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Fractal catastrophes
Fractal catastrophes
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- Meibohm, Jan (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för fysik (GU),Department of Physics (GU)
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- Gustavsson, Kristian, 1980 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för fysik (GU),Department of Physics (GU)
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Bec, J. (författare)
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- Mehlig, Bernhard, 1964 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för fysik (GU),Department of Physics (GU)
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(creator_code:org_t)
- 2020-01-21
- 2020
- Engelska.
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 22:1
- Relaterad länk:
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https://doi.org/10.1...
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https://gup.ub.gu.se...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences (hsv//eng)
Nyckelord
- fractals
- statistical mechanics
- large deviation theory
- spatial
- clustering
- catastrophe theory
- non-equilibrium physics
- inertial particles
- preferential concentration
- generalized dimensions
- large deviations
- heavy-particles
- turbulent
- statistics
- stability
- exponents
- number
- Physics
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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