Spontaneous trail formation in populations of auto-chemotactic walkers

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 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.

CONFORMAL PHASE TRANSITION IN QCD LIKE THEORIES AND BEYOND

The dynamics with an infrared stable fixed point in the conformal window in QCD like theories with a relatively large number of fermion flavors is reviewed. The emphasis is on the description of a clear signature for the conformal window, which in particular can be useful for lattice computer simulations of these gauge theories.

ON THE PHASE DIAGRAM OF ASYMPTOTICALLY FREE GAUGE THEORIES WITH ADDITIONAL FOUR-FERMION INTERACTION

In the ladder asymptotically free gauge models with one-loop running coupling constant and additional four-fermion interaction, the structure of the phase diagram in coupling constants is determined. The anomalous dimension γm of the composite operator [Formula: see text] is calculated on the full critical line of the diagram. The possibilities of the examination of the phase diagram of such theories in lattice computer simulations are discussed.