Pulsar kicks via spin-1 color superconductivity

We propose a new neutrino propulsion mechanism for neutron stars which can lead to strong velocity kicks, needed to explain the observed bimodal velocity distribution of pulsars. The spatial asymmetry in the neutrino emission is naturally provided by a stellar core containing spin-1 color-superconducting quark matter in the A phase. The neutrino propulsion mechanism switches on when the stellar core temperature drops below the transition temperature of this phase.     

Convergence of Julia polynomials

We study the approximation of conformal mappings with the polynomials defined by Keldysh and Lavrentiev from an extremal problem considered by Julia. These polynomials converge uniformly on the closure of any Smirnov domain to the conformal mapping of this domain onto a disk. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed through the smallest exterior angles at the boundary. Research supported in part by the National Security Agency under Grant No. MDA904-03-1-0081.     

Unusual reactivity of 3-chloro-1-pentafluorosulfanylpropene in nucleophilic substitution reactions

Treatment of 3-chloro-1-pentafluorosulfanylprop-1-ene 1 with KCN yielded the product of prototropic rearrangement ClCHCHCH₂SF₅, whereas reactions with NaN₃ and KSCN gave the S_N2 products. Ab initio calculations at MP2/6-311++G** level are used to explain the unusual behaviour of cyanide. It was found that proton transfers from both 1 to CN⁻ and from HCN to the anion of 1 are exothermic. In contrast, azide and thiocyanate ions are too weakly basic to deprotonate 1.     

Recent advances in laser self-injection locking to high-Q microresonators

The stabilization and manipulation of laser frequency by means of an external cavity are nearly ubiquitously used in fundamental research and laser applications. While most of the laser light transmits through the cavity, in the presence of some back-scattered light from the cavity to the laser, the self-injection locking effect can take place, which locks the laser emission frequency to the cavity mode of similar frequency. The self-injection locking leads to dramatic reduction of laser linewidth and noise. Using this approach, a common semiconductor laser locked to an ultrahigh-Q microresonator can obtain sub-Hertz linewidth, on par with state-of-the-art fiber lasers. Therefore it paves the way to manufacture high-performance semiconductor lasers with reduced footprint and cost. Moreover, with high laser power, the optical nonlinearity of the microresonator drastically changes the laser dynamics, offering routes for simultaneous pulse and frequency comb generation in the same microresonator. Particularly, integrated photonics technology, enabling components fabricated via semiconductor CMOS process, has brought increasing and extending interest to laser manufacturing using this method. In this article, we present a comprehensive tutorial on analytical and numerical methods of laser self-injection locking, as well a review of most recent theoretical and experimental achievements.     

Higher‐order analogues of the Tracy‐Widom distribution and the Painlevé II hierarchy

We study Fredholm determinants related to a family of kernels that describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are natural higher‐order analogues of the Airy kernel and are built out of functions associated with the Painlevé I hierarchy. The Fredholm determinants related to those kernels are higher‐order generalizations of the Tracy‐Widom distribution. We give an explicit expression for the determinants in terms of a distinguished smooth solution to the Painlevé II hierarchy. In addition, we compute large gap asymptotics for the Fredholm determinants. © 2009 Wiley Periodicals, Inc.     

Simple Curves on Surfaces

We study simple closed geodesics on a hyperbolic surface of genus g with b geodesic boundary components and c cusps. We show that the number of such geodesics of length at most L is of order L^6g+2b+2c–6. This answers a long-standing open question.     

A benchmark solution for 2D Stokes flow over cavity

Two-dimensional Stokes flow in a half plane with coupled cavity having the form of semi-ellipse is considered. The exact solution for the boundary problem is obtained. The solution can be a benchmark for numerical approaches. An example of the benchmarking is given.