| Autor: |
J Meibohm, K Gustavsson, J Bec, B Mehlig |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
New Journal of Physics, Vol 22, Iss 1, p 013033 (2020) |
| Druh dokumentu: |
article |
| ISSN: |
1367-2630 |
| DOI: |
10.1088/1367-2630/ab60f7 |
| Popis: |
We analyse the spatial inhomogeneities (‘spatial clustering’) in the distribution of particles accelerated by a force that changes randomly in space and time. To quantify spatial clustering, the phase-space dynamics of the particles must be projected to configuration space. Folds of a smooth phase-space manifold give rise to catastrophes (‘caustics’) in this projection. When the inertial particle dynamics is damped by friction, however, the phase-space manifold converges towards a fractal attractor. It is believed that caustics increase spatial clustering also in this case, but a quantitative theory is missing. We solve this problem by determining how projection affects the distribution of finite-time Lyapunov exponents (FTLEs). Applying our method in one spatial dimension we find that caustics arising from the projection of a dynamical fractal attractor (‘fractal catastrophes’) make a distinct and universal contribution to the distribution of spatial FTLEs. Our results explain a projection formula for the spatial fractal correlation dimension, and how a fluctuation relation for the distribution of FTLEs for white-in-time Gaussian force fields breaks upon projection. We explore the implications of our results for heavy particles in turbulence, and for wave propagation in random media. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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