Inertia Induces Strong Orientation Fluctuations of Nonspherical Atmospheric Particles.

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.

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 feed-forward networks and dynamical systems, where the growth or decay of local perturbations is characterized 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 visualize the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities.

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 explain the key mechanisms at play.

Alignment of Nonspherical Active Particles in Chaotic Flows.

We study the orientation statistics of spheroidal, axisymmetric microswimmers, with shapes ranging from disks to rods, swimming in chaotic, moderately turbulent flows. Numerical simulations show that rodlike active particles preferentially align with the flow velocity. To explain the underlying mechanism, we solve a statistical model via the perturbation theory. We show that such an alignment is caused by correlations of fluid velocity and its gradients along particle paths combined with fore-aft symmetry breaking due to both swimming and particle nonsphericity. Remarkably, the discovered alignment is found to be a robust kinematical effect, independent of the underlying flow evolution. We discuss its possible relevance for aquatic ecology.

Heavy particles in a persistent random flow with traps.

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.

Distribution of label spacings for genome mapping in nanochannels.

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice, its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here, we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.

Hairpins in the conformations of a confined polymer.

If a semiflexible polymer confined to a narrow channel bends around by 180°, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here, we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte-Carlo simulations of confined discrete wormlike chains. We develop a simple model that qualitatively explains the form of the extension distribution. The model shows that the tail of the distribution at short extensions is determined by conformations with one hairpin.

Interpreting the genomic landscape of speciation: a road map for finding barriers to gene flow.

Speciation, the evolution of reproductive isolation among populations, is continuous, complex, and involves multiple, interacting barriers. Until it is complete, the effects of this process vary along the genome and can lead to a heterogeneous genomic landscape with peaks and troughs of differentiation and divergence. When gene flow occurs during speciation, barriers restricting gene flow locally in the genome lead to patterns of heterogeneity. However, genomic heterogeneity can also be produced or modified by variation in factors such as background selection and selective sweeps, recombination and mutation rate variation, and heterogeneous gene density. Extracting the effects of gene flow, divergent selection and reproductive isolation from such modifying factors presents a major challenge to speciation genomics. We argue one of the principal aims of the field is to identify the barrier loci involved in limiting gene flow. We first summarize the expected signatures of selection at barrier loci, at the genomic regions linked to them and across the entire genome. We then discuss the modifying factors that complicate the interpretation of the observed genomic landscape. Finally, we end with a road map for future speciation research: a proposal for how to account for these modifying factors and to progress towards understanding the nature of barrier loci. Despite the difficulties of interpreting empirical data, we argue that the availability of promising technical and analytical methods will shed further light on the important roles that gene flow and divergent selection have in shaping the genomic landscape of speciation.

Neutral processes forming large clones during colonization of new areas.

In species reproducing both sexually and asexually clones are often more common in recently established populations. Earlier studies have suggested that this pattern arises due to natural selection favouring generally or locally successful genotypes in new environments. Alternatively, as we show here, this pattern may result from neutral processes during species' range expansions. We model a dioecious species expanding into a new area in which all individuals are capable of both sexual and asexual reproduction, and all individuals have equal survival rates and dispersal distances. Even under conditions that favour sexual recruitment in the long run, colonization starts with an asexual wave. After colonization is completed, a sexual wave erodes clonal dominance. If individuals reproduce more than one season, and with only local dispersal, a few large clones typically dominate for thousands of reproductive seasons. Adding occasional long-distance dispersal, more dominant clones emerge, but they persist for a shorter period of time. The general mechanism involved is simple: edge effects at the expansion front favour asexual (uniparental) recruitment where potential mates are rare. Specifically, our model shows that neutral processes (with respect to genotype fitness) during the population expansion, such as random dispersal and demographic stochasticity, produce genotype patterns that differ from the patterns arising in a selection model. The comparison with empirical data from a post-glacially established seaweed species (Fucus radicans) shows that in this case, a neutral mechanism is strongly supported.

Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence.

The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parametrization of the distribution of ice crystals in clouds, and potentially lead to an improved understanding of radiation reflection or particle aggregation through collisions in clouds.

Relative velocities in bidisperse turbulent suspensions.

