Book review: le gouvernement des catastrophes

Le gouvernement des catastrophes, Sandrine Revet, Julien Langumier (Eds), Karthala, 2013, 286 p

From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations

We show that the flocking transition in the Vicsek model is best understood as a liquid-gas transition, rather than an order-disorder one. The full phase separation observed in flocking models with Z2 rotational symmetry is, however, replaced by a microphase separation leading to a smectic arrangement of traveling ordered bands. Remarkably, continuous deterministic descriptions do not account for this difference, which is only recovered at the fluctuating hydrodynamics level. Scalar and vectorial order parameters indeed produce different types of number fluctuations, which we show to be essential in selecting the inhomogeneous patterns. This highlights an unexpected role of fluctuations in the selection of flock shapes.Comment: 5 p., 5 fig.. Supplementary material: 7 movie

Ab-initio Gutzwiller method: first application to Plutonium

Except for small molecules, it is impossible to solve many electrons systems without imposing severe approximations. If the configuration interaction approaches (CI) or Coupled Clusters techniques \cite{FuldeBook} are applicable for molecules, their generalization for solids is difficult. For materials with a kinetic energy greater than the Coulomb interaction, calculations based on the density functional theory (DFT), associated with the local density approximation (LDA) \cite{Hohenberg64, Kohn65} give satisfying qualitative and quantitative results to describe ground state properties. These solids have weakly correlated electrons presenting extended states, like $sp$ materials or covalent solids. The application of this approximation to systems where the wave functions are more localized ($d$ or $f$-states) as transition metals oxides, heavy fermions, rare earths or actinides is more questionable and can even lead to unphysical results : for example, insulating FeO and CoO are predicted to be metalic by the DFT-LDA..

Krymsk®1 (VVA-1), A dwarfing rootstock suitable for high density plum orchards in the Netherlands

Krymsk®:1 (Prunus tomentosa × Prunus cerasifera) was selected by Gennady Eremin at the Krymsk Breeding Station in Russia in 1966. Since 1994, it has been tested as a rootstock for several plum cultivars in The Netherlands. Graft compatibility was good for scion cultivars ‘Avalon’, ‘Excalibur’, ‘Jubileum’, ‘Opal’, and ‘Victoria’. Growth and production efficiency of plum on Krymsk®:1 was compared with that of plum on St. Julien A and, depending on the cultivar, also with Ferlenain, Otesani 8 and Pixy. With all cultivars, trees on rootstock Krymsk®:1 were by far the least vigorous, most precocious, and most production efficient. The production efficiency of ‘Avalon’ and ‘Excalibur’ on Krymsk®:1 grown for 10 years was 0.41 and 0.26 kg/cm² trunk cross sectional area, respectively, 3.4 and 4.3 times higher on Krymsk®:1 than on St. Julien A. With ‘Opal’ the production efficiency calculated over the first 5 years after planting was 2 to 3 times higher than on St. Julien A, but this difference became non significant after 7 years of cultivation. This was due to the much higher increase in production per tree during the 5th and 6th leaf of the trees on St. Julien A than on Krymsk®:1. Fruit size of ‘Opal’, ‘Avalon’ and ‘Excalibur’ was similar for trees grown on Krymsk®:1 and St. Julien A. With ‘Victoria’ fruit size was significantly larger (5 g) with Krymsk®:1 than with St. Julien A. Krymsk®:1 also increased the percentage of first pick by 15%, the sugar content by 9%, enhanced the development of fruit overcolour and reduced the percentage of fruits with gummosis in ‘Victoria’ plums. Dutch fruit growers show great interest in Krymsk®:1 as a rootstock for plum, as this rootstock makes high density plum orchards feasible. Growers switching to trees on Krymsk®1 have to take more care of their trees, especially in the first years after planting. Pruning, irrigation, and fertilization of the trees need much more attention in order to keep the trees vigorous and ensure good production levels. From 2002 to spring 2008, 120,000 plum trees on Krymsk®1 have been planted in The Netherlands and planting densities have increased from 830 up to 2,285 trees/ha. The main cultivar planted is ‘Victoria’

Frank-Wolfe Algorithms for Saddle Point Problems

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solver over polytopes, thereby partially answering a 30 year-old conjecture. We also survey other convergence results and highlight gaps in the theoretical underpinnings of FW-style algorithms. Motivating applications without known efficient alternatives are explored through structured prediction with combinatorial penalties as well as games over matching polytopes involving an exponential number of constraints.Comment: Appears in: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS 2017). 39 page

A nonlinear model for rotationally constrained convection with Ekman pumping

It is a well established result of linear theory that the influence of differing mechanical boundary conditions, i.e., stress-free or no-slip, on the primary instability in rotating convection becomes asymptotically small in the limit of rapid rotation. This is accounted for by the diminishing impact of the viscous stresses exerted within Ekman boundary layers and the associated vertical momentum transport by Ekman pumping. By contrast, in the nonlinear regime recent experiments and supporting simulations are now providing evidence that the efficiency of heat transport remains strongly influenced by Ekman pumping in the rapidly rotating limit. In this paper, a reduced model is developed for the case of low Rossby number convection in a plane layer geometry with no-slip upper and lower boundaries held at fixed temperatures. A complete description of the dynamics requires the existence of three distinct regions within the fluid layer: a geostrophically balanced interior where fluid motions are predominately aligned with the axis of rotation, Ekman boundary layers immediately adjacent to the bounding plates, and thermal wind layers driven by Ekman pumping in between. The reduced model uses a classical Ekman pumping parameterization to alleviate the need for spatially resolving the Ekman boundary layers. Results are presented for both linear stability theory and a special class of nonlinear solutions described by a single horizontal spatial wavenumber. It is shown that Ekman pumping allows for significant enhancement in the heat transport relative to that observed in simulations with stress-free boundaries. Without the intermediate thermal wind layer the nonlinear feedback from Ekman pumping would be able to generate a heat transport that diverges to infinity. This layer arrests this blowup resulting in finite heat transport at a significantly enhanced value.Comment: 38 pages, 14 figure

The effects of Ekman pumping on quasi-geostrophic Rayleigh-Benard convection

Numerical simulations of 3D, rapidly rotating Rayleigh-Benard convection are performed using an asymptotic quasi-geostrophic model that incorporates the effects of no-slip boundaries through (i) parameterized Ekman pumping boundary conditions, and (ii) a thermal wind boundary layer that regularizes the enhanced thermal fluctuations induced by pumping. The fidelity of the model, obtained by an asymptotic reduction of the Navier-Stokes equations that implicitly enforces a pointwise geostrophic balance, is explored for the first time by comparisons of simulations against the findings of direct numerical simulations and laboratory experiments. Results from these methods have established Ekman pumping as the mechanism responsible for significantly enhancing the vertical heat transport. This asymptotic model demonstrates excellent agreement over a range of thermal forcing for Pr ~1 when compared with results from experiments and DNS at maximal values of their attainable rotation rates, as measured by the Ekman number (E ~ 10^{-7}); good qualitative agreement is achieved for Pr > 1. Similar to studies with stress-free boundaries, four spatially distinct flow morphologies exists. Despite the presence of frictional drag at the upper and/or lower boundaries, a strong non-local inverse cascade of barotropic (i.e., depth-independent) kinetic energy persists in the final regime of geostrophic turbulence and is dominant at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries, Ekman friction is found to attenuate the efficiency of the upscale energy transport and, unlike the case of stress-free boundaries, rapidly saturates the barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is strong enough to prevent the development of a coherent dipole vortex condensate. Instead vortex pairs are found to be intermittent, varying in both time and strength.Comment: 20 pages, 10 figure