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Dissertation angenommen durch: Universität Duisburg-Essen, Campus
Duisburg, Fakultät für Naturwissenschaften, Institut für Physik,
2004-11-30
BetreuerIn: Prof. Dr. Haye Hinrichsen , Universität Wuerzburg, Fakultät für Naturwissenschaften, Institut für Physik
GutachterIn: Prof. Dr. Haye Hinrichsen , Universität Wuerzburg, Fakultät für Naturwissenschaften, Institut für Physik
GutachterIn: Prof. Dr. Klaus Usadel , Universität Duisburg-Essen, Campus Duisburg, Fakultät für Naturwissenschaften, Institut für Physik
Schlüsselwörter in Englisch: computer simulations, spreading processes, nonequilibrium, directed percolation, aggregation,coagulation, phase transition
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Abstrakt in Englisch
In this thesis, several stochastic models are investigated, which are
subjected to irreversible dynamics. Motivation for the presented work
stems, on the one hand, from particular physical systems under
consideration, which are modeled by the studied stochastic processes.
Besides that, the models discussed in this thesis are, on the other
hand, generally interesting from the point of view of statistical
physics, since they describe systems far from thermodynamic
equilibrium. Interesting properties to be encountered are, e.g.,
dynamical scaling behavior or continuous phase transitions. The first
issue to be addressed, is the investigation of irreversibly aggregating
systems, where the main emphasis is laid on aggregation of monopolarly
charged clusters suspended in a fluid. For this purpose, rate equations
are analyzed and Brownian dynamics simulations are performed. It is
shown that the system crosses over from power-law cluster growth to
sub-logarithmic cluster growth. Asymptotically, the cluster size
distribution evolves towards a universal scaling form, which implies a
'self-focussing' of the size distribution. Another emphasis of this
thesis is the investigation of nonequilibrium critical phenomena, in
particular, the study of phase transitions into absorbing states
(states that may be reached irreversibly). To this end, the continuous
nonequilibrium phase transition of directed percolation, which serves
as a paradigm for absorbing-state phase transitions, is analyzed by a
novel approach. Despite the lack of a partition function for directed
percolation, this novel approach follows the ideas of Yang-Lee theory
of equilibrium statistical mechanics, by investigating the complex
roots of the survival probability. Stochastic models such as directed
percolation mimic spreading processes, e.g., the spreading of an
infectious disease. The effect of long-time memory, which is not
included in directed percolation and which corresponds to immunization
in epidemic spreading, is investigated through an appropriate model.
This model includes dynamical percolation (perfect immunization) as a
special case, as well as directed percolation (no immunization). The
critical behavior of this model is studied by means of Monte Carlo
simulations, in particular for weak immunization. A further
generalization is investigated, which allows spontaneous mutations and
different species of spreading agents (pathogens). Restricting the
analysis to perfect immunization and two spatial dimensions, it is
shown by Monte Carlo simulations, that immunization leads to a
crossover from dynamical to directed percolation. Other properties of
this model are discussed in detail.
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