| 1. |
- Dubey, Anshuman, et al.
(författare)
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Fractal dimensions and trajectory crossings in correlated random walks
- 2018
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Ingår i: Physical Review E. - 2470-0045 .- 2470-0053. ; 98
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Tidskriftsartikel (refereegranskat)abstract
- © 2018 American Physical Society. We study spatial clustering in a discrete-time, one-dimensional, stochastic, toy model of heavy particles in turbulence and calculate the spectrum of multifractal dimensions Dq as functions of a dimensionless parameter, α, that plays the role of an inertia parameter. Using the fact that it suffices to consider the linearized dynamics of the model at small separations, we find that Dq=D2/(q-1) for q=2,3,. The correlation dimension D2 turns out to be a nonanalytic function of the inertia parameter in this model. We calculate D2 for small α up to the next-to-leading order in the nonanalytic term.
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| 2. |
- Meibohm, Jan, et al.
(författare)
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Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number
- 2016
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Ingår i: Physical Review Fluids. - 2469-990X. ; 1:8
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Tidskriftsartikel (refereegranskat)abstract
- We analyse the angular velocity of a small neutrally buoyant spheroid log rolling in a simple shear. When the effect of fluid inertia is negligible the angular velocity ω equals half the fluid vorticity. We compute by singular perturbation theory how weak fluid inertia reduces the angular velocity in an unbounded shear, and how this reduction depends upon the shape of the spheroid (on its aspect ratio). In addition we determine the angular velocity by direct numerical simulations. The results are in excellent agreement with the theory at small but not too small values of the shear Reynolds number, for all aspect ratios considered. For the special case of a sphere we find ω/s=−1/2+0.0540 Re_s^3/2 where s is the shear rate, and Re_s is the shear Reynolds number. This result differs from that derived by Lin et al. [J. Fluid Mech. 44 (1970) 1] who obtained a numerical coefficient roughly three times larger.
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| 3. |
- Meibohm, Jan, et al.
(författare)
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Chiral fermions in asymptotically safe quantum gravity
- 2016
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Ingår i: European Physical Journal C. - : Springer Science and Business Media LLC. - 1434-6044 .- 1434-6052. ; 76:5
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Tidskriftsartikel (refereegranskat)abstract
- We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93: 084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
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| 4. |
- Meibohm, Jan, et al.
(författare)
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Fractal catastrophes
- 2020
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 22:1
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 5. |
- Meibohm, Jan, et al.
(författare)
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Heavy particles in a persistent random flow with traps
- 2019
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Ingår i: Physical Review E. - 2470-0045. ; 100:2
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Tidskriftsartikel (refereegranskat)abstract
- We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modeled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional fluid-velocity fields are always compressible, the model exhibits spatial trapping regions where particles tend to accumulate. We determine the statistics of fluid-velocity gradients in the vicinity of these traps and show how this allows one to determine the spatial Lyapunov exponent and the rate of caustic formation. We compare our analytical results with numerical simulations of the model and explore the limits of validity of the theory. Finally, we discuss implications for higher-dimensional systems.
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| 6. |
- Meibohm, Jan
(författare)
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On the phase-space distribution of heavy particles in turbulence
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Turbulent fluids laden with small, heavy particles are common in nature. Prominent examples of such turbulent suspensions are water droplets in warm clouds, as well as particulate matter or living organisms in the turbulent upper layer of oceans. Because of their inertia, heavy particles tend to distribute inhomogeneously over phase-space, and over configuration space. This phenomenon is referred to as clustering, and it is believed to have a strong impact on the rate of collisions between particles. The collision dynamics, in turn, is crucial for the time evolution of turbulent suspensions, as collisions enable the particles to grow in size. In this thesis, I study the phase-space distribution of heavy particles in turbulence in terms of a simplified, statistical model that qualitatively captures the particle dynamics on the smallest length scales of turbulence. I use methods from dynamical systems theory, and the theory of large deviations, to describe the long-time behaviour of the particle distribution. In most parts of the thesis, I investigate suspensions of identical particles, and study statistical observables that characterise clustering in phase-space, and in configuration space. For these ‘mono-disperse’ suspensions I analyse phase-space clustering in a one- dimensional limit by computing the large-deviation statistics of phase-space finite-time Lyapunov exponents, and the phase-space Renyi dimensions. Spatial clustering is studied by means of a projection from phase-space to configuration space. I show how the large-deviation statistics of spatial finite-time Lyapunov exponents is affected by this projection, and the effects it has on the spatial correlation dimension. Finally, I extend the analysis to particle suspensions of two different sizes. I show that this ‘poly-dispersity’ has a strong effect on the phase-space distribution of particles, where it leads to a plateau in the distribution of separations and relative velocities.
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| 7. |
- Meibohm, Jan, et al.
(författare)
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Paths to caustic formation in turbulent aerosols
- 2021
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Ingår i: Physical Review Fluids. - : American Physical Society (APS). - 2469-990X. ; 6:6
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Tidskriftsartikel (refereegranskat)abstract
- The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations in the spatial particle-number density, and in collision velocities. For large particle inertia, the fluid velocity at the particle position is essentially a white-noise signal and caustic formation is analogous to Kramers escape. Here we show that caustic formation at small particle inertia is different. Caustics tend to form in the vicinity of particle trajectories that experience a specific history of fluid-velocity gradients, characterized by low vorticity and a violent strain exceeding a large threshold. We develop a theory that explains our findings in terms of an optimal path to caustic formation that is approached in the small inertia limit.
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| 8. |
- Meibohm, Jan, et al.
(författare)
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Relative velocities in bidisperse turbulent suspensions
- 2017
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Ingår i: Physical Review E. - 2470-0045 .- 2470-0053. ; 96
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Tidskriftsartikel (refereegranskat)abstract
- © 2017 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analyzing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes numbers. This number, St, is a measure of particle inertia which in turn depends on particle size. When the Stokes numbers are similar, the distribution exhibits power-law tails, just as in the case of equal St. The power-law exponent is a nonanalytic function of the mean Stokes number St, so that the exponent cannot be calculated in perturbation theory around the advective limit. When the Stokes-number difference is larger, the power law disappears, but the tails of the distribution still dominate the relative-velocity moments, if St is large enough.
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| 9. |
- Meibohm, Jan, et al.
(författare)
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Temperature Dependent Soft X-ray Absorption Spectroscopy of Liquids
- 2014
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Ingår i: Review of Scientific Instruments. - : American Institute of Physics (AIP). - 0034-6748 .- 1089-7623. ; 85
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Tidskriftsartikel (refereegranskat)abstract
- A novel sample holder is introduced which allows for temperature dependent soft x-ray absorption spectroscopy of liquids in transmission mode. The setup is based on sample cells with x-ray transmis- sive silicon nitride windows. A cooling circuit allows for temperature regulation of the sample liquid between −10 ◦C and +50 ◦C. The setup enables to record soft x-ray absorption spectra of liquids in transmission mode with a temperature resolution of 0.5 K and better. Reliability and reproducibility of the spectra are demonstrated by investigating the characteristic temperature-induced changes in the oxygen K-edge x-ray absorption spectrum of liquid water. These are compared to the corresponding changes in the oxygen K-edge spectra from x-ray Raman scattering.
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