The role of structures in collective processes [Elektronische Ressource] : social dynamics and molecular self-assembly / vorgelegt von Marta Balbás Gambra

Marta Balbás Gambra

Sujets

• Physik

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2009
• Nombre de lectures: 16
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

The role of structures in collective processes
social dynamics and molecular self-assembly
Marta Balbás Gambra
Munich December 2009The role of structures in collective processes
social dynamics and molecular self-assembly
Marta Balbás Gambra
Dissertation
an der Fakultät für Physik
der Ludwig-Maximilians-Universität
München
vorgelegt von
Marta Balbás Gambra
aus Madrid
München, den 11. Dezember 2009Gutachter: Prof. Dr. Erwin Frey
Prof. Dr. Stephan Kehrein
Tag der mündlichen Prüfung: 29. Januar 2010a mi madreContents
Zusammenfassung vii
Abstract ix
1 Evolutionary social dynamics 1
1.1 Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Square lattices . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Random graphs . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.3 The Watts-Strogatz model . . . . . . . . . . . . . . . . . . . 6
1.1.4 Scale free networks . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Modelling social systems . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.1 Evolutionary game theory . . . . . . . . . . . . . . . . . . . 10
1.2.2 Opinion models . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2.3 Infection models . . . . . . . . . . . . . . . . . . . . . . . . 22
2 The evolution of mafias 25
2.1 Towards a mathematical description . . . . . . . . . . . . . . . . . . 26
2.2 Deterministic mean field approximation . . . . . . . . . . . . . . . . 29
2.2.1 Symmetric model (SM) . . . . . . . . . . . . . . . . . . . . 29
2.2.2 Fully asymmetric model (FAM) . . . . . . . . . . . . . . . . 31
2.2.3 Fully policed model (FAPM) . . . . . . . . . . . 33
2.3 The role of social structures . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.1 Symmetric model . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.2 Fully asymmetric model . . . . . . . . . . . . . . . . . . . . 44
2.3.3 Fully policed model . . . . . . . . . . . . . . . . 51
2.4 Individuals may move . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.1 Symmetric model . . . . . . . . . . . . . . . . . . . . . . . . 62
2.4.2 Fully asymmetric model . . . . . . . . . . . . . . . . . . . . 66
2.4.3 Local mean field approximation in square lattices . . . . . . . 70
2.4.4 Fully asymmetric policed model . . . . . . . . . . . . . . . . 73
2.5 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . 79
iiiiv Contents
3 Pattern diversity in self-assembled monolayers 81
3.1 Self-assembly and order in two dimensional systems . . . . . . . . . 82
3.1.1 The principles of self-assembly of monolayers . . . . . . . . 82
3.1.2 Fréchet dendrons as building blocks . . . . . . . . . . . . . . 84
3.1.3 Understanding order in two dimensional systems . . . . . . . 85
3.2 Experimental observations . . . . . . . . . . . . . . . . . . . . . . . 86
3.3 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.1 The interaction-site model . . . . . . . . . . . . . . . . . . . 89
3.3.2 Theoretically predicted ordered motifs . . . . . . . . . . . . . 91
3.3.3 Theory versus experiment . . . . . . . . . . . . . . . . . . . 96
3.4 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . 99
Appendices
A Agent based stochastic simulations 101
B Building uncorrelated scale free networks 103
C Monte Carlo simulations 105
Bibliography 108
List of publications 119
Acknowledgements 121List of Figures
1.1 Square lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Random and complete graphs . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Watts-Strogatz model . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Barabási-Albert graph . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Scale free graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 SM: bifurcation diagram . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 SM: stability diagram and separatrix . . . . . . . . . . . . . . . . . . 31
2.3 FAM: bifurcation diagram . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 FAM: stability diagram and separatrix . . . . . . . . . . . . . . . . . 33
