Diffusion in Agitated Frictional Granular Matter Near the Jamming Transition
| Autor: | Itamar Procaccia, H. G. E. Hentschel, Saikat Roy |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Area fraction
Physics Mathematics::Functional Analysis High Energy Physics::Lattice High Energy Physics::Phenomenology FOS: Physical sciences Condensed Matter - Soft Condensed Matter Scaling theory 01 natural sciences 010305 fluids & plasmas Nonlinear Sciences::Chaotic Dynamics Mathematics::Group Theory Granular matter 0103 physical sciences Soft Condensed Matter (cond-mat.soft) Diffusion (business) 010306 general physics Scaling Mathematical physics |
| DOI: | 10.48550/arxiv.1905.08698 |
| Popis: | We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction $\phi$ and mean-square velocity fluctuations $\langle v^2\rangle$ the mean-square displacement of the disks $\langle d^2\rangle$ spans 4-5 orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behabvior at long times. The statistics of $\langle d^n\rangle$ at all times are multiscaling, since the probability distribution function (pdf) of displacements has very broad wings. Even where a diffusion constant can be identified it is a complex function of $\phi$ and $\langle v^2\rangle$. By identifying the relevant length and time scales and their interdependence one can rescale the data for the mean square displacement and the pdf of displacements into collapsed scaling functions for all $\phi$ and $\langle v^2\rangle$. These scaling functions provide a predictive tool, allowing to infer from one set of measurements (at a given $\phi$ and $\langle v^2\rangle$) what are the expected results at any value of $\phi$ and $\langle v^2\rangle$. Comment: 9 pages, 9 figs Submitted to Phys. Rev. E |
| Databáze: | OpenAIRE |
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