| Zugriffsnummer | 37533 |
| Dokumenttyp | Dissertation |
| Peer Review | unbekannt |
| Sprache | Englisch |
| Titel | On nonequilibrium statistical physics of self-propelled particles - from single-particle transport to emergent macroscopic patterns |
| Autor(in); Institution |
Großmann, Robert; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin; 4.2, Bild- und Wellenoptik, PTB-Braunschweig
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| Quelle/Jahr | (2016), VIII, 168 S. |
| Dissertationsvermerk | Dissertation, Technische Universität Berlin, 2016 |
| Verlag | Berlin: |
| Freie Schlagworte | active matter ; pattern formation ; nonequilibrium statistical mechanics ; collective dynamics |
| Zusammenfassung | Pattern formation in active matter is a paradigm for self-organization far from thermodynamic equilibrium. The term active matter refers to complex systems composed of self-propelled particles which are characterized by the ability to convert energy of their surroundings into kinetic energy. This thesis contributes to the theoretical description of active matter. A central concern is the relation of single-particle transport properties and the collective Dynamics resulting from inter-particle interactions. Equations for measurable observables are therefore analytically derived from particle-based models thereby allowing to link the dynamics on different length- and timescales as well as several levels of complexity. In the first part, diffusion properties of individual self-propelled particles are analyzed. Based on a geometric perspective on self-propelled motion, a model is derived within which the dynamics of active particles in isotropic as well as anisotropic environments is described in a unified framework. In this context, the mathematical apparatus used in this work, which is based on the theory of stochastic processes and nonlinear dynamics, is illustrated. Furthermore, a stochastic clock model for the intra-particular processes that control changes in the direction of motion is proposed. Resulting predictions are compared to experimental data from observations of microorganisms and, in particular, the existence of optimal parameter values – in the sense of a maximization of the diffusivity – is reported. The second part of this thesis is concerned with kinetic and hydrodynamic theories for the description of emergent structures in self-propelled particle systems interacting via a velocity-alignment mechanism. Throughout, the focus of the investigation is thereby on the identification of essential interaction mechanisms that lead to certain large-scale structures. Along these lines, the turbulent-like vortex dynamics as observed in dense bacterial suspensions is traced back to the interplay of competing velocity-alignment interactions. Further, the alignment-induced aggregation of particles which in turn leads to the formation of ordered, large-scale density bands is interpreted physically as a nonequilibrium phase-separation process. Potential control mechanisms for these pattern-formation phenomena are discussed. Finally, the general question how the motion of locally interacting individual entities, in turn implying a dynamic interaction network, affects the emergence of order in nonequilibrium systems is addressed. For this purpose, an ensemble of random walkers is studied each of which carries an internal degree of freedom (a phase oscillator or a classical spin vector) that adopts to the neighboring walkers. Notably, superdiffusive transport – in contrast to normal diffusion, in which case a defect-mediated Berezinskii-Kosterlitz-Thouless transition to quasi long-range order is observed – may cause a phase transition to long-range order in two dimensions. This is a genuine nonequilibrium phenomenon as the emergence of long-range order is impossible according to the Mermin-Wagner theorem in corresponding systems at thermodynamic equilibrium. |