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[over ¯], 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[over ¯] is large enough.

One-Parameter Scaling Theory for DNA Extension in a Nanochannel.

Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play.

Angular Dynamics of a Small Particle in Turbulence.

We compute the angular dynamics of a neutrally buoyant nearly spherical particle immersed in an unsteady fluid. We assume that the particle is small, that its translational slip velocity is negligible, and that unsteady and convective inertia are small perturbations. We derive an approximation for the torque on the particle that determines the first inertial corrections to Jeffery's equation. These corrections arise as a consequence of local vortex stretching and can be substantial in turbulence, where local vortex stretching is strong and closely linked to the irreversibility of turbulence.

Statistical model for collisions and recollisions of inertial particles in mixing flows.

Finding a quantitative description of the rate of collisions between small particles suspended in mixing flows is a long-standing problem. Here we investigate the validity of a parameterisation of the collision rate for identical particles subject to Stokes force, based on results for relative velocities of heavy particles that were recently obtained within a statistical model for the dynamics of turbulent aerosols. This model represents the turbulent velocity fluctuations by Gaussian random functions. We find that the parameterisation gives quantitatively good results in the limit where the "ghost-particle approximation" applies. The collision rate is a sum of two contributions due to "caustics" and to "clustering". Within the statistical model we compare the relative importance of these two collision mechanisms. The caustic formation rate is high when the particle inertia becomes large, and we find that caustics dominate the collision rate as soon as they form frequently. We compare the magnitude of the caustic contribution to the collision rate to the formation rate of caustics.

Preferential Sampling and Small-Scale Clustering of Gyrotactic Microswimmers in Turbulence.

Recent studies show that spherical motile microorganisms in turbulence subject to gravitational torques gather in down-welling regions of the turbulent flow. By analyzing a statistical model we analytically compute how shape affects the dynamics, preferential sampling, and small-scale spatial clustering. We find that oblong organisms may spend more time in up-welling regions of the flow, and that all organisms are biased to regions of positive fluid-velocity gradients in the upward direction. We analyze small-scale spatial clustering and find that oblong particles may either cluster more or less than spherical ones, depending on the strength of the gravitational torques.

Erratum: Role of inertia for the rotation of a nearly spherical particle in a general linear flow [Phys. Rev. E 91, 053023 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.91.053023.

Model for melting of confined DNA.

When DNA molecules are heated they denature. This occurs locally so that loops of molten single DNA strands form, connected by intact double-stranded DNA pieces. The properties of this "melting" transition have been intensively investigated. Recently there has been a surge of interest in this question, in part caused by experiments determining the properties of partially bound DNA confined to nanochannels. But how does such confinement affect the melting transition? To answer this question we introduce and solve a model predicting how confinement affects the melting transition for a simple model system by first disregarding the effect of self-avoidance. We find that the transition is smoother for narrower channels. By means of Monte Carlo simulations we then show that a model incorporating self-avoidance shows qualitatively the same behavior and that the effect of confinement is stronger than in the ideal case.

Scaling regimes of a semiflexible polymer in a rectangular channel.

We derive scaling relations for the extension statistics and the confinement free energy for a semiflexible polymer confined to a channel with a rectangular cross section. Our motivation is recent numerical results [Gupta et al., J. Chem. Phys. 140, 214901 (2014)] indicating that extensional fluctuations are quite different in rectangular channels compared to square channels. Our results are of direct relevance for interpreting current experiments on DNA molecules confined to nanochannels, as many experiments are performed for rectangular channels with large aspect ratios, while theoretical and simulation results are usually obtained for square channels.

Role of inertia for the rotation of a nearly spherical particle in a general linear flow.

We analyze the angular dynamics of a neutrally buoyant, nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, a regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and by assuming that inertial effects are small but finite.

Effect of weak fluid inertia upon Jeffery orbits.

We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the "Jeffery orbits." We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. We analyze how the linear stability of the "log-rolling" orbit depends on particle shape and find it to be unstable for prolate spheroids. This resolves a puzzle in the interpretation of direct numerical simulations of the problem. In general, both unsteady and nonlinear terms in the Navier-Stokes equations are important.