The linear instability of the stratified plane Couette flow

We present the stability analysis of a plane Couette flow which is stably stratified in the vertical direction orthogonally to the horizontal shear. Interest in such a flow comes from geophysical and astrophysical applications where background shear and vertical stable stratification commonly coexist. We perform the linear stability analysis of the flow in a domain which is periodic in the stream-wise and vertical directions and confined in the cross-stream direction. The stability diagram is constructed as a function of the Reynolds number Re and the Froude number Fr, which compares the importance of shear and stratification. We find that the flow becomes unstable when shear and stratification are of the same order (i.e. Fr $\sim$ 1) and above a moderate value of the Reynolds number Re$\gtrsim$700. The instability results from a resonance mechanism already known in the context of channel flows, for instance the unstratified plane Couette flow in the shallow water approximation. The result is confirmed by fully non linear direct numerical simulations and to the best of our knowledge, constitutes the first evidence of linear instability in a vertically stratified plane Couette flow. We also report the study of a laboratory flow generated by a transparent belt entrained by two vertical cylinders and immersed in a tank filled with salty water linearly stratified in density. We observe the emergence of a robust spatio-temporal pattern close to the threshold values of F r and Re indicated by linear analysis, and explore the accessible part of the stability diagram. With the support of numerical simulations we conclude that the observed pattern is a signature of the same instability predicted by the linear theory, although slightly modified due to streamwise confinement

Order Out of Chaos: Slowly Reversing Mean Flows Emerge from Turbulently Generated Internal Waves

We demonstrate via direct numerical simulations that a periodic, oscillating mean flow spontaneously develops from turbulently generated internal waves. We consider a minimal physical model where the fluid self-organizes in a convective layer adjacent to a stably stratified one. Internal waves are excited by turbulent convective motions, then nonlinearly interact to produce a mean flow reversing on timescales much longer than the waves' period. Our results demonstrate for the first time that the three-scale dynamics due to convection, waves, and mean flow is generic and hence can occur in many astrophysical and geophysical fluids. We discuss efforts to reproduce the mean flow in reduced models, where the turbulence is bypassed. We demonstrate that wave intermittency, resulting from the chaotic nature of convection, plays a key role in the mean-flow dynamics, which thus cannot be captured using only second-order statistics of the turbulent motions

Fast Genetic Algorithms

For genetic algorithms using a bit-string representation of length~$n$, the general recommendation is to take $1/n$ as mutation rate. In this work, we discuss whether this is really justified for multimodal functions. Taking jump functions and the $(1+1)$ evolutionary algorithm as the simplest example, we observe that larger mutation rates give significantly better runtimes. For the \jump_{m,n} function, any mutation rate between $2/n$ and $m/n$ leads to a speed-up at least exponential in $m$ compared to the standard choice. The asymptotically best runtime, obtained from using the mutation rate $m/n$ and leading to a speed-up super-exponential in $m$, is very sensitive to small changes of the mutation rate. Any deviation by a small (1 \pm \eps) factor leads to a slow-down exponential in $m$. Consequently, any fixed mutation rate gives strongly sub-optimal results for most jump functions. Building on this observation, we propose to use a random mutation rate $\alpha/n$, where $\alpha$ is chosen from a power-law distribution. We prove that the $(1+1)$ EA with this heavy-tailed mutation rate optimizes any \jump_{m,n} function in a time that is only a small polynomial (in~$m$) factor above the one stemming from the optimal rate for this $m$. Our heavy-tailed mutation operator yields similar speed-ups (over the best known performance guarantees) for the vertex cover problem in bipartite graphs and the matching problem in general graphs. Following the example of fast simulated annealing, fast evolution strategies, and fast evolutionary programming, we propose to call genetic algorithms using a heavy-tailed mutation operator \emph{fast genetic algorithms}

Parametric instability and wave turbulence driven by tidal excitation of internal waves

We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically stretched and sheared by the tidal base flow. While keeping the key physical ingredients only, such a model is efficient to simulate planetary regimes where tidal amplitudes and dissipation are small. With this model, we prove that tidal flows are able to drive parametric subharmonic resonances of internal waves, in a way reminiscent of the elliptical instability in rotating fluids. The growth rates computed via Direct Numerical Simulations (DNS) are in very good agreement with WKB analysis and Floquet theory. We also investigate the turbulence driven by this instability mechanism. With spatio-temporal analysis, we show that it is a weak internal wave turbulence occurring at small Froude and buoyancy Reynolds numbers. When the gap between the excitation and the Brunt-V\"ais\"al\"a frequencies is increased, the frequency spectrum of this wave turbulence displays a -2 power law reminiscent of the high-frequency branch of the Garett and Munk spectrum (Garrett & Munk 1979) which has been measured in the oceans. In addition, we find that the mixing efficiency is altered compared to what is computed in the context of DNS of stratified turbulence excited at small Froude and large buoyancy Reynolds numbers and is consistent with a superposition of waves.Comment: Accepted for publication in Journal of Fluid Mechanics, 27 pages, 21 figure

MAP7 regulates axon morphogenesis by recruiting kinesin-1 to microtubules and modulating organelle transport.

