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Locatelli, Emanuele (2014) Dynamical and collective properties of active and passive particles in Single File. [Tesi di dottorato]

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Abstract (inglese)

Particles motion inside complex, irregular or crowded environments is a common phenomenon ranging from microscopic to macroscopic scales. It can be involved in everyday practical problems, like traffic, in fundamental biological mechanisms, like growth and reproduction of cells, and in important industrial or chemical applications, like oil catalysis. In many cases, transport in crowded environments is guided by 'active' elements, i.e. units that consume energy in order to produce motion. Among systems belonging in this class, the diffusion of hard-core particles in a channel so narrow they cannot pass each other, known as Single File Diffusion, has assumed a particular role. Single File Diffusion is responsible for the transport of ions in membrane channels, the diffusion in nano- and micro-porous materials and has been observed in many other natural and artificial systems.
Aim of this thesis is to investigate Single File system of passive (purely diffusive) or active (self propelled) particles, focusing on the effects of the activity on the Single File motion and on the Single File properties in the presence of absorbing boundaries. Most of the work has been carried out developing analytical and numerical tools within the framework of the Stochastic Processes. By using single particle techniques in a microfluidic approach, we obtained an excellent comparison between experimental data and numerical model of particles emptying a Single File channel with open ends.
In this thesis, after a brief introduction in the framework of confined diffusion processes, we will review the most relevant works in the theoretical and experimental literature of Single File Diffusion, with particular attention to an analytical technique, the Reflection Principle Method, which will be extensively used in this thesis. We will investigate the properties of Single File systems of diffusing particles in presence of two absorbing boundaries, with particular interest to the survival probability, i.e. the probability to find a particle between the boundaries at time t. We will provide an analytical solution of the emptying process, i.e. we calculate the probability characterizing the progressive decrease of the number of particles in the presence of absorbing boundaries, and for the survival probability of a Tagged Particle within the file, either in the presence or in the absence of a constant external force. We also characterize the trend of the characteristic survival times (also called Mean First Passage Times) as function of the system size and of the initial number of particles. We also investigate numerically the case when only the central particle is affected by the absorbing boundaries. We find an exponential decay of the survival probability, as it happens for normal diffusive processes, even in the presence of overcrowding. We will then introduce activity in a Single File system, through a Self-Propelled Particle model, for which we will provide a detailed characterization. In particular, within this model, particles can be either runners or tumblers, if their motion is dominated by straight runs or by changes of direction, respectively. Under Single File conditions, runners tend to form dynamical aggregates: these clusters are continuously formed and disassembled due to random fluctuations of the activity. For tumblers, the survival probabilities are still well described by the analytical theory developed for passive diffusing particles. Conversely, the formation of dynamical clusters enhances anomalous behaviours in the characteristic survival times of runners and induces a remarkable capacity to overcome the action of an external force.

Abstract (italiano)

