6,900 research outputs found
Lie Groups and mechanics: an introduction
The aim of this paper is to present aspects of the use of Lie groups in
mechanics. We start with the motion of the rigid body for which the main
concepts are extracted. In a second part, we extend the theory for an arbitrary
Lie group and in a third section we apply these methods for the diffeomorphism
group of the circle with two particular examples: the Burger equation and the
Camassa-Holm equation
Discrete Routh Reduction
This paper develops the theory of abelian Routh reduction for discrete
mechanical systems and applies it to the variational integration of mechanical
systems with abelian symmetry. The reduction of variational Runge-Kutta
discretizations is considered, as well as the extent to which symmetry
reduction and discretization commute. These reduced methods allow the direct
simulation of dynamical features such as relative equilibria and relative
periodic orbits that can be obscured or difficult to identify in the unreduced
dynamics. The methods are demonstrated for the dynamics of an Earth orbiting
satellite with a non-spherical correction, as well as the double
spherical pendulum. The problem is interesting because in the unreduced
picture, geometric phases inherent in the model and those due to numerical
discretization can be hard to distinguish, but this issue does not appear in
the reduced algorithm, where one can directly observe interesting dynamical
structures in the reduced phase space (the cotangent bundle of shape space), in
which the geometric phases have been removed. The main feature of the double
spherical pendulum example is that it has a nontrivial magnetic term in its
reduced symplectic form. Our method is still efficient as it can directly
handle the essential non-canonical nature of the symplectic structure. In
contrast, a traditional symplectic method for canonical systems could require
repeated coordinate changes if one is evoking Darboux' theorem to transform the
symplectic structure into canonical form, thereby incurring additional
computational cost. Our method allows one to design reduced symplectic
integrators in a natural way, despite the noncanonical nature of the symplectic
structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added,
fixed typo
Spacelike surfaces with free boundary in the Lorentz-Minkowski space
We investigate a variational problem in the Lorentz-Minkowski space \l^3
whose critical points are spacelike surfaces with constant mean curvature and
making constant contact angle with a given support surface along its common
boundary. We show that if the support surface is a pseudosphere, then the
surface is a planar disc or a hyperbolic cap. We also study the problem of
spacelike hypersurfaces with free boundary in the higher dimensional
Lorentz-Minkowski space \l^{n+1}.Comment: 16 pages. Accepted in Classical and Quantum Gravit
Friction force microscopy : a simple technique for identifying graphene on rough substrates and mapping the orientation of graphene grains on copper
At a single atom thick, it is challenging to distinguish graphene from its substrate using conventional techniques. In this paper we show that friction force microscopy (FFM) is a simple and quick technique for identifying graphene on a range of samples, from growth substrates to rough insulators. We show that FFM is particularly effective for characterizing graphene grown on copper where it can correlate the graphene growth to the three-dimensional surface topography. Atomic lattice stickâslip friction is readily resolved and enables the crystallographic orientation of the graphene to be mapped nondestructively, reproducibly and at high resolution. We expect FFM to be similarly effective for studying graphene growth on other metal/locally crystalline substrates, including SiC, and for studying growth of other two-dimensional materials such as molybdenum disulfide and hexagonal boron nitride
A millimeter-wave antireflection coating for cryogenic silicon lenses
We have developed and tested an antireflection (AR) coating method for
silicon lenses at cryogenic temperatures and millimeter wavelengths. Our
particular application is a measurement of the cosmic microwave background. The
coating consists of machined pieces of Cirlex glued to the silicon. The
measured reflection from an AR coated flat piece is less than 1.5% at the
design wavelength. The coating has been applied to flats and lenses and has
survived multiple thermal cycles from 300 to 4 K. We present the manufacturing
method, the material properties, the tests performed, and estimates of the loss
that can be achieved in practical lenses
Discovery of a New 89 Second X-ray Pulsar XTE J1906+09
We report on the discovery of a new pulsating X-ray source during Rossi X-ray
Timing Explorer observations of a low galactic latitude field centered at RA
(J2000) = 19 hr 05 m 43 s and Dec (J2000) = +08 deg 58 arcmin 48 arcsec.
