A new estimate on Evans' Weak KAM approach

We consider a recent formulation of weak KAM theory proposed by Evans. As well as for classical integrability, for one dimensional mechanical Hamiltonian systems all the computations can be explicitly done. This allows us on the one hand to illustrate the geometric content of the theory, on the other hand to prove new lower bounds which extend also to the generic n degrees of freedom case

Rossby-wave turbulence in a rapidly rotating sphere

We use a quasi-geostrophic numerical model to study the turbulence of rotating flows in a sphere, with realistic Ekman friction and bulk viscous dissipation. The forcing is caused by the destabilization of an axisymmetric Stewartson shear layer, generated by differential rotation, resulting in a forcing at rather large scales. <P> The equilibrium regime is strongly anisotropic and inhomogeneous but exhibits a steep <i>m^-5</i> spectrum in the azimuthal (periodic) direction, at scales smaller than the injection scale. This spectrum has been proposed by Rhines for a Rossby wave turbulence. For some parameter range, we observe a turbulent flow dominated by a large scale vortex located in the shear layer, reminding us of the Great Red Spot of Jupiter

Numerical Simulations of Dynamos Generated in Spherical Couette Flows

We numerically investigate the efficiency of a spherical Couette flow at generating a self-sustained magnetic field. No dynamo action occurs for axisymmetric flow while we always found a dynamo when non-axisymmetric hydrodynamical instabilities are excited. Without rotation of the outer sphere, typical critical magnetic Reynolds numbers $Rm_c$ are of the order of a few thousands. They increase as the mechanical forcing imposed by the inner core on the flow increases (Reynolds number $Re$). Namely, no dynamo is found if the magnetic Prandtl number $Pm=Rm/Re$ is less than a critical value $Pm_c\sim 1$. Oscillating quadrupolar dynamos are present in the vicinity of the dynamo onset. Saturated magnetic fields obtained in supercritical regimes (either $Re>2 Re_c$ or $Pm>2Pm_c$) correspond to the equipartition between magnetic and kinetic energies. A global rotation of the system (Ekman numbers $E=10^{-3}, 10^{-4}$) yields to a slight decrease (factor 2) of the critical magnetic Prandtl number, but we find a peculiar regime where dynamo action may be obtained for relatively low magnetic Reynolds numbers ($Rm_c\sim 300$). In this dynamical regime (Rossby number $Ro\sim -1$, spheres in opposite direction) at a moderate Ekman number ($E=10^{-3}$), a enhanced shear layer around the inner core might explain the decrease of the dynamo threshold. For lower $E$ ($E=10^{-4}$) this internal shear layer becomes unstable, leading to small scales fluctuations, and the favorable dynamo regime is lost. We also model the effect of ferromagnetic boundary conditions. Their presence have only a small impact on the dynamo onset but clearly enhance the saturated magnetic field in the ferromagnetic parts. Implications for experimental studies are discussed

Experimental study of super-rotation in a magnetostrophic spherical Couette flow

We report measurements of electric potentials at the surface of a spherical container of liquid sodium in which a magnetized inner core is differentially rotating. The azimuthal angular velocities inferred from these potentials reveal a strong super-rotation of the liquid sodium in the equatorial region, for small differential rotation. Super-rotation was observed in numerical simulations by Dormy et al. [1]. We find that the latitudinal variation of the electric potentials in our experiments differs markedly from the predictions of a similar numerical model, suggesting that some of the assumptions used in the model - steadiness, equatorial symmetry, and linear treatment for the evolution of both the magnetic and velocity fields - are violated in the experiments. In addition, radial velocity measurements, using ultrasonic Doppler velocimetry, provide evidence of oscillatory motion near the outer sphere at low latitude: it is viewed as the signature of an instability of the super-rotating region

Zonal shear and super-rotation in a magnetized spherical Couette flow experiment

We present measurements performed in a spherical shell filled with liquid sodium, where a 74 mm-radius inner sphere is rotated while a 210 mm-radius outer sphere is at rest. The inner sphere holds a dipolar magnetic field and acts as a magnetic propeller when rotated. In this experimental set-up called DTS, direct measurements of the velocity are performed by ultrasonic Doppler velocimetry. Differences in electric potential and the induced magnetic field are also measured to characterize the magnetohydrodynamic flow. Rotation frequencies of the inner sphere are varied between -30 Hz and +30 Hz, the magnetic Reynolds number based on measured sodium velocities and on the shell radius reaching to about 33. We have investigated the mean axisymmetric part of the flow, which consists of differential rotation. Strong super-rotation of the fluid with respect to the rotating inner sphere is directly measured. It is found that the organization of the mean flow does not change much throughout the entire range of parameters covered by our experiment. The direct measurements of zonal velocity give a nice illustration of Ferraro's law of isorotation in the vicinity of the inner sphere where magnetic forces dominate inertial ones. The transition from a Ferraro regime in the interior to a geostrophic regime, where inertial forces predominate, in the outer regions has been well documented. It takes place where the local Elsasser number is about 1. A quantitative agreement with non-linear numerical simulations is obtained when keeping the same Elsasser number. The experiments also reveal a region that violates Ferraro's law just above the inner sphere.Comment: Phys Rev E, in pres

