arXiv subjects

B. Mehlig

Publications and source records attributed to B. Mehlig.

At least 19 recordsLinked to original sources

arXiv2026

Resistance tensors for aggregate particles with Stokesian dynamics

The response of particles to low-Reynolds flow can be compactly predicted with resistance or mobility tensors. However, the difficulty of obtaining accurate values for the elements of these tensors for specific geometries has held back work on particles with complex shapes. Here we show how Stokesian dynamics can be adapted to efficiently compute the resistance and mobility tensors of rigid and flexible aggregates, including confinement by walls. We introduce SHAPES, an implementation of the method, and demonstrate its capabilities for complex geometries including curved fibres, chiral dipoles, interacting aggregates, and active swimmers. Aggregates are represented by assemblies of beads designed to reproduce the geometry and motion of rigid or flexible particles. This coarse-grained description preserves the essential hydrodynamic interactions while substantially reducing computational cost. The method accurately reproduces known exact and approximate solutions, as well as experimental observations. The ability to compute the complete resistance and mobility tensors provides new insight into how aggregate shape controls translation, rotation, and coupling to fluid-velocity gradients. Previous descriptions often relied on simplified models retaining only a few symmetry-allowed couplings. While useful, such reduced descriptions are not always structurally stable under small perturbations of particle shape. Computing the full tensors makes it possible to draw robust conclusions and relate them to shape symmetry and hydrodynamic interactions. In particular, the method allows systematic analysis of non-Jeffery couplings to the strain rate that arise for helicoidal aggregates. SHAPES therefore provides a versatile framework for studying rigid and flexible aggregates in microfluidic, biological, and environmental flows.

physics.flu-dyn↗

arXiv2026

Statistical orientation and distribution of columnar ice crystals in turbulent flows

We study the motion of columnar ice crystals that form in clouds over a range of low temperature. Our focus here is on elongated ice crystals, which are smaller than the size of the smallest eddies in the flow, with a moderate aspect ratio comprised between $3$ and $5$. We determine turbulent solutions of the Navier-Stokes equations over a range of turbulent kinetic energy dissipation characteristic of clouds ($4.41\;{\rm cm}^2/{\rm s}^3 \le \varepsilon \le 1120\;{\rm cm}^2/{\rm s}^3$) by using direct numerical simulations, and we follow the motion of crystals using simplified but realistic models for the motion of non-spherical, elongated particles. The influence of the fluid inertia leads to a preferential alignment of the crystals perpendicular to the direction of gravity, the alignment effect being opposed by the turbulent fluctuations. Along with the strong alignment of the crystal axis perpendicular to gravity, we observe only a weak alignment with the vorticity, much weaker than in the absence of gravity. The settling velocity depends only weakly on the orientation of the crystals, but is strongly enhanced when $\varepsilon$ increases, an effect that we attribute to preferential concentration in the flow. As the inertia of the columnar ice crystals considered here is significant, we observe a strong spatial clustering. Finally, we discuss the relevance of the effects identified here on the collision frequency between ice crystals in cloud conditions.

physics.flu-dyn↗

arXiv2025

Fluid-inertia torques from particle-shape symmetry

Numerical simulation of particle motion in fluids at low particle Reynolds numbers is often based on empirical force and torque models obtained by fitting force and torque from ab-initio computations for simple particle shapes such as spheres, spheroids, or cylindrical disks and fibres. To do the same for more complex particles shapes, one needs to first know how particle shape constrains the dependence of force and torque on flow velocity, its gradient, and on particle orientation. Here we use symmetry analysis and perturbation theory to determine the form of the hydrodynamic torque on a particle settling in a quiescent fluid at low but non-zero particle Reynolds numbers, for particle shapes with different point-group symmetries. The symmetry conclusions are verified by comparing with explicit calculations for nearly spherical particles.

physics.flu-dyn↗

arXiv2025

Smart navigation of a gravity-driven glider with adjustable centre-of-mass

Artificial gliders are designed to disperse as they settle through a fluid, requiring precise navigation to reach target locations. We show that a compact glider settling in a viscous fluid can navigate by dynamically adjusting its centre-of-mass. Using fully resolved direct numerical simulations (DNS) and reinforcement learning, we find two optimal navigation strategies that allow the glider to reach its target location accurately. These strategies depend sensitively on how the glider interacts with the surrounding fluid. The nature of this interaction changes as the particle Reynolds number Re$_p$ changes. Our results explain how the optimal strategy depends on Re$_p$. At large Re$_p$, the glider learns to tumble rapidly by moving its centre-of-mass as its orientation changes. This generates a large horizontal inertial lift force, which allows the glider to travel far. At small Re$_p$, by contrast, high viscosity hinders tumbling. In this case, the glider learns to adjust its centre-of-mass so that it settles with a steady, inclined orientation that results in a horizontal viscous force. The horizontal range is much smaller than for large Re$_p$, because this viscous force is much smaller than the inertial lift force at large Re$_p$. *These authors contributed equally.

