Biological matter is driven far from thermodynamic equilibrium by active processes on the molecular scale. These processes are usually driven by the chemical reaction of a fuel and generate spontaneous movements and mechanical stresses in the system, even in the absence of external forces or torques. Moreover these active stresses effectively fluidify the material. The cell cytoskeleton, suspensions of swimming microorganisms or tissues are prominent examples of active fluids. Active processes in biological systems often exhibit chiral asymmetries. Examples are the chirality of cytoskeletal filaments which interact with motor proteins, the chirality of the beat of cilia and flagella as well as the helical trajectories of many biological micro-swimmers. Moreover, large scale chiral flows have been observed in the cell cortex of C. elegans and Xenopus embryos. Active force generation induces force and torque dipoles in the material. If all forces are internal the total force and torque vanish as required by the conservation of momentum and angular momentum. The density of force dipoles is an active stress in the material. In addition, active chiral processes allow for the existence of active torque dipoles which enter the conservation of angular momentum and generate an active antisymmetric stress and active angular momentum fluxes. We developed a generic description of active fluids that takes into account active chiral processes and explicitly keeps track of spin and orbital angular momentum densities. We derived constitutive equations for an active chiral fluid based on identifying the entropy production rate from the rate of change of the free energy and linearly expanding thermodynamic fluxes in terms of thermodynamic forces. We identified four elementary chiral motors that correspond to localized distributions of chiral force and torque dipoles that differ by their symmetry and produce different chiral fluid flows and intrinsic rotation fields. We employ our theory to analyze different active chiral processes. We first show that chiral flows can occur spontaneously in an active fluid even in the absence of chiral processes. For this we investigate the Taylor-Couette motor, that is an active fluid confined between two concentric cylinders. For sufficiently high active stresses the fluid generates spontaneous rotations of the two cylinders with respect to each other thus breaking the chiral symmetry of the system spontaneously. We then investigate cases where active chiral processes on the molecular scale break the chiral symmetry of the whole system. We show that chiral flows occur in films of chiral motors and derive a generic theory for thin films of active fluids. We discuss our results in the context of carpets of beating cilia or E. coli swimming close to a surface. Finally, we discuss chiral flows that are observed in the cellular cortex of the nematode C. elegans at the one cell stage. Two distinct chiral flow events are observed. The first chiral flow event (i) is a screw like chiral rotation of the two cell halves with respect to each other and occurs around 15min after fertilization. This event coincides with the establishment of cortical cell polarity. The second chiral flow event (ii) is a chiral rotation of the entire cell cortex around the anterior posterior axis of the whole cell and occurs around 30min after fertilization. Measuring densities of molecular motors during episode (i) we fit the flow patterns observed using only two fit parameters: the hydrodynamic length and cortical chirality. The flows during (ii) can be understood assuming an increase of the hydrodynamic length. We hypothesize that the cell actively regulates the cortical viscosity and the friction of the cortex with the eggshell and cytosol. We show that active chiral processes in soft biological matter give rise to interesting new physics and are essential to understand the material properties of many biological systems, such as the cell cortex.

Biological matter is driven far from thermodynamic equilibrium by active processes on the molecular scale. These processes are usually driven by the chemical reaction of a fuel and generate spontaneous movements and mechanical stresses in the system, even in the absence of external forces or torques. Moreover these active stresses effectively fluidify the material. The cell cytoskeleton, suspensions of swimming microorganisms or tissues are prominent examples of active fluids. Active processes in biological systems often exhibit chiral asymmetries. Examples are the chirality of cytoskeletal filaments which interact with motor proteins, the chirality of the beat of cilia and flagella as well as the helical trajectories of many biological micro-swimmers. Moreover, large scale chiral flows have been observed in the cell cortex of C. elegans and Xenopus embryos. Active force generation induces force and torque dipoles in the material. If all forces are internal the total force and torque vanish as required by the conservation of momentum and angular momentum. The density of force dipoles is an active stress in the material. In addition, active chiral processes allow for the existence of active torque dipoles which enter the conservation of angular momentum and generate an active antisymmetric stress and active angular momentum fluxes. We developed a generic description of active fluids that takes into account active chiral processes and explicitly keeps track of spin and orbital angular momentum densities. We derived constitutive equations for an active chiral fluid based on identifying the entropy production rate from the rate of change of the free energy and linearly expanding thermodynamic fluxes in terms of thermodynamic forces. We identified four elementary chiral motors that correspond to localized distributions of chiral force and torque dipoles that differ by their symmetry and produce different chiral fluid flows and intrinsic rotation fields. We employ our theory to analyze different active chiral processes. We first show that chiral flows can occur spontaneously in an active fluid even in the absence of chiral processes. For this we investigate the Taylor-Couette motor, that is an active fluid confined between two concentric cylinders. For sufficiently high active stresses the fluid generates spontaneous rotations of the two cylinders with respect to each other thus breaking the chiral symmetry of the system spontaneously. We then investigate cases where active chiral processes on the molecular scale break the chiral symmetry of the whole system. We show that chiral flows occur in films of chiral motors and derive a generic theory for thin films of active fluids. We discuss our results in the context of carpets of beating cilia or E. coli swimming close to a surface. Finally, we discuss chiral flows that are observed in the cellular cortex of the nematode C. elegans at the one cell stage. Two distinct chiral flow events are observed. The first chiral flow event (i) is a screw like chiral rotation of the two cell halves with respect to each other and occurs around 15min after fertilization. This event coincides with the establishment of cortical cell polarity. The second chiral flow event (ii) is a chiral rotation of the entire cell cortex around the anterior posterior axis of the whole cell and occurs around 30min after fertilization. Measuring densities of molecular motors during episode (i) we fit the flow patterns observed using only two fit parameters: the hydrodynamic length and cortical chirality. The flows during (ii) can be understood assuming an increase of the hydrodynamic length. We hypothesize that the cell actively regulates the cortical viscosity and the friction of the cortex with the eggshell and cytosol. We show that active chiral processes in soft biological matter give rise to interesting new physics and are essential to understand the material properties of many biological systems, such as the cell cortex.

