Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers [Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013)1751-811310.1088/1751-8113/46/3/035501; Nath, Phys. Rev. E 88, 013010 (2013)PLEEE81539-375510.1103/PhysRevE.88.013010] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000 K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Magnetohydrodynamic stability of stochastically driven accretion flows

We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise. © 2013 American Physical Society.

Mechanism of attenuation of skeletal muscle atrophy by zinc-α2-glycoprotein

The mechanism by which the adipokine zinc-a2-glycoprotein (ZAG) increases the mass of gastrocnemius, but not soleus muscle of diabetic mice, has been evaluated both in vivo and in vitro. There was an increased phosphorylation of both double-stranded RNA-dependent protein kinase and its substrate, eukaryotic initiation factor-2a, which was attenuated by about two-thirds in gastrocnemius but not soleus muscle of ob/ob mice treated with ZAG (50 µg, iv daily) for 5 d. ZAG also reduced the expression of the phospho forms of p38MAPK and phospholipase A2, as well as expression of the ubiquitin ligases (E3) muscle atrophy F-box/atrogin-1 and muscle RING finger protein, and the increased activity of both caspase-3 and casapse-8 to values found in nonobese controls. ZAG also increased the levels of phospho serine-threonine kinase and mammalian target of rapamycin in gastrocnemius muscle and reduced the phosphorylation of insulin receptor substrate-1 (Ser307) associated with insulin resistance. Similar changes were seen with ZAG when murine myotubes were incubated with high glucose concentrations (10 and 25 mm), showing that the effect of ZAG was direct. ZAG produced an increase in cAMP in murine myotubes, and the effects of ZAG on protein synthesis and degradation in vitro could be replicated by dibutyryl cAMP. ZAG increased cAMP levels of gastrocnemius but not soleus muscle. These results suggest that protein accretion in skeletal muscle in response to ZAG may be due to changes in intracellular cAMP and also that ZAG may have a therapeutic application in the treatment of muscle wasting conditions.

Mesozoic to recent evolution of the Andean forearc of northern Chile (22-24 s)

The Andean forearc of northern Chile comprises four morphotectonic units, which include from east to west: 1) The Cordillera de la Costa: composed of Jurassic granites and andesites, thought to represent a volcanic arc, the Mejillones terrane, an accreted allochthonous terrane, and the Lower Cretaceous Coloso basin, which formed through forearc extension along the suture between the Mejillones terrane and the Jurassic arc. Palaeomagnetic studies of the above units have identified approximately 29+/-11 degrees of clockwise rotation. Rotation is due to extension (caused by subduction roll back and slab pull), at an angle to the direction of absolute motion of the South American Plate. 2) The Central Depression: a large arid basin containing isolated fault-bounded blocks of pre-Mesozoic metamorphosed igneous rocks, Triassic sediments and volcanics, and Jurassic carbonates, deposited in a. back-arc basin setting. The isolated blocks formed through extension along previous thrust faults, these originated through compression of the back-arc basin due to accretion of the Jurassic volcanic arc. 3) The Precordillera.: composed of Permian-Triassic rift-related sediments and volcanics, Jurassic continental sediments synchronous with back-arc basin sedimentation, and Cretaceous and Oligo-Miocene continental sediments deposited in foreland basins. Palaeomagnetism has identified clockwise rotation in rocks ranging in age from Jurassic-Miocene. Rotation in the Precordillera. affected larger structural blocks than in the Cordillera de la Costa. 4) The Salar Depression: a. series of arid continental basins developed on continental crust. These basins nay have originated in the Triassic, when rifting of the South American craton is thought to have taken place. In conclusion, palaeomagnetic and geological evidence is consistent with the view that the north Chilean forearc was largely under an extensional stress regime. However, the presence of extensive compressional structures in Palaeocene and older rocks in the forearc together with the currently active foreland thrust belt of Argentina. indicate that throughout the evolution of the Andean Orogen, a delicate balance between compressional and extensional tectonic regimes has existed.

Population lensing vs thermal lensing in Yb:YAG rods and disks

The induced lenses in the Yb:YAG rods and disks end-pumped by a Gaussian beam were analyzed both analytically and numerically. The thermally assisted mechanisms of the lens formation were considered to include: the conventional volume thermal index changes ("dn/dT"), the bulging of end faces, the photoelastic effect, and the bending (for a disk). The heat conduction equations (with an axial heat flux for a disk and a radial heat flux for a rod), and quasi-static thermoelastic equations (in the plane-stress approximation with free boundary conditions) were solved to find the thermal lens power. The population rate equation with saturation (by amplified spontaneous emission or an external wave) was examined to find the electronic lens power in the active elements.