Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles

We investigate the collective behavior of self-propelled particles (SPPs) undergoing competitive processes of pattern formation and rotational relaxation of their self-propulsion velocities. In full accordance with previous work, we observe transitions between different steady states of the SPPs caused by the intricate interplay among the involved effects of pattern formation, orientational order, and coupling between the SPP density and orientation fields. Based on rigorous analytical and numerical calculations, we prove that the rate of the orientational relaxation of the SPP velocity field is the main factor determining the steady states of the SPP system. Further, we determine the boundaries between domains in the parameter plane that delineate qualitatively different resting and moving states. In addition, we analytically calculate the collective velocity $\vec{v}$ of the SPPs and show that it perfectly agrees with our numerical results. We quantitatively demonstrate that $\vec{v}$ does not vanish upon approaching the transition boundary between the moving pattern and homogeneous steady states.Comment: 3 Figure

Flory radius of polymers in a periodic field: An exact analytic theory

We found an exact expression for the Flory radius R F of Gaussian polymers placed in an external periodic field. This solution is expressed in terms of the two parameters η and a that describe the reduced strength of an external field and the period of the field to the polymer gyration radius ratio, respectively. R F is found to be a decaying function of η for any values of a . Provided that the gyration radius is of the order of the period of an external field or less, the ground-state (GS) approximation of the exact result for R F is shown to give qualitatively incorrect results. In addition to the “ground-state” contribution, the exact solution for R F contains an additional term that is overlooked by the GS approximation. This term gives rise to the fact that R F as a function of η exhibits power law behavior (rather than exponential decay obtained from the GS result) once η exceeds the threshold value ηcon