Mankin R, Laas K, Sauga A
Institute of Mathematics and Natural Sciences, Tallinn University, Tallinn, Estonia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061131. doi: 10.1103/PhysRevE.83.061131. Epub 2011 Jun 20.
The temporal behavior of the mean-square displacement and the velocity autocorrelation function of a particle subjected to a periodic force in a harmonic potential well is investigated for viscoelastic media using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise, by an internal Mittag-Leffler noise with a finite memory time, and by an additive external noise. It is shown that the presence of a multiplicative noise has a profound effect on the behavior of the autocorrelation functions. Particularly, for correlation functions the model predicts a crossover between two different asymptotic power-law regimes. Moreover, a dependence of the correlation function on the frequency of the external periodic forcing occurs that gives a simple criterion to discern the multiplicative noise in future experiments. It is established that additive external and internal noises cause qualitatively different dependences of the autocorrelation functions on the external forcing and also on the time lag. The influence of the memory time of the internal noise on the dynamics of the system is also discussed.
利用广义朗之万方程，研究了处于简谐势阱中且受到周期力作用的粒子在粘弹性介质中的均方位移和速度自相关函数的时间行为。与环境参数涨落的相互作用通过乘性白噪声、具有有限记忆时间的内米塔格 - 莱夫勒噪声以及加性外部噪声进行建模。结果表明，乘性噪声的存在对自相关函数的行为有深远影响。特别是，对于相关函数，该模型预测了两种不同渐近幂律 regime 之间的交叉。此外，相关函数对外部周期强迫频率存在依赖性，这为未来实验中辨别乘性噪声提供了一个简单标准。已确定加性外部噪声和内部噪声会导致自相关函数对外部强迫以及时间滞后产生定性不同的依赖性。还讨论了内部噪声的记忆时间对系统动力学的影响。