physics.flu-dyn↗

arXiv2025

Transport barriers for microswimmers in unsteady flow

Certain flow structures trap active microorganisms over extended periods, impacting mortality and growth by inhibiting foraging, exploration, and predator evasion. We show that transport barriers and trapping of a microswimmer in unsteady vortex flow can be understood in terms of Lagrangian coherent structures (LCS) in phase space, taking into account both flow and swimming dynamics. These phase-space LCS constrain when and how artificial microswimmers can be trained by reinforcement learning to escape traps. Our results suggest that phase-space LCS can explain training failure and success in a broad class of navigation problems.

physics.flu-dyn↗

arXiv2024

Does small-scale turbulence matter for ice growth in mixed-phase clouds?

Representing the glaciation of mixed-phase clouds in terms of the Wegener-Bergeron-Findeisen process is a challenge for many weather and climate models, which tend to overestimate this process because cloud dynamics and microphysics are not accurately represented. As turbulence is essential for the transport of water vapour from evaporating liquid droplets to ice crystals, we developed a statistical model using established closures to assess the role of small-scale turbulence. The model successfully captures results of direct numerical simulations, and we use it to assess the role of small-scale turbulence. We find that small-scale turbulence broadens the droplet-size distribution somewhat, but it does not significantly affect the glaciation time on submetre scales. However, our analysis indicates that turbulence on larger spatial scales is likely to affect ice growth. While the model must be amended to describe larger scales, the present work facilitates a path forward to understanding the role of turbulence in the Wegener-Bergeron-Findeisen process.

physics.flu-dyn↗

arXiv2024

Torques on curved atmospheric fibres

Small particles are transported over long distances in the atmosphere, with significant environmental impact. The transport of symmetric particles is well understood, but atmospheric particles, such as curved microplastic fibres or ash particles, are generally asymmetric. This makes the description of their transport properties uncertain. Here, we derive a model for how planar curved fibres settle in quiescent air. The model explains that fluid-inertia torques may align such fibres at oblique angles with gravity as seen in recent laboratory experiments, and shows that inertial alignment is a general and thus important factor for the transport of atmospheric particles.

physics.flu-dyn↗

arXiv2023

Hydrodynamic force on a small squirmer moving with a time-dependent velocity at small Reynolds numbers

We calculate the hydrodynamic force on a small spherical, unsteady squirmer moving with a time-dependent velocity in a fluid at rest, taking into account convective and unsteady fluid inertia effects in perturbation theory. Our results generalise those of Lovalenti and Brady (1993) from passive to active spherical particles. We find that convective inertia changes the history-contribution to the hydrodynamic force, as it does for passive particles. We determine how the hydrodynamic force depends on the swimming gait of the unsteady squirmer. Since swimming breaks the spherical symmetry of the problem, the force is not completely determined by the outer solution of the asymptotic matching problem, as it is for passive spheres. There are additional contributions due to the inhomogeneous solution of the inner problem. We also compute the disturbance flow, illustrating convective and unsteady effects when the particle experiences a sudden start followed by a sudden stop.

physics.flu-dyn↗

arXiv2023

Looking at the posterior: accuracy and uncertainty of neural-network predictions

Bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. By looking at these posterior distributions, one can separate the origin of uncertainty into aleatoric and epistemic contributions. One goal of uncertainty quantification is to inform on prediction accuracy. Here we show that prediction accuracy depends on both epistemic and aleatoric uncertainty in an intricate fashion that cannot be understood in terms of marginalized uncertainty distributions alone. How the accuracy relates to epistemic and aleatoric uncertainties depends not only on the model architecture, but also on the properties of the dataset. We discuss the significance of these results for active learning and introduce a novel acquisition function that outperforms common uncertainty-based methods. To arrive at our results, we approximated the posteriors using deep ensembles, for fully-connected, convolutional and attention-based neural networks.

cs.LG↗

arXiv2023

Statistical models for the dynamics of heavy particles in turbulence

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 collision velocities. To describe these effects of particle inertia, it is necessary to 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 non-dimensional 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 summarise their successes and failures. Annu. Rev. Fluid Mech. 56: In press. DOI: 10.1146/annurev-fluid-032822-014140.