Neuronal cell morphogenesis depends on proper regulation of microtubule-based transport, but the underlying mechanisms are not well understood. Here, we report our study of MAP7, a unique microtubule-associated protein that interacts with both microtubules and the motor protein kinesin-1. Structure-function analysis in rat embryonic sensory neurons shows that the kinesin-1 interacting domain in MAP7 is required for axon and branch growth but not for branch formation. Also, two unique microtubule binding sites are found in MAP7 that have distinct dissociation kinetics and are both required for branch formation. Furthermore, MAP7 recruits kinesin-1 dynamically to microtubules, leading to alterations in organelle transport behaviors, particularly pause/speed switching. As MAP7 is localized to branch sites, our results suggest a novel mechanism mediated by the dual interactions of MAP7 with microtubules and kinesin-1 in the precise control of microtubule-based transport during axon morphogenesis

A Quasi-Bayesian Perspective to Online Clustering

When faced with high frequency streams of data, clustering raises theoretical and algorithmic pitfalls. We introduce a new and adaptive online clustering algorithm relying on a quasi-Bayesian approach, with a dynamic (i.e., time-dependent) estimation of the (unknown and changing) number of clusters. We prove that our approach is supported by minimax regret bounds. We also provide an RJMCMC-flavored implementation (called PACBO, see https://cran.r-project.org/web/packages/PACBO/index.html) for which we give a convergence guarantee. Finally, numerical experiments illustrate the potential of our procedure

Preferred sizes and ordering in surface nanobubble populations

Two types of homogeneous surface nanobubble populations, created by different means, are analyzed statistically on both their sizes and spatial positions. In the first type (created by droplet-deposition, case A) the bubble size R is found to be distributed according to a generalized gamma law with a preferred radius R*=20 nm. The radial distribution function shows a preferred spacing at ~5.5 R*. These characteristics do not show up in comparable Monte-Carlo simulations of random packings of hard disks with the same size distribution and the same density, suggesting a structuring effect in the nanobubble formation process. The nanobubble size distribution of the second population type (created by ethanol-water exchange, case B) is a mixture of two clearly separated distributions, hence, with two preferred radii. The local ordering is less significant, due to the looser packing of the nanobubbles.Comment: 5 pages, 5 figure

Auditory display of seismic data: On the use of experts' categorizations and verbal descriptions as heuristics for geoscience

International audienceAuditory display can complement visual representations in order to better interpret scientific data. A previous article showed that the free categorization of “audified seismic signals” operated by listeners can be explained by various geophysical parameters. The present article confirms this result and shows that cognitive representations of listeners can be used as heuristics for the characterization of seismic signals. Free sorting tests are conducted with audified seismic signals, with the earthquake/seismometer relative location, playback audification speed, and earthquake magnitude as controlled variables. The analysis is built on partitions (categories) and verbal comments (categorization criteria). Participants from different backgrounds (acousticians or geoscientists) are contrasted in order to investigate the role of the participants' expertise. Sounds resulting from different earthquake/station distances or azimuths, crustal structure and topography along the path of the seismic wave, earthquake magnitude, are found to (a) be sorted into different categories, (b) elicit different verbal descriptions mainly focused on the perceived number of events, frequency content, and background noise level. Building on these perceptual results, acoustic descriptors are computed and geophysical interpretations are proposed in order to match the verbal descriptions. Another result is the robustness of the categories with respect to the audification speed factor

Knowledge-aware Complementary Product Representation Learning

Learning product representations that reflect complementary relationship plays a central role in e-commerce recommender system. In the absence of the product relationships graph, which existing methods rely on, there is a need to detect the complementary relationships directly from noisy and sparse customer purchase activities. Furthermore, unlike simple relationships such as similarity, complementariness is asymmetric and non-transitive. Standard usage of representation learning emphasizes on only one set of embedding, which is problematic for modelling such properties of complementariness. We propose using knowledge-aware learning with dual product embedding to solve the above challenges. We encode contextual knowledge into product representation by multi-task learning, to alleviate the sparsity issue. By explicitly modelling with user bias terms, we separate the noise of customer-specific preferences from the complementariness. Furthermore, we adopt the dual embedding framework to capture the intrinsic properties of complementariness and provide geometric interpretation motivated by the classic separating hyperplane theory. Finally, we propose a Bayesian network structure that unifies all the components, which also concludes several popular models as special cases. The proposed method compares favourably to state-of-art methods, in downstream classification and recommendation tasks. We also develop an implementation that scales efficiently to a dataset with millions of items and customers