Selecting a common direction

摘要: The problem of alignment cells (or other objects) that interact in an angle-dependent way was described Mogilner and Edelstein-Keshet (1995). In this sequel we consider detail a special limiting case nearly complete alignment. This occurs when the rotational diffusion individual objects becomes very slow. case, motion is essentially deterministic, individuals or tend to gather clusters at various orientations. (Numerical solutions show angular distribution develops sharp peaks discrete orientations.) To understand behaviour deterministic models with analytic tools, represent as number delta-like peaks. approximation true solution by set (infinitely sharp) will be referred peak ansatz. For weak but nonzero diffusion, are smoothed out. analysis leads singular perturbation which investigate. We briefly discuss applications similar techniques.