Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application

With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterising the magnitude of the Coriolis force. By converting the original Navier-Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares-of-polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterising the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach

The Role of fast magnetosonic waves in the release and conversion via reconnection of energy stored by a current sheet

Using a simple two-dimensional, zero-beta model, we explore the manner by which reconnection at a current sheet releases and dissipates free magnetic energy. We find that only a small fraction (3%-11% depending on current sheet size) of the energy is stored close enough to the current sheet to be dissipated abruptly by the reconnection process. The remaining energy, stored in the larger-scale field, is converted to kinetic energy in a fast magnetosonic disturbance propagating away from the reconnection site, carrying the initial current and generating reconnection-associated flows (inflow and outflow). Some of this reflects from the lower boundary (the photosphere) and refracts back to the X-point reconnection site. Most of this inward wave energy is reflected back again, and continues to bounce between X-point and photosphere until it is gradually dissipated, over many transits. This phase of the energy dissipation process is thus global and lasts far longer than the initial purely local phase. In the process a significant fraction of the energy (25%-60%) remains as undissipated fast magnetosonic waves propagating away from the reconnection site, primarily upward. This flare-generated wave is initiated by unbalanced Lorentz forces in the reconnection-disrupted current sheet, rather than by dissipation-generated pressure, as some previous models have assumed. Depending on the orientation of the initial current sheet the wave front is either a rarefaction, with backward directed flow, or a compression, with forward directed flow

Najat EL Hachmi’s El último patriarca, a Sociolinguistic Reading

It is a surprising fact that Sociolinguistics has approached the realm of Literature with low intensity. It particularly draws the attention because it is a notoriously social discourse frame and even more if we regard for this discipline ambition for verisimilitude. Starting from this ground, the author of this study proposes a sociolinguistic reading of El último patriarca by connecting the characters’ sociolinguistic landmarks with their social fight. The character Manel-Mimoun will try to become an implacable patriarch and his daughter will attempt to be a free woman that conquers a new identity. Through this reading journey a kind of linguistic and literary tourism is triggered. It is like visiting an emotional landscape that frequently will consist of visiting hidden corners of our sentimental and historical geography, spaces that are forgotten on purpose

Acute knockdown of Kv4.1 regulates repetitive firing rates and clock gene expression in the suprachiasmatic nucleus and daily rhythms in locomotor behavior

AbstractRapidly activating and inactivating A-type K+currents (IA) encoded by Kv4.2 and Kv4.3 pore-forming (α) subunits of the Kv4 subfamily are key regulators of neuronal excitability. Previous studies have suggested a role for Kv4.1 α-subunits in regulating the firing properties of mouse suprachiasmatic nucleus (SCN) neurons. To test this, we utilized an RNA-interference strategy to knockdown Kv4.1, acutely and selectively, in the SCN. Current-clamp recordings revealed that thein vivoknockdown of Kv4.1 significantly (p&lt; 0.0001) increased mean ± SEM repetitive firing rates in SCN neurons during the day (6.4 ± 0.5 Hz) and at night (4.3 ± 0.6 Hz), compared with nontargeted shRNA-expressing SCN neurons (day: 3.1 ± 0.5 Hz; night: 1.6 ± 0.3 Hz). IAwas also significantly (p&lt; 0.05) reduced in Kv4.1-targeted shRNA-expressing SCN neurons (day: 80.3 ± 11.8 pA/pF; night: 55.3 ± 7.7 pA/pF), compared with nontargeted shRNA-expressing (day: 121.7 ± 10.2 pA/pF; night: 120.6 ± 16.5 pA/pF) SCN neurons. The magnitude of the effect of Kv4.1-targeted shRNA expression on firing rates and IAwas larger at night. In addition, Kv4.1-targeted shRNA expression significantly (p&lt; 0.001) increased mean ± SEM nighttime input resistance (Rin; 2256 ± 166 MΩ), compared to nontargeted shRNA-expressing SCN neurons (1143 ± 93 MΩ). Additional experiments revealed that acute knockdown of Kv4.1 significantly (p&lt; 0.01) shortened, by ∼0.5 h, the circadian period of spontaneous electrical activity, clock gene expression and locomotor activity demonstrating a physiological role for Kv4.1-encoded IAchannels in regulating circadian rhythms in neuronal excitability and behavior.</jats:p

Berry Phase Quantum Thermometer

We show how Berry phase can be used to construct an ultra-high precision quantum thermometer. An important advantage of our scheme is that there is no need for the thermometer to acquire thermal equilibrium with the sample. This reduces measurement times and avoids precision limitations.Comment: Updated to published version. I. Fuentes previously published as I. Fuentes-Guridi and I. Fuentes-Schulle