@misc{MokhtariPattersonHoefling, author = {Mokhtari, Zahra and Patterson, Robert I. A. and H{\"o}fling, Felix}, title = {Spontaneous trail formation in populations of auto-chemotactic walkers}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-84466}, abstract = {We study the formation of trails in populations of self-propelled agents that make oriented deposits of pheromones and also sense such deposits to which they then respond with gradual changes of their direction of motion. Based on extensive off-lattice computer simulations aiming at the scale of insects, e.g., ants, we identify a number of emerging stationary patterns and obtain qualitatively the non-equilibrium \add{state} diagram of the model, spanned by the strength of the agent--pheromone interaction and the number density of the population. In particular, we demonstrate the spontaneous formation of persistent, macroscopic trails, and highlight some behaviour that is consistent with a dynamic phase transition. This includes a characterisation of the mass of system-spanning trails as a potential order parameter. We also propose a dynamic model for a few macroscopic observables, including the sub-population size of trail-following agents, which captures the early phase of trail formation.}, language = {en} } @misc{StraubeWinkelmannHoefling, author = {Straube, Arthur and Winkelmann, Stefanie and H{\"o}fling, Felix}, title = {Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles}, issn = {1438-0064}, doi = {10.12752/8817}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88179}, abstract = {Our theoretical study concerns an urea-urease-based pH oscillator confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the limit cycle, which controls the dynamics for giant vesicles and dominates the strongly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, amenable to analytic treatments, and show that the accuracy of predictions, including the period of oscillations, is highly sensitive to the choice of the reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The accurate description of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.}, language = {en} }