A model for Rayleigh-B\'enard magnetoconvection

A model for three-dimensional Rayleigh-B\'{e}nard convection in low-Prandtl-number fluids near onset with rigid horizontal boundaries in the presence of a uniform vertical magnetic field is constructed and analyzed in detail. The kinetic energy $K$, the convective entropy $\Phi$ and the convective heat flux ($Nu-1$) show scaling behaviour with $\epsilon = r-1$ near onset of convection, where $r$ is the reduced Rayleigh number. The model is also used to investigate various magneto-convective structures close to the onset. Straight rolls, which appear at the primary instability, become unstable with increase in $r$ and bifurcate to three-dimensional structures. The straight rolls become periodically varying wavy rolls or quasiperiodically varying structures in time with increase in $r$ depending on the values of Prandtl number $Pr$. They become irregular in time, with increase in $r$. These standing wave solutions bifurcate first to periodic and then quasiperiodic traveling wave solutions, as $r$ is raised further. The variations of the critical Rayleigh number $Ra_{os}$ and the frequency $\omega_{os}$ at the onset of the secondary instability with $Pr$ are also studied for different values of Chandrasekhar's number $Q$.Comment: 11 pages (To appear in EPJB

Role of uniform horizontal magnetic field on convective flow

The effect of uniform magnetic field applied along a fixed horizontal direction in Rayleigh-B\'enard convection in low-Prandtl-number fluids has been studied using a low dimensional model. The model shows the onset of convection (primary instability) in the form of two dimensional stationary rolls in the absence of magnetic field, when the Rayleigh number $R$ is raised above a critical value $R_c$. The flow becomes three dimensional at slightly higher values of Rayleigh number via wavy instability. These wavy rolls become chaotic for slightly higher values of $R$ in low-Prandtl-number ($P_r$) fluids. A uniform magnetic field along horizontal plane strongly affects all kinds of convective flows observed at higher values of $R$ in its absence. As the magnetic field is raised above certain value, it orients the convective rolls in its own direction. Although the horizontal magnetic field does not change the threshold for the primary instability, it affects the threshold for secondary (wavy) instability. It inhibits the onset of wavy instability. The critical Rayleigh number $R_o (Q,P_r)$ at the onset of wavy instability, which depends on Chandrasekhar's number $Q$ and $P_r$, increases monotonically with $Q$ for a fixed value of $P_r$. The dimensionless number $R_o (Q, P_r)/(R_c Q P_r)$ scales with $Q$ as $Q^{-1}$. A stronger magnetic field suppresses chaos and makes the flow two dimensional with roll pattern aligned along its direction.Comment: 6 pages, 8 figure

Augmented Superfield Approach to Gauge-invariant Massive 2-Form Theory

We discuss the complete sets of the off-shell nilpotent (i.e. s^2_{(a)b} = 0) and absolutely anticommuting (i.e. s_b s_{ab} + s_{ab} s_b = 0) Becchi-Rouet-Stora-Tyutin (BRST) (s_b) and anti-BRST (s_{ab}) symmetries for the (3+1)-dimensional (4D) gauge-invariant massive 2-form theory within the framework of augmented superfield approach to BRST formalism. In this formalism, we obtain the coupled (but equivalent) Lagrangian densities which respect both BRST and anti-BRST symmetries on the constrained hypersurface defined by the Curci-Ferrari type conditions. The absolute anticommutativity property of the (anti-)BRST transformations (and corresponding generators) is ensured by the existence of the Curci-Ferrari type conditions which emerge very naturally in this formalism. Furthermore, the gauge-invariant restriction plays a decisive role in deriving the proper (anti-)BRST transformations for the St{\"u}ckelberg-like vector field.Comment: LaTeX file, 22 pages, no figures, version to appear in Eur. Phys. J. C (2017

Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-B\'{e}nard convection with uniform rotation

We present the results of direct numerical simulations of flow patterns in a low-Prandtl-number ($Pr = 0.1$) fluid above the onset of oscillatory convection in a Rayleigh-B\'{e}nard system rotating uniformly about a vertical axis. Simulations were carried out in a periodic box with thermally conducting and stress-free top and bottom surfaces. We considered a rectangular box ($L_x \times L_y \times 1$) and a wide range of Taylor numbers ($750 \le Ta \le 5000$) for the purpose. The horizontal aspect ratio $\eta = L_y/L_x$ of the box was varied from $0.5$ to $10$. The primary instability appeared in the form of two-dimensional standing waves for shorter boxes ($0.5 \le \eta < 1$ and $1 < \eta < 2$). The flow patterns observed in boxes with $\eta = 1$ and $\eta = 2$ were different from those with $\eta < 1$ and $1 < \eta < 2$. We observed a competition between two sets of mutually perpendicular rolls at the primary instability in a square cell ($\eta = 1$) for $Ta < 2700$, but observed a set of parallel rolls in the form of standing waves for $Ta \geq 2700$. The three-dimensional convection was quasiperiodic or chaotic for $750 \le Ta < 2700$, and then bifurcated into a two-dimensional periodic flow for $Ta \ge 2700$. The convective structures consisted of the appearance and disappearance of straight rolls, rhombic patterns, and wavy rolls inclined at an angle $\phi = \frac{\pi}{2} - \arctan{(\eta^{-1})}$ with the straight rolls.Comment: 32 pages, 14 figures, 1 tabl

Secost: Sequential co-supervision for large scale weakly labeled audio event detection

Weakly supervised learning algorithms are critical for scaling audio event detection to several hundreds of sound categories. Such learning models should not only disambiguate sound events efficiently with minimal class-specific annotation but also be robust to label noise, which is more apparent with weak labels instead of strong annotations. In this work, we propose a new framework for designing learning models with weak supervision by bridging ideas from sequential learning and knowledge distillation. We refer to the proposed methodology as SeCoST (pronounced Sequest) -- Sequential Co-supervision for training generations of Students. SeCoST incrementally builds a cascade of student-teacher pairs via a novel knowledge transfer method. Our evaluations on Audioset (the largest weakly labeled dataset available) show that SeCoST achieves a mean average precision of 0.383 while outperforming prior state of the art by a considerable margin.Comment: Accepted IEEE ICASSP 202