Alignment of Rods and Partition of Integers

Details Alignment of Rods and Partition of Integers Alignment of Rods and Partition of Integers

2005-12-09

arxiv.org/abs/cond-mat/0512192v2

Phys. Rev. E 73, 031109 (2006)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 4 figures

Scientific paper

10.1103/PhysRevE.73.031109

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.

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