTION-DIFFUSION SYSTEMS 39
3.3 MAPPING TO A FIELD THEORY 43
3.4 T H E WETTERICH EQUATION 47
3.5 MEAN-FIELD AND THE EQUATION OF MOTION 53
3.6 T H E DERIVATIVE EXPANSION 54
3.7 DIMENSIONLESS FLOW EQUATION 58
4 RENORMALIZATION O F T H E COAGULATION PROCESS BELOW T H E CRITICAL
DIMENSION 6 3
4.1 MATHEMATICAL PROPERTIES OF THE EFFECTIVE AVERAGE ACTION 64
4.2 THE ONE-LOOP EXPANSION AND RESTRICTIONS ON THE FLOW EQUATION 66
4.3 RELATION BETWEEN THE COAGULATION PROCESS AND THE ANNIHILATION
PROCESS . . . 72 4.4 T H E FIXED POINT AND THE UPPER CRITICAL DIMENSION
74
4.5 STUDY IN ONE DIMENSION 75
4.6 STUDY FOR D, D C 79
HTTP://D-NB.INFO/1031112650
IMAGE 2
X C O N T E N T S
4.7 STUDY FOR THE CRITICAL DIMENSION 81
4.8 CONCLUSION 83
5 NON-UNIVERSALITY ABOVE T H E CRITICAL DIMENSION 8 5
5.1 ONE-SITE OBJECTS ON A CUBIC LATTICE 86
5.2 EXACTNESS OF THE LOCAL POTENTIAL APPROXIMATION FOR ONE-SITE OBJECTS
. . . . 90
5.3 DIRECT MEASUREMENT OF THE NON-EQUILIBRIUM FORCE 93
5.4 GENERALIZATION T O EXTENDED OBJECTS ON BRAVAIS LATTICES 94
5.5 EXAMPLES OF EXTENDED OBJECTS 96
5.6 GENERAL EXACT FLOW EQUATION 100
5.7 THREE TYPES OF EXACT FLOW EQUATIONS 102
5.8 THREE-PARTICLE COAGULATION 103
5.9 CONCLUSION 104
6 VIOLATION O F T H E LAW O F MASS ACTION IN THREE AND HIGHER DIMENSIONS
105
6.1 THE KINETIC EQUATION 106
6.2 UNIVERSAL CORRECTION IN THREE DIMENSIONS 107
6.3 UNIVERSAL AND NON-UNIVERSAL EFFECTS IN ARBITRARY DIMENSIONS 113
6.3.1 ANALYSIS UP TO THE FIRST FLUCTUATION CORRECTION 114
6.3.2 THE GENERAL PICTURE 116
6.4 CONCLUSION 118
A SMOLUCHOWSKI THEORY FOR FINITE COAGULATION RATES IN THREE DIMENSIONS 1
1 9
B CORRECTION T O T H E INTERFACE DENSITY 1 2 1
B . L MUTATIONS TO THE PREDATOR 121
B.2 MUTATIONS T O THE PREY 124
BIBLIOGRAPHY 127
DANKSAGUNG 139
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| spelling | Winkler, Anton Verfasser aut Analytic approaches to stochastic many-particle systems Scaling and renormalization in microbial communities and in chemical kinetics von Anton Winkler 2012 X, 138 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Univ., Diss., 2012 (DE-588)4113937-9 Hochschulschrift gnd-content Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:19-151131 https://nbn-resolving.org/urn:nbn:de:bvb:19-151131 Resolving-System kostenfrei Volltext https://edoc.ub.uni-muenchen.de/15113/ Verlag kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025493999&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Winkler, Anton Analytic approaches to stochastic many-particle systems Scaling and renormalization in microbial communities and in chemical kinetics |
| subject_GND | (DE-588)4113937-9 |
| title | Analytic approaches to stochastic many-particle systems Scaling and renormalization in microbial communities and in chemical kinetics |
| title_auth | Analytic approaches to stochastic many-particle systems Scaling and renormalization in microbial communities and in chemical kinetics |
| title_exact_search | Analytic approaches to stochastic many-particle systems Scaling and renormalization in microbial communities and in chemical kinetics |
| title_full | Analytic approaches to stochastic many-particle systems Scaling and renormalization in microbial communities and in chemical kinetics von Anton Winkler |
| title_fullStr | Analytic approaches to stochastic many-particle systems Scaling and renormalization in microbial communities and in chemical kinetics von Anton Winkler |
| title_full_unstemmed | Analytic approaches to stochastic many-particle systems Scaling and renormalization in microbial communities and in chemical kinetics von Anton Winkler |
| title_short | Analytic approaches to stochastic many-particle systems |
| title_sort | analytic approaches to stochastic many particle systems scaling and renormalization in microbial communities and in chemical kinetics |
| title_sub | Scaling and renormalization in microbial communities and in chemical kinetics |
| topic_facet | Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:bvb:19-151131 https://edoc.ub.uni-muenchen.de/15113/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025493999&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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