On the Mahler measure of Jones polynomials under twisting

We show that the Mahler measures of the Jones polynomial and of the colored Jones polynomials converge under twisting for any link. Moreover, almost all of the roots of these polynomials approach the unit circle under twisting. In terms of Mahler measure convergence, the Jones polynomial behaves like hyperbolic volume under Dehn surgery. For pretzel links P(a_1,...,a_n), we show that the Mahler measure of the Jones polynomial converges if all a_i tend to infinity, and approaches infinity for a_i = constant if n tend to infinity, just as hyperbolic volume. We also show that after sufficiently many twists, the coefficient vector of the Jones polynomial and of any colored Jones polynomial decomposes into fixed blocks according to the number of strands twisted.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-1.abs.htm

Jet modification in the next decade: a pedestrian outlook

In this review, intended for non-specialists and beginners, we recount the current status of the theory of jet modification in dense matter. We commence with an outline of the "traditional" observables which may be calculated without recourse to event generators. These include single and double hadron suppression, nuclear modification factor versus reaction plane etc. All of these measurements are used to justify both the required underlying physical picture of jet modification as well as the final obtained values of jet transport coefficients. This is followed by a review of the more modern observables which have arisen with the ability to reconstruct full jets, and the challenges faced therein. This is followed by a preview of upcoming theoretical developments in the field and an outlook on how the interface between these developments, phenomenological improvements, and upcoming data will allow us to quantitatively determine properties of the medium which effect the modification of hard jets.Comment: 21 pages, 10 figure

Analytical studies of particle dynamics in bending waves in planetary rings

Particles inside a planetary ring are subject to forcing due to the central planet, moons in inclined orbits, self-gravity of the ring and other forces due to radiation drag, collisional effects and Lorentz force due to magnetic field of the planet. We write down the equations of motion of a single particle inside the ring and solve them analytically. We find that the importance of the shear caused by variation of the radial velocity component with local vertical direction cannot be ignored and it may be responsible for damping of the bending waves in planetary rings as observed by the Voyager data. We present the wave profile resulting from the dissipation. We estimate that the surface mass density of the C ring to be of the order of $\sigma \sim 1.2-1.6$gm cm$^{-2}$, and the height $h \sim 2.2-2.4$m. These theoretical results are in agreement with observations.Comment: 17 pages 3 figures MNRAS (In press

Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps

We prove the existence of continuous boundary extensions (Cannon-Thurston maps) for the inclusion of a vertex space into a tree of (strongly) relatively hyperbolic spaces satisfying the qi-embedded condition. This implies the same result for inclusion of vertex (or edge) subgroups in finite graphs of (strongly) relatively hyperbolic groups. This generalises a result of Bowditch for punctured surfaces in 3 manifolds and a result of Mitra for trees of hyperbolic metric spaces.Comment: 27pgs No figs, v3: final version, incorporating referee's comments, to appear in Geometriae Dedicat

Pitfalls of participatory programs : evidence from a randomized evaluation in education in India

Statement of responsibility on t.p. reads: Abhijit V. Banerjee, Rukmini Benerji [i.e. Banerji], Esther Duflo, Rachel Glennerster and Stuti KhemaniSeptember 5, 200

Thermal conductivity and diffusion-mediated localization in Fe_{1-x}Cr_{x} Alloys

We apply a new Kubo-Greenwood type formula combined with a generalized Feynman diagram- matic technique to report a first principles calculation of the thermal transport properties of disordered Fe_{1-x}Cr_{x} alloys. The diagrammatic approach simplifies the inclusion of disorder-induced scattering effects on the two particle correlation functions and hence renormalizes the heat current operator to calculate configuration averaged lattice thermal conductivity and diffusivity. The thermal conductivity K(T) in the present case shows an approximate quadratic T-dependence in the low temperature regime (T < 20 K), which subsequently rises smoothly to a T-independent saturated value at high T . A numerical estimate of mobility edge from the thermal diffusivity data yields the fraction of localized states. It is concluded that the complex disorder scattering processes, in force-constant dominated disorder alloys such as Fe-Cr, tend to localize the vibrational modes quite significantly.Comment: 5 pages, 5 figure

Ali Wyne on Understanding Poverty Edited by Abhijit Vinayak Banerjee, Roland Bénabou, and Dilip Mookherjee. Oxford: Oxford University Press, 2006. 496pp.

A review of: Understanding Poverty Edited by Abhijit Vinayak Banerjee, Roland Bénabou, and Dilip Mookherjee. Oxford: Oxford University Press, 2006. 496pp