论文标题
监视Lévy-Process跨界车
Monitoring Lévy-Process Crossovers
论文作者
论文摘要
两种或多种类型的扩散过程之间的交叉代表了非平衡统计物理学中的一个充满活力的主题。在这项工作中，我们提出了两个模型，以在不同的Lévy过程之间产生交叉：在第一个模型中，我们在扩散方程的拉普拉斯项项中逐渐更改衍生物的顺序，而在第二个模型中，我们考虑了第二个模型，而在第二个模型中，我们考虑了第二个分数传播扩散项的组合，则通过变化时间的系数来表征。 通过考虑半分析（即分析以及数值）程序来遵循时间依赖性溶液来说明这些建议。我们发现两个不同的制度之间的变化，结果表明，远离交叉制度，这两个模型在定性上产生了相似的结果，尽管这些变化可能以两种模型的不同形式发生。预计本文引入的模型对于描述复杂系统中经常发生的不同扩散状态之间的交叉非常有用。
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different Lévy processes: in the first model we change gradually the order of the derivative in the Laplacian term of the diffusion equation, whereas in the second one we consider a combination of fractional-derivative diffusive terms characterized by coefficients that change in time. The proposals are illustrated by considering semi-analytical (i.e., analytical together with numerical) procedures to follow the time-dependent solutions. We find changes between two different regimes and it is shown that, far from the crossover regime, both models yield qualitatively similar results, although these changes may occur in different forms for the two models. The models introduced herein are expected to be useful for describing crossovers among distinct diffusive regimes that occur frequently in complex systems.
