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Borile, 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]

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Abstract (inglese)

Interacting 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.

Abstract (italiano)

I sistemi di particelle interagenti sono una particolare classe di processi stocastici in cui singoli gradi di libertà interagiscono secondo leggi probabilistiche su di un grafo che definisce la particolare topologia spaziale del modello. Dal punto di vista meccanico - statistico questi modelli sono particolarmente interessanti in quanto sono genuinamente fuori equilibrio ed introducono nuove classi di universalità e transizioni di fase dinamiche. Tra questi processi, i sistemi con stati assorbenti sono caratterizzati da punti nello spazio delle fasi in cui la dinamica diventa banale e che una volta visitati non possono essere abbandonati. Date le numerose possibili interpretazioni, questi modelli hanno trovato numerose applicazioni in aree differenti: dalla Fisica alla Biologia, dall'Ecologia alla Sociologia e la Finanza, fino, nelle loro versioni quantistiche, alla teoria del controllo quantistico. Tuttavia, nonostante la loro importanza per le loro possibili applicazioni, è ancora carente una comprensione teorica unificata di questi sistemi.

In Ecologia teorica, molte domande fondamentali sulla dinamica degli ecosistemi forniscono lo spunto per uno sviluppo ulteriore della teoria dei sistemi di particelle interagenti. In particolare, in questa tesi affronteremo i seguenti argomenti: i) Rottura spontanea della simmetria neutrale. Un problema centrale in ecologia è la spiegazione dei meccanismi responsabili della biodiversità e della stabilità. La teoria neutrale fornisce risultati in accordo con le osservazioni sperimentali, ma la sua validità è ancora fortemente dibattuta. In particolare, non è chiaro come essa possa produrre gli effetti non neutrali osservati. In una teoria completamente specie-simmetrica, dimostriamo che dinamiche non lineari posso produrre uno stato stazionario caratterizzato da stabilità ed una ricca biodiversità tramite la rottura spontanea della simmetria neutrale. ii) Habitat eterogeneo. E' noto che l'habitat può influenzare grandemente la dinamica di un ecosistema. In prima approssimazione, questi effetti possono essere mimati introducendo un campo esterno aleatorio di tipo <<quenched>> che rompe localmente la simmetria tra specie. Proponiamo qui una soluzione efficace di questo problema nel limite di tempi lunghi. iii) Ruolo delle condizioni al contorno. Per i sistemi fuori dall'equilibrio vicino a punti critici si conosce poco sul ruolo delle condizioni al contorno sul diagramma di fase del sistema. Noi studiamo un importante modello critico fuori dall'equilibrio con condizioni miste al contorno che preservano la simmetria globale del sistema.

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Tipo di EPrint:Tesi di dottorato
Relatore:Maritan, Amos
Dottorato (corsi e scuole):Ciclo 25 > Scuole 25 > FISICA
Data di deposito della tesi:30 Gennaio 2013
Anno di Pubblicazione:30 Gennaio 2013
Parole chiave (italiano / inglese):Statistical Mechanics Theoretical Physics Ecology Interacting Particle Systems Disorder Dynamical Symmetry Absorbing
Settori scientifico-disciplinari MIUR:Area 02 - Scienze fisiche > FIS/02 Fisica teorica, modelli e metodi matematici
Struttura di riferimento:Dipartimenti > Dipartimento di Fisica e Astronomia "Galileo Galilei"
Codice ID:5819
Depositato il:16 Ott 2013 11:27
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