Application of statistical mechanics to collective motion in biology

Our goal is to describe the collective motion of organisms in the presence of fluctuations. Therefore, we discuss biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In our models the particles corresponding to organisms locally interact with their neighbours according to simple rules depending on the particular situation considered. Numerical simulations indicate the existence of new types of transitions. Depending on the control parameters both disordered and long-range ordered phases can be observed. In particular, we demonstrate that (i) there is a transition from disordered to ordered motion at a finite noise level even in one dimension and (ii) particles segregate into lanes or jam into a crystalline structure in a model of pedestrians.