Il moto di particelle in mezzi irregolari, complessi o affollati è un fenomeno comune, dalla scala microscopica a quella macroscopica. Lo si può incontrare tanto in situazioni comuni, come il traffico, quanto in meccanismi biologici, come la riproduzione e la crescita delle cellule, e in importanti processi chimici e tecnologici, come la catalisi di idrocarburi. In molti casi, il trasporto in mezzi confinati o affollati è guidato da elementi 'attivi', cioè unità che consumano energia per sostenere il loro stato di moto. Fra i diversi sistemi soggetti a confinamento, particolare rilevanza è rivestita dalla diffusione di sfere impenetrabili in un canale così stretto da non permettere il passaggio di più di una particella alla volta, conosciuto come diffusione in Single File. La diffusione in Single File è il meccanismo responsabile del trasporto di ioni attraverso la membrana cellulare, della diffusione in materiali micro e nanoporosi ed è stata osservata in molti altri sistemi naturali ed artificiali.
Scopo di questa tesi è lo studio su scala mesoscopica di particelle passive (diffusive) o attive (auto-propellenti) in condizioni di Single File, con particolare attenzione all'effetto dell'attività sulla dinamica e sulle proprietà delle particelle nel caso siano presenti condizioni al contorno assorbenti. Gran parte del lavoro è stato svolto nello sviluppo di risultati analitici e numerici nel contesto dei Processi Stocastici. Inoltre, mediante tecniche di manipolazione ottica di singola particella in canali microfluidici, abbiamo ottenuto una eccellente confronto fra dati sperimentali e numerici per il processo di svuotamento di un sistema di particelle in condizioni di Single File.
In questa tesi, dopo una breve introduzione ai processi diffusivi fortemente confinati, passeremo in rassegna i lavori più rilevanti della letteratura teorica e sperimentale sulla Single File Diffusion, con particolare attenzione ad un formalismo matematico, il Reflection Principle Method, che sarà applicato in maniera estensiva nel corso della tesi. Studieremo poi le proprietà di un sistema di particelle diffusive in Single File in presenza di condizioni al contorno assorbenti, concentrandoci sulla survival probability, cioè la probabilità di trovare una particella fra gli estremi del sistema al tempo t. Mostreremo come, in condizioni di Single File, abbiamo ottenuto una soluzione analitica per il processo di svuotamento, cioè calcoleremo la probabilità che caratterizza la progressiva diminuzione del numero di particelle in presenza di condizioni al contorno assorbenti, e per la survival probability di una particella 'marcata' all'interno della Single File sia in presenza che in assenza di una forza esterna costante. Caratterizzeremo gli andamenti dei tempi caratteristici di sopravvivenza, chiamati Tempi Medi di Primo Passaggio, in funzione della taglia del canale e del numero iniziale di particelle. Indagheremo inoltre numericamente il caso in cui solo la particella centrale del sistema in Single File subisce l'effetto delle condizioni al contorno assorbenti. Osserviamo un decadimento esponenziale della survival probability, come accade nell'usuale moto Browniano, anche in presenza di estremo confinamento. Introdurremo l'attività nella Single File attraverso un modello di particelle Self-Propelled, di cui descriveremo le proprietà in dettaglio. In particolare in questo modello le particelle possono essere o runners o tumblers, a seconda che la loro traiettoria sia dominata da lunghi tratti rettilinei o da cambi di direzione. In condizioni di Single File, i runners tendono a formare aggregati dinamici: questi cluster vengono continuamente formati e distrutti dalle fluttuazioni casuali della forza propulsiva. Per i tumblers, le probabilità di sopravvivenza sono ben descritte dalla teoria analitica sviluppata per le particelle passive. Per contro, la formazione di cluster dinamici accresce i comportamenti anomali nei tempi caratteristici di sopravvivenza dei runners e ne induce una notevole capacità di opporsi all'azione di un campo esterno.

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Tipo di EPrint:Tesi di dottorato
Relatore:Pierno, Matteo
Correlatore:Baldovin, Fulvio - Orlandini, Enzo
Dottorato (corsi e scuole):Ciclo 26 > Scuole 26 > FISICA
Data di deposito della tesi:30 Gennaio 2014
Anno di Pubblicazione:30 Gennaio 2014
Parole chiave (italiano / inglese):Single File Diffusion, confined diffusion, anomalous diffusion, active motion, Survival Probability, Fractional Brownian Motion, dynamical clusters, emptying process, Mean First Passage Time, Microfluidics, optical traps, runner, tumbler, diffusione sotto confinamento, diffusione anomala, materia attiva, probabilità di sopravvivenza, cluster dinamici, processo di svuotamento, Tempo Medio di Primo Passaggio, Microfluidica, trappola ottica
Settori scientifico-disciplinari MIUR:Area 02 - Scienze fisiche > FIS/03 Fisica della materia
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:6771
Depositato il:21 Mag 2015 11:47
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