Michaelis D, Abdullaev F Kh, Darmanyan S A, Lederer F
Fraunhofer Institute for Applied Optics and Precision Engineering, Jena, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 2):056205. doi: 10.1103/PhysRevE.71.056205. Epub 2005 May 12.
We study the effects of rapid periodic and stochastic modulations of parameters in systems described by the complex parametric Ginzburg-Landau equation. Amplitude equations, which govern the dynamics of the field averaged over the rapid modulations, are derived. For temporal modulations of the linear detuning the threshold for the transition from Ising to Bloch walls is shifted depending on the strength of the perturbation. In contrast to this, rapid perturbations of the linear gain lead only to a decrease of the amplitude of both wall types leaving the bifurcation point of the Ising-Bloch transition unchanged. Stochastic perturbations of the detuning lead to a Brownian motion of the Bloch wall beyond bifurcation where the velocity is given analytically. All theoretical predictions are confirmed by numerical simulations of the full stochastic Ginzburg-Landau equation.
我们研究了由复参数金兹堡 - 朗道方程描述的系统中参数的快速周期性和随机调制的影响。推导了控制快速调制下平均场动力学的振幅方程。对于线性失谐的时间调制，从伊辛壁到布洛赫壁转变的阈值会根据扰动强度而移动。与此相反，线性增益的快速扰动仅导致两种壁类型的振幅减小，而伊辛 - 布洛赫转变的分岔点保持不变。失谐的随机扰动导致布洛赫壁在分岔点之后出现布朗运动，其速度可以解析给出。所有理论预测都通过全随机金兹堡 - 朗道方程的数值模拟得到了证实。
