Ben-Naim E, Krapivsky P L
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Mar;73(3 Pt 1):031109. doi: 10.1103/PhysRevE.73.031109. Epub 2006 Mar 13.
We study dynamical ordering of rods. In this process, rod alignment via pairwise interactions competes with diffusive wiggling. Under strong diffusion, the system is disordered, but at weak diffusion, the system is ordered. We present an exact steady-state solution for the nonlinear and nonlocal kinetic theory of this process. We find the Fourier transform as a function of the order parameter, and show that Fourier modes decay exponentially with the wave number. We also obtain the order parameter in terms of the diffusion constant. This solution is obtained using iterated partitions of the integer numbers.
我们研究杆的动态排列。在这个过程中，通过成对相互作用实现的杆排列与扩散摆动相互竞争。在强扩散情况下，系统是无序的，但在弱扩散情况下，系统是有序的。我们给出了该过程非线性和非局部动力学理论的精确稳态解。我们找到了作为序参量函数的傅里叶变换，并表明傅里叶模式随波数呈指数衰减。我们还根据扩散常数得到了序参量。这个解是通过对整数进行迭代划分得到的。
