| 1. |
- Balabanov, Oleksandr, et al.
(author)
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Bayesian Posterior Approximation With Stochastic Ensembles
- 2023
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In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. - 1063-6919. - 9798350301298 ; 2023-June, s. 13701-13711
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Conference paper (peer-reviewed)abstract
- We introduce ensembles of stochastic neural networks to approximate the Bayesian posterior, combining stochastic methods such as dropout with deep ensembles. The stochas-tic ensembles are formulated as families of distributions and trained to approximate the Bayesian posterior with variational inference. We implement stochastic ensembles based on Monte Carlo dropout, DropConnect and a novel non-parametric version of dropout and evaluate them on a toy problem and CIFAR image classification. For both tasks, we test the quality of the posteriors directly against Hamil-tonian Monte Carlo simulations. Our results show that stochastic ensembles provide more accurate posterior esti-mates than other popular baselines for Bayesian inference.
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| 2. |
- Bec, J., et al.
(author)
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Statistical Models for the Dynamics of Heavy Particles in Turbulence
- 2024
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In: ANNUAL REVIEW OF FLUID MECHANICS. - 0066-4189 .- 1545-4479. ; 56, s. 189-213
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Research review (peer-reviewed)abstract
- When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy particles, with mass densities larger than that of the carrying fluid, can detach from the flow. This results in preferential sampling, small-scale fractal clustering, and large relative velocities. To describe these effects of particle inertia, one must consider both particle positions and velocities in phase space. In recent years, statistical phase-space models have significantly contributed to our understanding of inertial-particle dynamics in turbulence. These models help to identify the key mechanisms and nondimensional parameters governing the particle dynamics and have made qualitative and, in some cases, quantitative predictions. This article reviews statistical phase-space models for the dynamics of small, yet heavy, spherical particles in turbulence. We evaluate their effectiveness by comparing their predictions with results from numerical simulations and laboratory experiments, and we summarize their successes and failures.
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| 3. |
- Bhowmick, T., et al.
(author)
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Inertia Induces Strong Orientation Fluctuations of Nonspherical Atmospheric Particles
- 2024
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In: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 132:3
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Journal article (peer-reviewed)abstract
- The orientation of nonspherical particles in the atmosphere, such as volcanic ash and ice crystals, influences their residence times and the radiative properties of the atmosphere. Here, we demonstrate experimentally that the orientation of heavy submillimeter spheroids settling in still air exhibits decaying oscillations, whereas it relaxes monotonically in liquids. Theoretical analysis shows that these oscillations are due to particle inertia, caused by the large particle-fluid mass-density ratio. This effect must be accounted for to model solid particles in the atmosphere.
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| 4. |
- Cabrera, F., et al.
(author)
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Experimental validation of fluid inertia models for a cylinder settling in a quiescent flow
- 2022
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In: Physical Review Fluids. - 2469-990X. ; 7:2
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Journal article (peer-reviewed)abstract
- The precise description of the motion of anisotropic particles in a flow rests on the understanding of the force and torque acting on them. Here, we study experimentally small, very elongated particles settling in a fluid at small Reynolds number. In our experiments, we can, to a very good approximation, relate the rate of rotation of cylindrical tungsten rods, of aspect ratios = 8 and = 16, settling in pure glycerol, to the torque they are experiencing. This allows us to compare the measured torque with expressions obtained either in the slender-rod limit or in the case of spheroids. Both theories predict a simple angle dependence for the torque, which is found to capture very well the experimental results. The slender-rod theory overestimates the results for the two aspect ratios considered, while the expression obtained for a spheroid provides a better approximation for = 16. Comparing our results with those of previous experiments provides further insight on the conditions of validity of the slender-rod theory. The translational dynamics is shown to be in qualitative agreement with the slender-rod and spheroid models, the former one being found to represent better the experimental data.
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| 5. |
- Candelier, F., et al.
(author)
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Inertial torque on a squirmer
- 2022
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In: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 953
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Journal article (peer-reviewed)abstract
- A small spheroid settling in a quiescent fluid experiences an inertial torque that aligns it so that it settles with its broad side first. Here we show that an active particle experiences such a torque too, as it settles in a fluid at rest. For a spherical squirmer, the torque is T '=-9/8m(f)(v(s)((0) )boolean AND v(g)((0))) where v(s)((0) )is the swimming velocity, v(g)((0)) is the settling velocity in the Stokes approximation and mf is the equivalent fluid mass. This torque aligns the swimming direction against gravity: swimming up is stable, swimming down is unstable.
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| 6. |
- Candelier, F., et al.