Active matter describes systems that convert energy from their environment into directed motion. Therefore, these systems are in intrinsic nonequilibrium, unlike their passive counterparts. From a theoretical point of view, such active systems have been modeled by agent-based models, as well as hydrodynamic approaches, which allowed for the investigation of a wide range of observed collective phenomena characterizing active matter. In this thesis we develop a microscopic field-theoretical approach to describe generic properties of active systems. This description combines the phase field crystal model with a polar order parameter and a self-propulsion term. First, we validate this approach by reproducing results obtained with corresponding agent-based models, such as binary collisions, collective migration and vortex formation. We also perform a direct comparison between our model and a microscopic phase field description of active matter. Next, we use this continuum approach to simulate some larger active systems and to analyze the coarsening process in active crystals, as well as the mechanisms leading to mobile clusters. We show the generality of our approach by extending it to binary mixtures of interacting active and passive particles. Also in this case, we first validate the model by reproducing known results, such as enhanced crystallization via active doping and the suppression of collective migration in an active bath in the presence of fixed obstacles. Interestingly, for the regime of mobile passive particles in an active bath a laning state is found, which is characterized by an alignment of the active particles that is globally nematic, but polar within each lane. This state represents a theoretical prediction feasible to be validated experimentally. Finally, we explore the field of topological active matter. We develop an agent-based model to describe self-propelled particles on curved surfaces and study the complex spatiotemporal patterns that emerge. / Aktive Materie beschreibt Systeme, die Energie aus ihrer Umgebung in gerichtete bewegung umwandeln. Im Gegensatz zur passiven Materie befinden sich diese Systeme nie im physikalischen Gleichgewicht und offenbaren dadurch interessante physikalische Phänomene. Vom theoretischen Standpunkt her wurde aktive Materie bereits simuliert, typischerweise durch agenten-basierte Modelle oder hydrodynamische Ansätze, die es ermöglichen eine Vielzahl der auftretenden kollektiven Bewegungsprinzipien zu untersuchen. In dieser Doktorarbeit entwickeln wir einen mikroskopischen Kontinuumsansatz um die generischen Eigenschaften von aktiven Systemen zu untersuchen. Unsere Beschreibung kombiniert das Phasenfeld-Kristall Modell mit einem polaren Ordnungsparameter und einem Antriebsterm. Zuerst validieren wir den Ansatz durch Reproduktion bekannter Ergebnisse agenten-basierter Modelle, wie binäre Kollisionen, kollektive Bewegung und Wirbelformationen. Des Weiteren führen wir einen direkten Vergleich zwischen unserem Modell und einer mikroskopischen Phasenfeldbeschreibung aktiver Materie durch. Danach nutzen wir den kontinuierlichen Ansatz um große aktive Systeme zu simulieren und analysieren den Vergröberungsprozess in aktiven Kristallen und Mechanismen der mobilen Aggregatbildung. Wir illustrieren die Allgemeingültigkeit unseres Simulationsansatzes durch die Erweiterung auf binäre Systeme, in denen sowohl aktive als auch passive Partikel enthalten sind. Auch in diesem Fall validieren wir das Modell durch Vergleiche mit bekannten Resultaten, wie zum Beispiel die verstärkte Kristallisation durch aktives Doping oder die Unterdrückung kollektiver Bewegung durch die Einführung von Hindernissen in einem aktiven Bad. Interessanterweise finden wir bei der Präsenz mobiler passiver Partikel in einem aktiven Bad einen Fahrspur-Zustand, in welchem die aktiven Partikel nematische Fahrspuren bilden und sich nur jeweils innerhalb einer Fahrspur nematisch polar anordnen. Dieser bisher unbekannte Zustand stellt eine theoretische Vorhersage dar, die experimentell geprüft werden kann. Schließlich begeben wir uns auf das Gebiet der topologischen aktiven Materie. Wir entwickeln ein agenten-basiertes Modell um selbst-angetriebene Partikel auf gekrümmten Oberflächen zu beschreiben und untersuchen die dabei auftretenden zeitlich und räumlich komplexen Muster.%, die dabei auftreten.

No description available.