Vincent U E, Nana-Nbendjo B R, McClintock P V E
Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):022913. doi: 10.1103/PhysRevE.87.022913. Epub 2013 Feb 22.
We investigate the collective dynamics of a network of inertia particles diffusing in a ratchet potential and interacting indirectly through their stochastic dynamical environment. We obtain analytically the condition for the existence of a stable collective state, and we show that the number N of particles in the network, and the strength k of their interaction with the environment, play key roles in synchronization and transport processes. Synchronization is preceded by symmetry-breaking associated with double-resonance oscillations and is shown to be strongly dependent on the network size: convergence to the synchronization manifold occurs much faster with a large network. For small networks, increasing the noise level enhances synchronization in the weakly coupled regime, while particles in a large network are weakly synchronized. Similarly, in the strongly coupled regime, particles in a small network are weakly synchronized; whereas the synchronization is strong and robust against noise when the network-size is large. Small and moderate networks maximize and stabilize efficient transport. Although the dynamics for larger networks is highly correlated, the transport current is erratic.
我们研究了在棘轮势中扩散并通过其随机动力学环境间接相互作用的惯性粒子网络的集体动力学。我们通过解析得到了稳定集体状态存在的条件，并且表明网络中粒子的数量(N)以及它们与环境相互作用的强度(k)在同步和输运过程中起着关键作用。同步之前伴随着与双共振振荡相关的对称性破缺，并且显示出强烈依赖于网络大小：在大型网络中，收敛到同步流形的速度要快得多。对于小型网络，在弱耦合 regime 中增加噪声水平会增强同步，而大型网络中的粒子同步较弱。类似地，在强耦合 regime 中，小型网络中的粒子同步较弱；而当网络规模较大时，同步很强且对噪声具有鲁棒性。小型和中型网络使高效输运最大化并使其稳定。尽管大型网络的动力学高度相关，但输运电流是不稳定的。