physics.flu-dyn↗

arXiv2023

Lagrangian supersaturation fluctuations at the cloud edge

Evaporation of cloud droplets accelerates when turbulence mixes dry air into the cloud, affecting droplet-size distributions in atmospheric clouds, combustion sprays, and jets of exhaled droplets. The challenge is to model local correlations between droplet numbers, sizes, and supersaturation, which determine supersaturation fluctuations along droplet paths (Lagrangian fluctuations). We derived a statistical model that accounts for these correlations. Its predictions are in quantitative agreement with results of direct numerical simulations, and it explains the key mechanisms at play.

physics.flu-dyn↗

arXiv2023

Caustic formation in a non-Gaussian model for turbulent aerosols

Caustics in the dynamics of heavy particles in turbulence accelerate particle collisions. The rate $\mathscr{J}$ at which these singularities form depends sensitively on the Stokes number St, the non-dimensional inertia parameter. Exact results for this sensitive dependence have been obtained using Gaussian statistical models for turbulent aerosols. However, direct numerical simulations of heavy particles in turbulence yield much larger caustic-formation rates than predicted by the Gaussian theory. In order to understand possible mechanisms explaining this difference, we analyse a non-Gaussian statistical model for caustic formation in the limit of small St. We show that at small St, $\mathscr{J}$ depends sensitively on the tails of the distribution of Lagrangian fluid-velocity gradients. This explains why different authors obtained different St-dependencies of $\mathscr{J}$ in numerical-simulation studies. The most-likely gradient fluctuation that induces caustics at small St, by contrast, is the same in the non-Gaussian and Gaussian models. Direct-numerical simulation results for particles in turbulence show that the optimal fluctuation is similar, but not identical, to that obtained by the model calculations.

physics.flu-dyn↗

arXiv2023

Finite-time Lyapunov exponents of deep neural networks

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep networks and dynamical systems, where the growth or decay of local perturbations is characterised by finite-time Lyapunov exponents. We show that the maximal exponent forms geometrical structures in input space, akin to coherent structures in dynamical systems. Ridges of large positive exponents divide input space into different regions that the network associates with different classes. These ridges visualise the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities.

cond-mat.dis-nn↗

arXiv2023

Inertia induces strong orientation fluctuations of non-spherical atmospheric particles

The orientation of non-spherical 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.

physics.flu-dyn↗

arXiv2022

Critical charges for droplet collisions

The collision efficiency of uncharged micron-sized water droplets in air is determined by the breakdown of hydrodynamics at droplet separations of the order of the mean-free path, by van-der-Waals forces, or a combination of the two. In contrast, electrostatic forces determine the collision efficiency of charged droplets if the charge is large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically-interacting droplets settling in quiescent air, including the breakdown of hydrodynamics at small interfacial distances. For oppositely charged droplets, the transition occurs when a saddle point of the relative droplet-dynamics exits the region where the hydrodynamics breaks down. For droplets with radii $16\,\mu$m and $20\,\mu$m, this occurs at $\sim 10^3$ elementary charges $e$. For smaller charges, the collision efficiency depends upon the Kn number (defined as the ratio of the mean-free-path of air to the mean droplet radius), whereas for larger charges it does not. For droplets charged with the same polarity, the critical charge is $\sim 10^4\,e$ for the above radii.

physics.flu-dyn↗

arXiv2022

Inertial torque on a squirmer

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 $\boldsymbol{T}^\prime = -{\tfrac{9}{8}} m_f (\boldsymbol{v}_s^{(0)} \wedge \boldsymbol{v}_g^{(0)})$ where $\boldsymbol{v}_s^{(0)}$ is the swimming velocity, $\boldsymbol{v}_g^{(0)}$ is the settling velocity in the Stokes approximation, and $m_f$ is the equivalent fluid mass. This torque aligns the swimming direction against gravity: swimming up is stable, swimming down is unstable.

physics.flu-dyn↗

arXiv2022

Unsteady and inertial dynamics of an active particle in a fluid

It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows for example to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.

physics.flu-dyn↗

arXiv2022

Constraints on parameter choices for successful reservoir computing

Echo-state networks are simple models of discrete dynamical systems driven by a time series. By selecting network parameters such that the dynamics of the network is contractive, characterized by a negative maximal Lyapunov exponent, the network may synchronize with the driving signal. Exploiting this synchronization, the echo-state network may be trained to autonomously reproduce the input dynamics, enabling time-series prediction. However, while synchronization is a necessary condition for prediction, it is not sufficient. Here, we study what other conditions are necessary for successful time-series prediction. We identify two key parameters for prediction performance, and conduct a parameter sweep to find regions where prediction is successful. These regions differ significantly depending on whether full or partial phase space information about the input is provided to the network during training. We explain how these regions emerge.

cs.LG↗