Significant pulsations were detected by both the PCA and HEXTE instruments
aboard RXTE at a fundamental period of 89.17 +/- 0.02 seconds, with higher
harmonics also visible in the 2-10 keV power spectrum. The folded lightcurve
from the source is multiply peaked at lower energies, and changes to single
peaked morphology above ~20 keV. The phase averaged spectrum from the source is
well fit by strongly absorbed power law or thermal bremsstrahlung spectral
models of photon index 1.9 +/- 0.1 or temperature 19.5 +/- 4.6 keV,
respectively. The mean neutral hydrogen column density is approximately 10^23
cm^-2, suggesting a distance of >10 kpc to the source and a minimum 2-10 keV
X-ray luminosity of 2*10^{35} ergs s^{-1}. By comparison with other pulsars
with similar periods and luminosities, we suggest that XTE J1906+09 has a
supergiant companion with an underfilled Roche lobe. We speculate further that
one of the M stars in a peculiar M star binary system may be the companion.Comment: 14 pages, 2 figures. Accepted by ApJ Letter
Surface differential rotation and prominences of the Lupus post T Tauri star RX J1508.6-4423
We present in this paper a spectroscopic monitoring of the Lupus post T Tauri star RX J1508.6-4423 carried out at two closely separated epochs (1998 May 06 and 10) with the UCL Echelle Spectrograph on the 3.9-m Anglo-Australian Telescope. Applying least-squares convolution and maximum entropy image reconstruction techniques to our sets of spectra, we demonstrate that this star features on its surface a large cool polar cap with several appendages extending to lower latitudes, as well as one spot close to the equator. The images reconstructed at both epochs are in good overall agreement, except for a photospheric shear that we interpret in terms of latitudinal differential rotation. Given the spot distribution at the epoch of our observations, differential rotation could only be investigated between latitudes 15° and 60°. We find in particular that the observed differential rotation is compatible with a solar-like law (i.e., with rotation rate decreasing towards high latitudes proportionally to sin 2l, where l denotes the latitude) in this particular latitude range. Assuming that such a law can be extrapolated to all latitudes, we find that the equator of RX J1508.6-4423 does one more rotational cycle than the pole every 50 ±10 d, implying a photospheric shear 2 to 3 times stronger than that of the Sun. We also discover that the Hα emission profile of RX J1508.6-4423 is most of the time double-peaked and strongly modulated with the rotation period of the star. We interpret this rotationally modulated emission as being caused by a dense and complex prominence system, the circumstellar distribution of which is obtained through maximum entropy Doppler tomography. These maps show in particular that prominences form a complete and inhomogeneous ring around the star, precisely at the corotation radius. We use the total Hα and HÎČ emission flux to estimate that the mass of the whole prominence system is about 10 20g. From our observation that the whole cloud system surrounding the star is regenerated in less than 4 d, we conclude that the braking time-scale of RX J1508.6-4423 is shorter than 1 Gyr, and that prominence expulsion is thus likely to contribute significantly to the rotational spindown of young low-mass stars
Routhian reduction for quasi-invariant Lagrangians
In this paper we describe Routhian reduction as a special case of standard
symplectic reduction, also called Marsden-Weinstein reduction. We use this
correspondence to present a generalization of Routhian reduction for
quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total
time derivative. We show how functional Routhian reduction can be seen as a
particular instance of reduction of a quasi-invariant Lagrangian, and we
exhibit a Routhian reduction procedure for the special case of Lagrangians with
quasi-cyclic coordinates. As an application we consider the dynamics of a
charged particle in a magnetic field.Comment: 24 pages, 3 figure
Discrete Variational Optimal Control
This paper develops numerical methods for optimal control of mechanical
systems in the Lagrangian setting. It extends the theory of discrete mechanics
to enable the solutions of optimal control problems through the discretization
of variational principles. The key point is to solve the optimal control
problem as a variational integrator of a specially constructed
higher-dimensional system. The developed framework applies to systems on
tangent bundles, Lie groups, underactuated and nonholonomic systems with
symmetries, and can approximate either smooth or discontinuous control inputs.
The resulting methods inherit the preservation properties of variational
integrators and result in numerically robust and easily implementable
algorithms. Several theoretical and a practical examples, e.g. the control of
an underwater vehicle, will illustrate the application of the proposed
approach.Comment: 30 pages, 6 figure
Chiral Anomalies via Classical and Quantum Functional Methods
In the quantum path integral formulation of a field theory model an anomaly
arises when the functional measure is not invariant under a symmetry
transformation of the Lagrangian. In this paper, generalizing previous work
done on the point particle, we show that even at the classical level we can
give a path integral formulation for any field theory model. Since classical
mechanics cannot be affected by anomalies, the measure of the classical path
integral of a field theory must be invariant under the symmetry. The classical
path integral measure contains the fields of the quantum one plus some extra
auxiliary ones. So, at the classical level, there must be a sort of
"cancellation" of the quantum anomaly between the original fields and the
auxiliary ones. In this paper we prove in detail how this occurs for the chiral
anomaly.Comment: 26 pages, Latex, misprint fixed, a dedication include
- âŠ