Analytical smoothing effect of solution for the boussinesq equations

In this paper, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H 1-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equation admet exactly same smoothing effect properties of incompressible Navier-Stokes equations

Long-term X-ray emission from Swift J1644+57

The X-ray emission from Swift J1644+57 is not steadily decreasing instead it shows multiple pulses with declining amplitudes. We model the pulses as reverse shocks from collisions between the late ejected shells and the externally shocked material, which is decelerated while sweeping the ambient medium. The peak of each pulse is taken as the maximum emission of each reverse shock. With a proper set of parameters, the envelope of peaks in the light curve as well as the spectrum can be modelled nicely.Comment: 6 pages, 2 figures, accepted for publication in MNRA

Revisiting Charmless Hadronic B_{u,d} Decays in QCD Factorization

Within the framework of QCD factorization (QCDF), we consider two different types of power correction effects in order to resolve the CP puzzles and rate deficit problems with penguin-dominated two-body decays of B mesons and color-suppressed tree-dominated $\pi^0\pi^0$ and $\rho^0\pi^0$ modes: penguin annihilation and soft corrections to the color-suppressed tree amplitude. We emphasize that the electroweak penguin solution to the $B\to K\pi$ CP puzzle via New Physics is irrelevant for solving the CP and rate puzzles related to tree-dominated decays. While some channels e.g. $K^-\pi^+,K^-\rho^0,\pi^+\pi^-,\rho^\pm\pi^\mp$ need penguin annihilation to induce the correct magnitudes and signs for their CP violation, some other decays such as $B^-\to K^-\pi^0,\pi^-\eta, K^-\eta$ and $\bar B^0\to \bar K^{*0}\eta,\pi^0\pi^0$ require the presence of both power corrections to account for the measured CP asymmetries. In general, QCDF predictions for the branching fractions and direct CP asymmetries of $\bar B\to PP,VP,VV$ decays are in good agreement with experiment. The predictions of pQCD and soft-collinear effective theory are included for comparison.Comment: 51 pages, 1 figur

A Morphological Approach to the Pulsed Emission from Soft Gamma Repeaters

We present a geometrical methodology to interpret the periodical light curves of Soft Gamma Repeaters based on the magnetar model and the numerical arithmetic of the three-dimensional magnetosphere model for the young pulsars. The hot plasma released by the star quake is trapped in the magnetosphere and photons are emitted tangent to the local magnetic field lines. The variety of radiation morphologies in the burst tails and the persistent stages could be well explained by the trapped fireballs on different sites inside the closed field lines. Furthermore, our numerical results suggests that the pulse profile evolution of SGR 1806-20 during the 27 December 2004 giant flare is due to a lateral drift of the emitting region in the magnetosphere.Comment: 7 figures, accepted by Ap

Supersymmetric Mean-Field Theory of t-J Model

The supersymmetric formulation of t-J model is studied in this paper at the mean-field level where $\delta$-T phase diagram is computed. We find that slave-fermion-like spiral phase is stable at low doping concentration, and the slave-boson-like d-wave fermionic spin pairing state becomes energetically favourable when $\delta\geq$ 0.23. An improvement in free energy using Gutzwiller's method lowers the transition doping concentration to 0.06. We also point out the existence of new branches of excitations in the supersymmetric theory.Comment: 11 pages and 2 figure

Umbral Moonshine and the Niemeier Lattices

In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice we attach a finite group by considering a naturally defined quotient of the lattice automorphism group, and for each conjugacy class of each of these groups we identify a vector-valued mock modular form whose components coincide with mock theta functions of Ramanujan in many cases. This leads to the umbral moonshine conjecture, stating that an infinite-dimensional module is assigned to each of the Niemeier lattices in such a way that the associated graded trace functions are mock modular forms of a distinguished nature. These constructions and conjectures extend those of our earlier paper, and in particular include the Mathieu moonshine observed by Eguchi-Ooguri-Tachikawa as a special case. Our analysis also highlights a correspondence between genus zero groups and Niemeier lattices. As a part of this relation we recognise the Coxeter numbers of Niemeier root systems with a type A component as exactly those levels for which the corresponding classical modular curve has genus zero.Comment: 181 pages including 95 pages of Appendices; journal version, minor typos corrected, Research in the Mathematical Sciences, 2014, vol.