11,198 research outputs found
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 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
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