Time and space generalized diffusion equation on graphs/networks
arXiv:2202.00318 · doi:10.1016/j.chaos.2022.111791
Abstract
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.
arXiv comment15 pages, 6 figures
References in corpus (10)
- Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
- Anomalous heat conduction and anomalous diffusion in one dimensional systems
- No Nonlocality. No Fractional Derivative
- Observation of anomalous diffusion and fractional self-similarity in one dimension
- Computing the matrix Mittag-Leffler function with applications to fractional calculus
- Effects of intersegmental transfers on target location by proteins
- Path Laplacian operators and superdiffusive processes on graphs. I. One-dimensional case
- Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice
- On anomalous diffusion and the out of equilibrium response function in one-dimensional models
- Anomalous Diffusion in One-Dimensional Disordered Systems: A Discrete Fractional Laplacian Method