2.5 FAPM: bifurcation diagram . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 FAPM: stability diagram and separatrix . . . . . . . . . . . . . . . . 35
2.7 Neighbourhoods on structures . . . . . . . . . . . . . . . . . . . . . 37
2.8 Degree distribution of scale free networks . . . . . . . . . . . . . . . 38
2.9 SM: phase portrait for exemplary parameters . . . . . . . . . . . . . . 39
2.10 SM: deterministic versus stochastic mean field stationary states . . . . 40
2.11 SM: stationary state for structures . . . . . . . . . . . . . . . . . . . 41
2.12 SM: mafia fraction and extinction probability on structures . . . . . . 42
2.13 SM: extinction as a function of on SFN . . . . . . . . . . . . . . . 42
2.14 SM: nucleation process on a lattice . . . . . . . . . . . . . . . . . . . 43
2.15 Extinction-coexistence transition as a function of the strength of the
mafia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.16 FAM: stationary state for structures . . . . . . . . . . . . . . . . . . 45
2.17 FAM: evolution of an isolated mafioso . . . . . . . . . . . . . . . . . 47
2.18 FAM: mafia fraction and extinction probability on structures . . . . . 48
2.19 FAM: nucleation process on a lattice . . . . . . . . . . . . . . . . . . 49
2.20 FAM: mafia fraction on a lattice—heuristic versus simulation . . . . . 50
2.21 FAM: mafia fractions as a function of on scale free networks . . . . 50
2.22 FAPM: stationary state for structures . . . . . . . . . . . . . . . . . . 52
2.23 FAPM: state for a square lattice where control elements dif-
fuse randomly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.24 FAPM: snapshot of the population structure on a square lattice . . . . 53
2.25 FAPM: mafia fraction and extinction probability on structures . . . . 54
2.26 FAPM: extinction-coexistence transition as a function of for SFN . . 55
2.27 FAPM: mafia fraction as a function of on SFN . . . . . . . . . . . . 55
2.28 Degree and cumulated degree distribution for a = 2:5 SFN . . . . . 56
vvi List of Figures
2.29 FAPM: Mafia fraction and extinction probability for police distribu-
tionsp andp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 2
2.30 FAPM: preferential police’s attachment to hubs . . . . . . . . . . . . 58
2.31 FAPM: extinction transition as a function ofp for three distributions
of the control elements . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.32 FAPM: population fractions for three distributions of the control ele-
ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.33 Active versus passive diffusion . . . . . . . . . . . . . . . . . . . . . 62
2.34 SM: directed diffusion of citizens . . . . . . . . . . . . . . . . . . . . 64
2.35 SM: dif of mafia and both species . . . . . . . . . . . . 65
2.36 SM: undirected diffusion of mafia . . . . . . . . . . . . . . . . . . . 65
2.37 FAM: directed diffusion of citizens . . . . . . . . . . . . . . . . . . . 67
2.38 FAM: dif of both species as a function of heterogeneity 69
2.39 Neighbourhood configurations on a square lattice . . . . . . . . . . . 70
2.40 FAM: stability diagram for the local mean field approximation . . . . 72
2.41 FAPM: directed diffusion of citizens, mafiosi, and both species . . . . 75
2.42 FAPM: undirected diffusion of and both species . . . 77
2.43 FAPM: directed and undirected mobility in various structures—population
fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.1 Dendrons chemical configuration . . . . . . . . . . . . . . . . . . . . 87
3.2 Experimental monolayers . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3 Molecular mechanics energy minimized Fréchet dendron . . . . . . . 88
3.4 Interaction-site model . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.5 Molecular conformations for a 8/12 dendron . . . . . . . . . . . . . . 92
3.6 Theoretically predicted supralayers for Fréchet dendrons 8/12 and 8/8 93
3.7 Zig-zag pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.8 Stability for the 8/12 molecule as a function ofa andT . . . . . . . . 96
3.9 Exemplary transition from the sawtooth pattern to disorder . . . . . . 97
3.10 Ground state energies for the 8/12 molecule as a function ofa . . . . 98
C.1 First image algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 107