Patterns and bifurcations in low-Prandtl number Rayleigh-Benard convection

We present a detailed bifurcation structure and associated flow patterns for low-Prandtl number ($P=0.0002, 0.002, 0.005, 0.02$) Rayleigh-B\'{e}nard convection near its onset. We use both direct numerical simulations and a 30-mode low-dimensional model for this study. We observe that low-Prandtl number (low-P) convection exhibits similar patterns and chaos as zero-P convection \cite{pal:2009}, namely squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares in contrast to zero-P convection where chaos appears at the onset itself. The range of Rayleigh number for which stationary 2D rolls exist decreases rapidly with decreasing Prandtl number. Our results are in qualitative agreement with results reported earlier

Multiwavelength Observations of an Eruptive Flare: Evidence for Blast Waves and Break-out

Images of an east-limb flare on 3 November 2010 taken in the 131 \AA\ channel of the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory provide a convincing example of a long current sheet below an erupting plasmoid, as predicted by the standard magnetic reconnection model of eruptive flares. However, the 171 \AA\ and 193 \AA\ channel images hint at an alternative scenario. These images reveal that large-scale waves with velocity greater than 1000 km/s propagated alongside and ahead of the erupting plasmoid. Just south of the plasmoid, the waves coincided with type-II radio emission, and to the north, where the waves propagated along plume-like structures, there was increased decimetric emission. Initially the cavity around the hot plasmoid expanded. Later, when the erupting plasmoid reached the height of an overlying arcade system, the plasmoid structure changed, and the lower parts of the cavity collapsed inwards. Hot loops appeared alongside and below the erupting plasmoid. We consider a scenario in which the fast waves and the type-II emission were a consequence of a flare blast wave, and the cavity collapse and the hot loops resulted from the break-out of the flux rope through an overlying coronal arcade.Comment: Solar Physics (published), 15 pages, 8 figure

Eruption of a plasma blob, associated M-class flare, and large-scale EUV wave observed by SDO

We present a multiwavelength study of the formation and ejection of a plasma blob and associated EUV waves in AR NOAA 11176, observed by SDO/AIA and STEREO on 25 March 2011. SDO/AIA images clearly show the formation and ejection of a plasma blob from the lower solar atmosphere at ~9 min prior to the onset of the M1.0 flare. This onset of the M-class flare happened at the site of the blob formation, while the blob was rising in a parabolic path with an average speed of ~300 km/s. The blob also showed twisting and de-twisting motion in the lower corona, and the blob speed varied from ~10-540 km/s. The faster and slower EUV wavefronts were observed in front of the plasma blob during its impulsive acceleration phase. The faster EUV wave propagated with a speed of ~785 to 1020 km/s, whereas the slower wavefront speed varied in between ~245 and 465 km/s. The timing and speed of the faster wave match the shock speed estimated from the drift rate of the associated type II radio burst. The faster wave experiences a reflection by the nearby AR NOAA 11177. In addition, secondary waves were observed (only in the 171 \AA channel), when the primary fast wave and plasma blob impacted the funnel-shaped coronal loops. The HMI magnetograms revealed the continuous emergence of new magnetic flux along with shear flows at the site of the blob formation. It is inferred that the emergence of twisted magnetic fields in the form of arch-filaments/"anemone-type" loops is the likely cause for the plasma blob formation and associated eruption along with the triggering of M-class flare. Furthermore, the faster EUV wave formed ahead of the blob shows the signature of fast-mode MHD wave, whereas the slower wave seems to be generated by the field line compression by the plasma blob. The secondary wave trains originated from the funnel-shaped loops are probably the fast magnetoacoustic waves.Comment: A&A (in press), 22 pages, 13 figure

Friedmann model with viscous cosmology in modified f(R,T)f(R,T) gravity theory

In this paper, we introduce bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function $f(R,T)$, where $R$ and $T$ denote the curvature scalar and the trace of the energy-momentum tensor, respectively within the framework of a flat Friedmann-Robertson-Walker model. As an equation of state for prefect fluid, we take $p=(\gamma-1)\rho$, where $0 \leq \gamma \leq 2$ and viscous term as a bulk viscosity due to isotropic model, of the form $\zeta =\zeta_{0}+\zeta_{1}H$, where $\zeta_{0}$ and $\zeta_{1}$ are constants, and $H$ is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non- viscous and viscous fluids, respectively by assuming a simplest particular model of the form of $f(R,T) = R+2f(T)$, where $f(T)=\alpha T$ ( $\alpha$ is a constant). A big-rip singularity is also observed for $\gamma<0$ at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of $\alpha$ to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits transition from decelerated phase to accelerated phase under certain constraints of $\zeta_0$ and $\zeta_1$. We compare the viscous models with the non-viscous one through the graph plotted between scale factor and cosmic time and find that bulk viscosity plays the major role in the expansion of the universe. A similar graph is plotted for deceleration parameter with non-viscous and viscous fluids and find a transition from decelerated to accelerated phase with some form of bulk viscosity.Comment: 19 pages, 3 figures, the whole paper has been revised to improve the quality of paper. Some references added. arXiv admin note: text overlap with arXiv:1307.4262 by other author

Lyapunov spectra of Coulombic and gravitational periodic systems

We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward computing Lypaunov characteristic exponents using an event-driven algorithm. The results indicate that the energy dependence of the largest Lyapunov exponent emulates that of Kolmogorov-entropy density for each system at different degrees of freedom. Our approach forms an effective and approximation-free tool toward studying the dynamical properties exhibited by the Coulombic and gravitational systems and finds applications in investigating indications of thermodynamic transitions in large versions of the spatially periodic systems.Comment: 9 pages, 4 figures (8 total subfigures

The Global Economic Crisis: Impact on India and Policy Responses

India's financial sector is not deeply integrated with the global financial system, which spared it the first round adverse effects of the global financial crisis and left Indian banks mostly unaffected. However, as the financial crisis morphed in to a full-blown global economic downturn, India could not escape the second round effects. The global crisis has affected India through three distinct channels: financial markets, trade flows, and exchange rates. The reversal in capital inflows, which created a credit crunch in domestic markets along with a severe deterioration in export demand, contributed to the decline of gross domestic product by more than 2 percentage points in the fiscal year 2008–2009. In line with efforts taken by governments and central banks all over the world, the Government and the Reserve Bank of India took aggressive countercyclical measures, sharply relaxing monetary policy and introducing a fiscal stimulus to boost domestic demand. However, this paper argues that with very limited fiscal maneuverability and the limited traction of monetary policy, policy measures to restore the Indian gross domestic product growth back to its potential rate of 8–9% must focus on addressing the structural constraints that are holding down private investment demand.india global financial crisis; gdp growth

Crisis, Imbalances, and India

With the revival of global economy, the issues of “exit policies” and rebalancing global growth have taken center stage in policy discussions. Since many emerging Asian economies presently have large current account surpluses, the issue of rebalancing has special significance for Asia. While India, like other Asian economies, suffered only an indirect impact from the financial crisis, its current policy challenges appear to be different from those facing the People’s Republic of China (PRC) and other East Asian economies, which have relied heavily on external demand and access to the United States market for their growth momentum. With a negative contribution of net exports to gross domestic product growth along with foreign exchange reserves, which amount to a mere one-ninth of the PRC’s, the issue of Trans-Pacific rebalancing of economic growth does not have the same connotations for India as it does for other East Asian economies. However, this paper argues that, given its large domestic market, India could help other East Asian economies in their efforts to achieve greater export diversification and rebalancing of growth.global financial crisis; rebalancing economic growth; indian economy; export diversification