图/网络上的时空广义扩散方程
Time and space generalized diffusion equation on graphs/networks
摘要：
正常扩散和反常扩散在许多复杂系统中普遍存在[1]。在这里，我们定义了一个时间和空间广义扩散方程（GDE），它使用分数时间导数和图/网络上的转换d-路径拉普拉斯算子。我们发现解析解这个方程，并证明它涵盖了制度的正常，子和superdiffusion作为一个函数的两个参数的模型。我们扩展的GDE考虑一个系统的正常和异常的扩散，可以观察到，例如在扩散的蛋白质沿DNA链的时间交替。我们在一维系统上模拟线性DNA链进行计算实验。结果表明，一个subdiffusive-superdiffusive交替政权允许扩散粒子探索更慢的小区域的链与更快的全球性的探索，比subdiffusive-subdiffusive政权。因此，交替的滑动（亚扩散）与跳跃和片段间转移（超扩散）机制显示了蛋白质-DNA相互作用的重要进展。
英文摘要：
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on graphs/networks. We find analytically the solution of this equation and prove that it covers the regimes of normal, sub- and superdiffusion as a function of the two parameters of the model. We extend the GDE to consider a system with temporal alternancy of normal and anomalous diffusion which can be observed for instance in the diffusion of proteins along a DNA chain. We perform computational experiments on a one-dimensional system emulating a linear DNA chain. It is shown that a subdiffusive-superdiffusive alternant regime allows the diffusive particle to explore more slowly small regions of the chain with a faster global exploration, than a subdiffusive-subdiffusive regime. Therefore, an alternancy of sliding (subdiffusive) with hopping and intersegmental transfer (superdiffusive) mechanisms show important advances for protein-DNA interactions.
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