3,145 research outputs found
McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions
Evidence is presented to suggest that, in three dimensions, spherical
6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32,
34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >=
54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and
12-designs for N=84, >= 86. The existence of some of these designs is
established analytically, while others are given by very accurate numerical
coordinates. The 24-point 7-design was first found by McLaren in 1963, and --
although not identified as such by McLaren -- consists of the vertices of an
"improved" snub cube, obtained from Archimedes' regular snub cube (which is
only a 3-design) by slightly shrinking each square face and expanding each
triangular face. 5-designs with 23 and 25 points are presented which, taken
together with earlier work of Reznick, show that 5-designs exist for N=12, 16,
18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9,
that these lists of t-designs are complete and that no others exist. One of the
constructions gives a sequence of putative spherical t-designs with N= 12m
points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.Comment: 16 pages, 1 figur
A gauge invariant chiral unitary framework for kaon photo- and electroproduction on the proton
We present a gauge invariant approach to photoproduction of mesons on
nucleons within a chiral unitary framework. The interaction kernel for
meson-baryon scattering is derived from the chiral effective Lagrangian and
iterated in a Bethe-Salpeter equation. Within the leading order approximation
to the interaction kernel, data on kaon photoproduction from SAPHIR, CLAS and
CBELSA/TAPS are analyzed in the threshold region. The importance of gauge
invariance and the precision of various approximations in the interaction
kernel utilized in earlier works are discussed.Comment: 23 pages, 13 figs, EPJ A styl
The support of the logarithmic equilibrium measure on sets of revolution in
For surfaces of revolution in , we investigate the limit
distribution of minimum energy point masses on that interact according to
the logarithmic potential , where is the Euclidean distance
between points. We show that such limit distributions are supported only on the
``out-most'' portion of the surface (e.g., for a torus, only on that portion of
the surface with positive curvature). Our analysis proceeds by reducing the
problem to the complex plane where a non-singular potential kernel arises whose
level lines are ellipses
Solving the difference initial-boundary value problems by the operator exponential method
We suggest a modification of the operator exponential method for the
numerical solving the difference linear initial boundary value problems. The
scheme is based on the representation of the difference operator for given
boundary conditions as the perturbation of the same operator for periodic ones.
We analyze the error, stability and efficiency of the scheme for a model
example of the one-dimensional operator of second difference
Dark energy constraints and correlations with systematics from CFHTLS weak lensing, SNLS supernovae Ia and WMAP5
We combine measurements of weak gravitational lensing from the CFHTLS-Wide
survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain
joint constraints on cosmological parameters, in particular, the dark energy
equation of state parameter w. We assess the influence of systematics in the
data on the results and look for possible correlations with cosmological
parameters.
We implement an MCMC algorithm to sample the parameter space of a flat CDM
model with a dark-energy component of constant w. Systematics in the data are
parametrised and included in the analysis. We determine the influence of
photometric calibration of SNIa data on cosmological results by calculating the
response of the distance modulus to photometric zero-point variations. The weak
lensing data set is tested for anomalous field-to-field variations and a
systematic shape measurement bias for high-z galaxies.
Ignoring photometric uncertainties for SNLS biases cosmological parameters by
at most 20% of the statistical errors, using supernovae only; the parameter
uncertainties are underestimated by 10%. The weak lensing field-to-field
variance pointings is 5%-15% higher than that predicted from N-body
simulations. We find no bias of the lensing signal at high redshift, within the
framework of a simple model. Assuming a systematic underestimation of the
lensing signal at high redshift, the normalisation sigma_8 increases by up to
8%. Combining all three probes we obtain -0.10<1+w<0.06 at 68% confidence
(-0.18<1+w<0.12 at 95%), including systematic errors. Systematics in the data
increase the error bars by up to 35%; the best-fit values change by less than
0.15sigma. [Abridged]Comment: 14 pages, 10 figures. Revised version, matches the one to be
published in A&A. Modifications have been made corresponding to the referee's
suggestions, including reordering of some section
Design and development of an automatic tool changer for an articulated robot arm
In the creative industries, the length of time between the ideation stage and the making of physical objects is decreasing due to the use of CAD/CAM systems and adicitive manufacturing. Natural anisotropic materials, such as solid wood can also be transformed using CAD/CAM systems, but only with subtractive processes such as machining with CNC routers. Whilst some 3 axis CNC routing machines are affordable to buy and widely available, more flexible 5 axis routing machines still present themselves as a too big investment for small companies. Small refurbished articulated robots can be a cheaper alternative but they require a
light end-effector. This paper presents a new lightweight tool changer that converts a small 3kg payload 6 DOF robot into a robot apprentice able to machine wood and similar soft materials
Three-dimensional sound propagation models using the parabolic-equation approximation and the split-step Fourier method
Author Posting. © IMACS, 2012. This article is posted here by permission of World Scientific Publishing for personal use, not for redistribution. The definitive version was published in Journal of Computational Acoustics 21 (2013): 1250018, doi:10.1142/S0218396X1250018X.The split-step Fourier method is used in three-dimensional parabolic-equation (PE) models to compute underwater sound propagation in one direction (i.e. forward). The method is implemented in both Cartesian (x, y, z) and cylindrical (r, θ, z) coordinate systems, with forward defined as along x and radial coordinate r, respectively. The Cartesian model has uniform resolution throughout the domain, and has errors that increase with azimuthal angle from the x axis. The cylindrical model has consistent validity in each azimuthal direction, but a fixed cylindrical grid of radials cannot produce uniform resolution. Two different methods to achieve more uniform resolution in the cylindrical PE model are presented. One of the methods is to increase the grid points in azimuth, as a function of r, according to nonaliased sampling theory. The other is to make use of a fixed arc-length grid. In addition, a point-source starter is derived for the three-dimensional Cartesian PE model. Results from idealized seamount and slope calculations are shown to compare and verify the performance of the three methods.This work was sponsored by the Office of Naval Research under the grants N00014-10-1-0040
and N00014-11-1-0701
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