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

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

A Framework for Finding Anomalous Objects at the LHC

Search for new physics events at the LHC mostly rely on the assumption that the events are characterized in terms of standard-reconstructed objects such as isolated photons, leptons, and jets initiated by QCD-partons. While such strategy works for a vast majority of physics beyond the standard model scenarios, there are examples aplenty where new physics give rise to anomalous objects (such as collimated and equally energetic particles, decays due to long lived particles etc.) in the detectors, which can not be classified as any of the standard-objects. Varied methods and search strategies have been proposed, each of which is trained and optimized for specific models, topologies, and model parameters. Further, as LHC keeps excluding all expected candidates for new physics, the need for a generic method/tool that is capable of finding the unexpected can not be understated. In this paper, we propose one such method that relies on the philosophy that all anomalous objects are $\it{not}$ standard-objects. The anomaly finder, we suggest, simply is a collection of vetoes that eliminate all standard-objects up to a pre-determined acceptance rate. Any event containing at least one anomalous object (that passes all these vetoes), can be identified as a candidate for new physics. Subsequent offline analyses can determine the nature of the anomalous object as well as of the event, paving a robust way to search for these new physics scenarios in a model-independent fashion. Further, since the method relies on learning only the standard-objects, for which control samples are readily available from data, one can build the analysis in an entirely data-driven way.Comment: 32 pages, 5 tables and 12 figures; v2: references added; v3: Practical guideline given for implementation at the LHC, comments added on the possibility of inclusion of Muons and b-jets in the framework. Accepted for publication in Nuclear Physics B; v4: Title fixed from v3 to match journal version, funding information update