具有振荡力的扭结动力学
Kink dynamics with oscillating forces
摘要：
众所周知，由金兹伯格-朗道自由能驱动的一维耗散系统的动力学可以用相互作用的扭结来描述：距离为$\ell$的两个相邻扭结感受到一个吸引力$F(\ell)\approx\exp(-\ell)$。这一结果是典型的非均匀性的能量消耗由于表面张力，但对于某些物理系统的弯曲刚度，而不是表面张力起主导作用的系统。我们表明，扭结动力学仍然适用，但力$F(\ell)$现在振荡，因此产生的配置是局部稳定的。我们还提出了一个新的推导扭结动力学，它适用于广义Ginzburg-Landau自由能与任意组合的表面张力，弯曲能，和高阶项。我们的推导是不是基于一个特定的多扭结近似和扭结动力学正确再现完整的动力学的原始模型。这使得我们可以放心地使用我们的推导来代替连续动力学，从而将模拟时间减少了几个数量级。
英文摘要：
It is well known that the dynamics of a one-dimensional dissipative system driven by the Ginzburg-Landau free energy may be described in terms of interacting kinks: two neighbouring kinks at distance $\ell$ feel an attractive force $F(\ell)\approx\exp(-\ell)$. This result is typical of a bistable system whose inhomogeneities have an energy cost due to surface tension, but for some physical systems bending rigidity rather than surface tension plays a leading role. We show that a kink dynamics is still applicable, but the force $F(\ell)$ is now oscillating, therefore producing configurations which are locally stable. We also propose a new derivation of kink dynamics, which applies to a generalized Ginzburg-Landau free energy with an arbitrary combination of surface tension, bending energy, and higher-order terms. Our derivation is not based on a specific multikink approximation and the resulting kink dynamics reproduces correctly the full dynamics of the original model. This allows to use our derivation with confidence in place of the continuum dynamics, reducing simulation time by orders of magnitude.
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