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

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

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

Scaling Deep Learning on GPU and Knights Landing clusters

The speed of deep neural networks training has become a big bottleneck of deep learning research and development. For example, training GoogleNet by ImageNet dataset on one Nvidia K20 GPU needs 21 days. To speed up the training process, the current deep learning systems heavily rely on the hardware accelerators. However, these accelerators have limited on-chip memory compared with CPUs. To handle large datasets, they need to fetch data from either CPU memory or remote processors. We use both self-hosted Intel Knights Landing (KNL) clusters and multi-GPU clusters as our target platforms. From an algorithm aspect, current distributed machine learning systems are mainly designed for cloud systems. These methods are asynchronous because of the slow network and high fault-tolerance requirement on cloud systems. We focus on Elastic Averaging SGD (EASGD) to design algorithms for HPC clusters. Original EASGD used round-robin method for communication and updating. The communication is ordered by the machine rank ID, which is inefficient on HPC clusters. First, we redesign four efficient algorithms for HPC systems to improve EASGD's poor scaling on clusters. Async EASGD, Async MEASGD, and Hogwild EASGD are faster \textcolor{black}{than} their existing counterparts (Async SGD, Async MSGD, and Hogwild SGD, resp.) in all the comparisons. Finally, we design Sync EASGD, which ties for the best performance among all the methods while being deterministic. In addition to the algorithmic improvements, we use some system-algorithm codesign techniques to scale up the algorithms. By reducing the percentage of communication from 87% to 14%, our Sync EASGD achieves 5.3x speedup over original EASGD on the same platform. We get 91.5% weak scaling efficiency on 4253 KNL cores, which is higher than the state-of-the-art implementation

Research methods & statistics for psychology: OER course packet

This packet was developed to teach psychological research methods and statistics as a no-cost, open access course. Secondary goals are to teach computational reproducibilty and create teaching materials that can be shared among colleagues teaching similar courses at Haverford College and around the globe. This packet includes links to video lectures, video tutorials, open access textbooks, statistical analysis activities, and a data sharing repository. This packet was developed during the 2020/21 academic year while the course was being taught remotely due to Covid. The syllabus and course materials were developed keeping asynchronous versus synchronous learning in mind. Use is governed by a CC-BY-NC license

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

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

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