Melting of a nonequilibrium vortex crystal in a fluid film with polymers : elastic versus fluid turbulence

We perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer-conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers \mbox{Re}, the film attains a steady state that is a square lattice of vortices and anti-vortices. We find that, as we increase the Weissenberg number \mbox{Wi}, a sequence of nonequilibrium phase transitions transforms this lattice, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low \mbox{Wi}, and quasiperiodically, for slightly larger \mbox{Wi}. Finally, the system becomes disordered and displays spatiotemporal chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the \mbox{Wi} - \Omega plane, where \Omega \propto {\mbox{Re}}, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter $\Lambda$ provides us with a natural measure for characterizing the phases and transitions in this diagram.Comment: 16 pages, 17 figure

How should emerging economies manage their foreign exchange reserves?

Asia has emerged as the balancing wheel of global finance. The countries of Asia now account for 70 per cent of global foreign exchange reserves, compared to only 30 percent in 1990 and 21 per cent in the early 1970s. This paper explores theoretical interpretations for the relatively high demand for international reserves by developing countries especially in the Far East. This paper provides calculations of the minimal necessary level of international reserves based on benchmarks proposed by Wijnholds and Kapteyn, as well as a discussion of costs of reserves’ holding. It therefore provides empirical proof that exchange reserve levels for many of the developing countries have far exceeded the desirable levels. Paper then discusses the steps that central banks in these developing countries can take for an effective reserve management.Foreign exchange ; emerging economies; reserves; reserve level; east asia

A Novel Method to Calculate Click Through Rate for Sponsored Search

Sponsored search adopts generalized second price (GSP) auction mechanism which works on the concept of pay per click which is most commonly used for the allocation of slots in the searched page. Two main aspects associated with GSP are the bidding amount and the click through rate (CTR). The CTR learning algorithms currently being used works on the basic principle of (#clicks_i/ #impressions_i) under a fixed window of clicks or impressions or time. CTR are prone to fraudulent clicks, resulting in sudden increase of CTR. The current algorithms are unable to find the solutions to stop this, although with the use of machine learning algorithms it can be detected that fraudulent clicks are being generated. In our paper, we have used the concept of relative ranking which works on the basic principle of (#clicks_i /#clicks_t). In this algorithm, both the numerator and the denominator are linked. As #clicks_t is higher than previous algorithms and is linked to the #clicks_i, the small change in the clicks which occurs in the normal scenario have a very small change in the result but in case of fraudulent clicks the number of clicks increases or decreases rapidly which will add up with the normal clicks to increase the denominator, thereby decreasing the CTR.Comment: 10 pages, 1 figur