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TitleEffects of non-linearities and disorder in systems with multiple absorbing states. A perspective for modeling the dynamics of complex ecosystems.
AuthorBorile, Claudio
Subject(s)FIS/02 Fisica teorica, modelli e metodi matematici
AbstractInteracting particle systems are a particular class of stochastic processes where single degrees of freedom interact through probabilistic rules defined over a graph which reflects the spatial topology of the model. From the statistical mechanics point of view these models are of particular interest since they are genuinely out-of-equilibrium processes and introduce new universality classes and dynamical phase transitions. Among these processes, systems with absorbing states are characterized by points in the state-space in which the dynamics becomes trivial and, once reached, cannot be leaved. Because of the several possible interpretations, these models have found many applications in different areas of science: from condensed matter Physics to Biology, from Ecology to Sociology and Finance and also, in their quantum versions, to quantum control theory. Despite their importance for possible applications, though, a unified understanding of these systems is still lacking. In theoretical ecology, many open fundamental questions about the dynamics of ecosystems provide the cue for a further development of the theory of interacting particle systems. In particular, in this thesis we will address three main topics: i) Spontaneous neutral symmetry breaking. A central problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory provides gross patterns in accord with empirical observations, but its validity is still highly debated. In particular, it is not clear how this theory can originate the observed non-neutral dynamics. Within a completely species-symmetric theory, we demonstrate that nonlinear dynamics can lead to a stationary state characterized by both stability and biodiversity by spontaneously breaking the neutral symmetry. ii) Habitat heterogeneities. It is known that habitat can have a great impact on the dynamics of species. In its most basic level of abstraction, its effects can be mimicked by an interacting particle system in a quenched random external field that locally breaks the species symmetry. We propose here an effective solution of the model in the long-times limit. iii) Role of boundary conditions. For non-equilibrium systems near a critical point, little is known about the role of the boundary conditions to the global phase diagram of the system. We analyze here a paradigmatic non-equilibrium critical model with mixed symmetry-preserving boundary conditions.
Date2013-01-30
TypeTesi di dottorato
TypeNonPeerReviewed
Formatpdf
Identifierhttp://paduaresearch.cab.unipd.it/5819/1/Borile_Claudio_tesi.pdf
IdentifierBorile, Claudio (2013) Effects of non-linearities and disorder in systems with multiple absorbing states. A perspective for modeling the dynamics of complex ecosystems. [Tesi di dottorato]
Relationhttp://paduaresearch.cab.unipd.it/5819/