(author)
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Second-order inertial forces and torques on a sphere in a viscous steady linear flow
- 2023
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In: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 954
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Journal article (peer-reviewed)abstract
- We compute the full set of second-order inertial corrections to the instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in a general steady linear flow. This is achieved by using matched asymptotic expansions and formulating the problem in a coordinate system co-moving with the background flow. Effects of unsteadiness and fluid-velocity gradients are assumed to be small, but to dominate in the far field over those of the velocity difference between the body and fluid, making the results essentially relevant to weakly positively or negatively buoyant particles. The outer solution (which at first order is responsible for the Basset-Boussinesq history force at short time and for shear-induced forces such as the Saffman lift force at long time) is expressed via a flow-dependent tensorial kernel. The second-order inner solution brings a number of different contributions to the force and torque. Some are proportional to the relative translational or angular acceleration between the particle and fluid, while others take the form of products of the rotation/strain rate of the background flow and the relative translational or angular velocity between the particle and fluid. Adding the outer and inner contributions, the known added-mass force or the spin-induced lift force are recovered, and new effects involving the velocity gradients of the background flow are revealed. The resulting force and torque equations provide a rational extension of the classical Basset-Boussinesq-Oseen equation incorporating all first- and second-order fluid inertia effects resulting from both unsteadiness and velocity gradients of the carrying flow.
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| 7. |
- Cedenblad, Lukas, et al.
(author)
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Planetesimals on Eccentric Orbits Erode Rapidly
- 2021
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In: Astrophysical Journal. - : American Astronomical Society. - 0004-637X .- 1538-4357. ; 921:2
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Journal article (peer-reviewed)abstract
- We investigate the possibility of erosion of planetesimals in a protoplanetary disk. We use theory and direct numerical simulations (lattice Boltzmann method) to calculate the erosion of large-much larger than the mean-free path of gas molecules-bodies of different shapes in flows. We find that erosion follows a universal power law in time, at intermediate times, independent of the Reynolds number of the flow and the initial shape of the body. Consequently, we estimate that planetesimals in eccentric orbits, of even very small eccentricity, rapidly (in about 100 yr) erodes away if the semimajor axis of their orbit lies in the inner disk-less than about 10 au. Even planetesimals in circular orbits erode away in approximately 10,000 yr if the semimajor axis of their orbits are <0.6 au.
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| 8. |
- Cichos, F., et al.
(author)
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Machine learning for active matter
- 2020
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In: Nature Machine Intelligence. - : Springer Science and Business Media LLC. - 2522-5839. ; 2:2, s. 94-103
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Journal article (peer-reviewed)abstract
- The availability of large datasets has boosted the application of machine learning in many fields and is now starting to shape active-matter research as well. Machine learning techniques have already been successfully applied to active-matter data-for example, deep neural networks to analyse images and track objects, and recurrent nets and random forests to analyse time series. Yet machine learning can also help to disentangle the complexity of biological active matter, helping, for example, to establish a relation between genetic code and emergent bacterial behaviour, to find navigation strategies in complex environments, and to map physical cues to animal behaviours. In this Review, we highlight the current state of the art in the application of machine learning to active matter and discuss opportunities and challenges that are emerging. We also emphasize how active matter and machine learning can work together for mutual benefit. This Review surveys machine learning techniques that are currently developed for a range of research topics in biological and artificial active matter and also discusses challenges and exciting opportunities. This research direction promises to help disentangle the complexity of active matter and gain fundamental insights for instance in collective behaviour of systems at many length scales from colonies of bacteria to animal flocks.
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| 9. |
- Collins, D., et al.
(author)
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Lord Kelvin's isotropic helicoid
- 2021
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In: Physical Review Fluids. - 2469-990X. ; 6:7
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Journal article (peer-reviewed)abstract
- Nearly 150 years ago, Lord Kelvin proposed the isotropic helicoid, a particle with isotropic yet chiral interactions with a fluid so that translation couples to rotation. An implementation of his design fabricated with a three-dimensional printer is found experimentally to have no detectable translation-rotation coupling, although the particle point-group symmetry allows this coupling. We explain these results by demonstrating that in Stokes flow, the chiral coupling of such isotropic helicoids made out of nonchiral vanes is due only to hydrodynamic interactions between these vanes. Therefore it is small. In summary, Kelvin's predicted isotropic helicoid exists, but only as a weak breaking of a symmetry of noninteracting vanes in Stokes flow.
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| 10. |
- Cui, Z., et al.
(author)
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Alignment statistics of rods with the Lagrangian stretching direction in a channel flow
- 2020
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In: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 901
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Journal article (peer-reviewed)abstract
- In homogeneous isotropic turbulence, slender rods are known to align with the Lagrangian stretching direction. However, how the degree of alignment depends on the aspect ratio of the rod is not understood. Moreover, particle-laden flows are often anisotropic and inhomogeneous. Therefore we study the alignment of rods with the Lagrangian stretching direction in a channel flow, which is approximately homogeneous and isotropic near the centre but inhomogeneous and anisotropic near the walls. Our main question is how the distribution of relative angles between a rod and the Lagrangian stretching direction depends on the aspect ratio of the rod and upon the distance of the rod from the channel wall. We find that this distribution exhibits two regimes: a plateau at small angles corresponding to random uncorrelated motion, and power-law tails due to large excursions. We find that slender rods near the channel centre align better with the Lagrangian stretching direction compared with those near the channel wall. These observations are explained in terms of simple statistical models based on Jeffery's equation, qualitatively near the channel centre and quantitatively near the channel wall. Lastly we discuss the consequences of our results for the distribution of relative angles between the orientations of nearby rods (Zhao et al., Phys. Rev. Fluids, vol. 4, 2019, 054602).
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