Abstract

Logarithmic oscillations superimposed on a power-law trend appear in the behavior of various complex hierarchical systems. In this paper, we study the logarithmic oscillations of relaxation curves in \(p\)-adic diffusion models that are used to describe the conformational dynamics of protein. We consider the case of a purely \(p\)-adic diffusion, as well as the case of \(p\)-adic diffusion with a reaction sink. We show that, relaxation curves for large times in these two cases are described by a power law on which logarithmic oscillations are superimposed whose period and amplitude are determined by the parameters of the model. We also provide a physical explanation of the emergence of oscillations in relaxation curves and discuss the relation of the results to the experiments on relaxation dynamics of protein.

中文翻译：

---

$$p$$ 中的振荡 -Adic 扩散过程和蛋白质构象动力学模拟

摘要

叠加在幂律趋势上的对数振荡出现在各种复杂层次系统的行为中。在本文中，我们研究了用于描述蛋白质构象动力学的\(p\) -adic扩散模型中弛豫曲线的对数振荡。我们考虑纯粹的\(p\) -adic扩散的情况，以及带有反应汇的\(p\) -adic扩散的情况。我们表明，这两种情况下的大时间弛豫曲线是通过幂律来描述的，在该幂律上叠加了对数振荡，其周期和幅度由模型的参数确定。我们还对弛豫曲线中振荡的出现提供了物理解释，并讨论了结果与蛋白质弛豫动力学实验的关系。