Generalized Species Sampling Priors with Latent Beta reinforcements

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data.Comment: For correspondence purposes, Edoardo M. Airoldi's email is [email protected]; Federico Bassetti's email is [email protected]; Michele Guindani's email is [email protected] ; Fabrizo Leisen's email is [email protected]. To appear in the Journal of the American Statistical Associatio

Economic evaluation of flexible IGCC plants with integrated membrane reactor modules

Integrated Gasification Combined Cycle with embedded membrane reactor modules (IGCC-MR) represents a new technology option for the co-production of electricity and pure hydrogen endowed with enhanced environmental performance capacity. It is an alternative to conventional coaland gas-fired power generation technologies. As a new technology, the IGCC-MR power plant needs to be evaluated in the presence of irreducible regulatory and fuel market uncertainties for the potential deployment of an initial fleet of demonstration plants at the commercial scale. This paper presents the development of a systematic and comprehensive three-step methodological framework to assess the economic value of flexible alternatives in the design and operations of an IGCC-MR plant under the aforementioned sources of uncertainty. The main objective is to demonstrate the potential value enhancements stemming to the long-term economic performance of flexible IGCC-MR project investments, by managing the uncertainty associated with future environmental regulations and fuel costs. The paper provides an overview of promising design flexibility concepts for IGCC-MR power plants and focuses on operational and constructional flexibility. The operational flexibility is realized through the option of a temporary shutdown of the plant with considerations of regulatory and market uncertainties. This option reduces the probability of loss and the downside risk compared to the base case. The constructional flexibility considers installation of a Carbon Capture and Storage (CCS) unit in the plant under three different alternatives: 1) installing CCS in the initial construction phase, 2) retrofitting CCS at a later stage and 3) retrofitting CCS with pre-investment at a later stage. Monte Carlo simulations and financial analysis are used to demonstrate that the most economically advantageous flexibility option is to install CCS in the initial IGCC-MR construction phase

Cortical fast-spiking parvalbumin interneurons enwrapped in the perineuronal net express the metallopeptidases Adamts8, Adamts15 and Neprilysin.

The in situ hybridization Allen Mouse Brain Atlas was mined for proteases expressed in the somatosensory cerebral cortex. Among the 480 genes coding for protease/peptidases, only four were found enriched in cortical interneurons: Reln coding for reelin; Adamts8 and Adamts15 belonging to the class of metzincin proteases involved in reshaping the perineuronal net (PNN) and Mme encoding for Neprilysin, the enzyme degrading amyloid β-peptides. The pattern of expression of metalloproteases (MPs) was analyzed by single-cell reverse transcriptase multiplex PCR after patch clamp and was compared with the expression of 10 canonical interneurons markers and 12 additional genes from the Allen Atlas. Clustering of these genes by K-means algorithm displays five distinct clusters. Among these five clusters, two fast-spiking interneuron clusters expressing the calcium-binding protein Pvalb were identified, one co-expressing Pvalb with Sst (PV-Sst) and another co-expressing Pvalb with three metallopeptidases Adamts8, Adamts15 and Mme (PV-MP). By using Wisteria floribunda agglutinin, a specific marker for PNN, PV-MP interneurons were found surrounded by PNN, whereas the ones expressing Sst, PV-Sst, were not

Genetic dissection of an amygdala microcircuit that gates conditioned fear

The role of different amygdala nuclei (neuroanatomical subdivisions) in processing Pavlovian conditioned fear has been studied extensively, but the function of the heterogeneous neuronal subtypes within these nuclei remains poorly understood. Here we use molecular genetic approaches to map the functional connectivity of a subpopulation of GABA-containing neurons, located in the lateral subdivision of the central amygdala (CEl), which express protein kinase C-δ (PKC-δ). Channelrhodopsin-2-assisted circuit mapping in amygdala slices and cell-specific viral tracing indicate that PKC-δ^+ neurons inhibit output neurons in the medial central amygdala (CEm), and also make reciprocal inhibitory synapses with PKC-δ^− neurons in CEl. Electrical silencing of PKC-δ^+ neurons in vivo suggests that they correspond to physiologically identified units that are inhibited by the conditioned stimulus, called Cel_(off) units. This correspondence, together with behavioural data, defines an inhibitory microcircuit in CEl that gates CEm output to control the level of conditioned freezing