A Model of Two Dimensional Turbulence Using Random Matrix Theory

We derive a formula for the entropy of two dimensional incompressible inviscid flow, by determining the volume of the space of vorticity distributions with fixed values for the moments Q_k= \int_w(x)^k d^2 x. This space is approximated by a sequence of spaces of finite volume, by using a regularization of the system that is geometrically natural and connected with the theory of random matrices. In taking the limit we get a simple formula for the entropy of a vortex field. We predict vorticity distributions of maximum entropy with given mean vorticity and enstrophy; also we predict the cylindrically symmetric vortex field with maximum entropy. This could be an approximate description of a hurricane.Comment: latex, 12 pages, 2 figures, acknowledgement adde

Determination of mass of IGR J17091-3624 from "Spectro-Temporal" variations during onset-phase of the 2011 outburst

The 2011 outburst of the black hole candidate IGR J17091-3624 followed the canonical track of state transitions along with the evolution of Quasi-Periodic Oscillation (QPO) frequencies before it began exhibiting various variability classes similar to GRS 1915+105. We use this canonical evolution of spectral and temporal properties to determine the mass of IGR J17091-3624, using three different methods, viz : Photon Index ($\Gamma$) - QPO frequency ($\nu$) correlation, QPO frequency ($\nu$) - Time (day) evolution and broadband spectral modelling based on Two Component Advective Flow. We provide a combined mass estimate for the source using a Naive Bayes based joint likelihood approach. This gives a probable mass range of 11.8 M$_{\odot}$ - 13.7 M$_{\odot}$. Considering each individual estimate and taking the lowermost and uppermost bounds among all three methods, we get a mass range of 8.7 M$_{\odot}$ - 15.6 M$_{\odot}$ with 90% confidence. We discuss the probable implications of our findings in the context of two component accretion flow.Comment: 10 pages, 5 figures (4 in colour), 2 tables. Accepted for publication in Ap

A reason for unreason: returns based beliefs in game theory

Players cooperate in experiments more than game theory would predict. We introduce the ‘returns-based beliefs’ approach: the expected returns of a particular strategy in proportion to total expected returns of all strategies. Using a decision analytic solution concept, Luce’s (1959) probabilistic choice model, and ‘hyperpriors’ for ambiguity in players’ cooperability, our approach explains empirical observations in various classes of games including the Prisoner’s and Traveler’s Dilemmas. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2 × 2 games shows that with loss aversion, returns-based beliefs explain the data better than other equilibrium concepts

Pan-African alkali granites and syenites of Kerala as imprints of taphrogenic magmatism in the South Indian shield

Granite and syenite plutons with alkaline affinities ranging in age from 550 to 750 Ma sporadically puncture the Precambrian granulites of the Kerala region. All the bodies are small (20 to 60 sq km), E-W to NW-SE elongated elliptical intrusives with sharp contacts and lie on or close to major late Proterozoic lineaments. Geochemical plots of A-F-M and An-Ab-Or relations show an apparent alkali enrichment trend on the former, but the plutons define relatively distinct fields on the latter. Most of the plutons are adamellitic to granitic by chemistry. The variations of SiO2 with log sub 10 K2O/MgO (1) brings out the distinct alkaline nature of the plutons. Some of the granites are extremely potassic, like the Peralimala pluton, which shows up to 11.8 percent K2O. On a SiO2-Al2O3-Na2O+K2O (mol percent) plot, the plutons vary from peraluminous to peralkaline, but none are nepheline normative. Low MgO, low to moderate CaO and high Fe2O3/FeO values are other common characteristics. Among trace elements, depletion of Ba, Sr and Rb with high K/Ba and K/Rb values are typical. Overall, the plutons show a trend of decreasing K/Rb ratio with increasing K content. Individual plutons show more clearly defined trends similar to those from granitic masses characterized by plagioclase fractionation

Large-Eddy Simulation of Axisymmetric Compression Corner Flow

The Wall-Modeled Large Eddy Simulation (WMLES) approach is used to study the interaction of a shock wave with a high Reynolds number turbulent boundary layer. Since the near wall region is modeled, high Reynolds number turbulent flows can be simulated at a moderate computational cost. The case considered is that of an axisymmetric Mach 2.85 turbulent boundary layer over a 30 compression corner. The Reynolds number of the boundary layer upstream of the interaction based on momentum thickness (Re theta = u sub infinity theta/v sub infinity) is ~12,000. The geometry and flow conditions match the experiments of Dunagan et al. (NASA TM 88227, 1986). The simulations were performed using equilibrium and non-equilibrium wall models. The agreement with experiment is encouraging for the finest grid with respect to the separation bubble length, unsteady shock structure and wall pressure distribution. Sensitivity ofWMLES results to grid, wall model, and blockage effects in the tunnel are reported