The Painlev\'e analysis for N=2 super KdV equations

The Painlev\'e analysis of a generic multiparameter N=2 extension of the Korteweg-de Vries equation is presented. Unusual aspects of the analysis, pertaining to the presence of two fermionic fields, are emphasized. For the general class of models considered, we find that the only ones which manifestly pass the test are precisely the four known integrable supersymmetric KdV equations, including the SKdV$_1$ case.Comment: Harvmac (b mode : 29 p); various minor modifications -- to appear in J. Math Phy

A cooperative Pd-Cu system for direct C-H bond arylation

The authors are grateful to the Royal Society (University Research Fellowship to CSJC) for financial support.A novel and efficient method for C-H arylation using well-defined Pd- and Cu-NHC systems has been developed. This process promotes the challenging construction of C-C bonds from arenes or heteroarenes using aryl bromides and chlorides. Mechanistic studies show that [Cu(OH)(NHC)] plays a key role in the C-H activation and is involved in the transmetallation with the Pd-NHC co-catalyst.Publisher PDFPeer reviewe

On the coupling between an ideal fluid and immersed particles

In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we reinterpret the work of Cendra et al. by substituting velocity interpolation from particle velocities for their principal connection. The consequence of writing evolution equations in terms of interpolation is two-fold. First, it gives estimates on the error incurred when interpolation is used to derive the evolution of the system. Second, this form of the equations of motion can inspire a family of particle and hybrid particle-spectral methods where the error analysis is "built-in". We also discuss the influence of other parameters attached to the particles, such as shape, orientation, or higher-order deformations, and how they can help with conservation of momenta in the sense of Kelvin's circulation theorem.Comment: to appear in Physica D, comments and questions welcom

Characters of graded parafermion conformal field theory

The graded parafermion conformal field theory at level k is a close cousin of the much-studied Z_k parafermion model. Three character formulas for the graded parafermion theory are presented, one bosonic, one fermionic (both previously known) and one of spinon type (which is new). The main result of this paper is a proof of the equivalence of these three forms using q-series methods combined with the combinatorics of lattice paths. The pivotal step in our approach is the observation that the graded parafermion theory -- which is equivalent to the coset osp(1,2)_k/ u(1) -- can be factored as (osp(1,2)_k/ su(2)_k) x (su(2)_k/ u(1)), with the two cosets on the right equivalent to the minimal model M(k+2,2k+3) and the Z_k parafermion model, respectively. This factorisation allows for a new combinatorial description of the graded parafermion characters in terms of the one-dimensional configuration sums of the (k+1)-state Andrews--Baxter--Forrester model.Comment: 36 page

A Simple Cellular Automation that Solves the Density and Ordering Problems

Cellular automata (CA) are discrete, dynamical systems that perform computations in a distributed fashion on a spatially extended grid. The dynamical behavior of a CA may give rise to emergent computation, referring to the appearance of global information processing capabilities that are not explicitly represented in the system's elementary components nor in their local interconnections.1 As such, CAs o?er an austere yet versatile model for studying natural phenomena, as well as a powerful paradigm for attaining ?ne-grained, massively parallel computation. An example of such emergent computation is to use a CA to determine the global density of bits in an initial state con?guration. This problem, known as density classi?cation, has been studied quite intensively over the past few years. In this short communication we describe two previous versions of the problem along with their CA solutions, and then go on to show that there exists yet a third version | which admits a simple solution

DASCH 100-yr light curves of high-mass X-ray binaries

We analyzed the 100-yr light curves of Galactic high-mass X-ray binaries using the Harvard photographic plate collection, made accessible through the DASCH project (Digital Access to a Sky Century at Harvard). As scanning is still in progress, we focus on the four objects that are currently well covered: the supergiant X-ray binary Cyg X-1 (V1357 Cyg), and the Be X-ray binaries 1H 1936+541 (BD+53 2262), RX J1744.7-2713 (HD 161103), and RX J2030.5+4751 (SAO 49725), the latter two objects being similar to gamma Cas. The star associated with Cyg X-1 does not show evidence for variability with an amplitude higher than 0.3 magnitude over a hundred years. We found significant variability of one magnitude with timescales of more than 10 years for SAO 49725, as well as a possible period of 500-600 days and an amplitude of 0.05 magnitude that might be the orbital, or super-orbital period of the system. The data is insufficient to conclude for HD 161103 but suggests a similar long-term variability. We thus observe an additional characteristic of gamma Cas-like objects: their long-term variability. This variability seems to be due to the slow evolution of a decretion disk around the Be star, but may be triggered by the presence of a compact object in the system, possibly a white dwarf. This characteristic could be used to identify further similar objects otherwise difficult to detect.Comment: Accepted for publication in Proceedings of Science (INTEGRAL 2012), Eds. A. Goldwurm, F. Lebrun and C. Winkler, based on a presentation at the 9th INTEGRAL Workshop "An INTEGRAL view of the high-energy sky (the first 10 years)", October 15-19, 2012, Paris, Franc

A Discrete Geometric Optimal Control Framework for Systems with Symmetries

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’Alembert- Pontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and, as a result, geometric structure and motion invariants are preserved. We illustrate our method by computing optimal trajectories for a simple model of an air vehicle flying through a digital terrain elevation map, and point out some of the numerical benefits that ensue