65,816 research outputs found
Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation
We study numerically the evolution of perturbed Korteweg-de Vries solitons
and of well localized initial data by the Novikov-Veselov (NV) equation at
different levels of the "energy" parameter . We show that as , NV behaves, as expected, similarly to its formal limit, the
Kadomtsev-Petviashvili equation. However at intermediate regimes, i.e. when is not very large, more varied scenarios are possible, in particular,
blow-ups are observed. The mechanism of the blow-up is studied
Stability of the proton-to-electron mass ratio
We report a limit on the fractional temporal variation of the
proton-to-electron mass ratio as, obtained by comparing the frequency of a
rovibrational transition in SF6 with the fundamental hyperfine transition in
Cs. The SF6 transition was accessed using a CO2 laser to interrogate spatial
2-photon Ramsey fringes. The atomic transition was accessed using a primary
standard controlled with a Cs fountain. This result is direct and model-free
Quantum theory of large amplitude collective motion and the Born-Oppenheimer method
We study the quantum foundations of a theory of large amplitude collective
motion for a Hamiltonian expressed in terms of canonical variables. In previous
work the separation into slow and fast (collective and non-collective)
variables was carried out without the explicit intervention of the Born
Oppenheimer approach. The addition of the Born Oppenheimer assumption not only
provides support for the results found previously in leading approximation, but
also facilitates an extension of the theory to include an approximate
description of the fast variables and their interaction with the slow ones.
Among other corrections, one encounters the Berry vector and scalar potential.
The formalism is illustrated with the aid of some simple examples, where the
potentials in question are actually evaluated and where the accuracy of the
Born Oppenheimer approximation is tested. Variational formulations of both
Hamiltonian and Lagrangian type are described for the equations of motion for
the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf
styl
Multi-limbed locomotion systems for space construction and maintenance
A well developed technology of coordination of multi-limbed locomotory systems is now available. Results from a NASA sponsored study of several years ago are presented. This was a simulation study of a three-limbed locomotion/manipulation system. Each limb had six degrees of freedom and could be used either as a locomotory grasping hand-holds, or as a manipulator. The focus of the study was kinematic coordination algorithms. The presentation will also include very recent results from the Adaptive Suspension Vehicle Project. The Adaptive Suspension Vehicle (ASV) is a legged locomotion system designed for terrestrial use which is capable of operating in completely unstructured terrain in either a teleoperated or operator-on-board mode. Future development may include autonomous operation. The ASV features a very advanced coordination and control system which could readily be adapted to operation in space. An inertial package with a vertical gyro, and rate gyros and accelerometers on three orthogonal axes provides body position information at high bandwidth. This is compared to the operator's commands, injected via a joystick to provide a commanded force system on the vehicle's body. This system is, in turn, decomposed by a coordination algorithm into force commands to those legs which are in contact with the ground
Exact relativistic treatment of stationary counter-rotating dust disks III. Physical Properties
This is the third in a series of papers on the construction of explicit
solutions to the stationary axisymmetric Einstein equations which can be
interpreted as counter-rotating disks of dust. We discuss the physical
properties of a class of solutions to the Einstein equations for disks with
constant angular velocity and constant relative density which was constructed
in the first part. The metric for these spacetimes is given in terms of theta
functions on a Riemann surface of genus 2. It is parameterized by two physical
parameters, the central redshift and the relative density of the two
counter-rotating streams in the disk. We discuss the dependence of the metric
on these parameters using a combination of analytical and numerical methods.
Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the
static limit which gives a solution of the Morgan and Morgan class and the
limit of a disk without counter-rotation. We study the mass and the angular
momentum of the spacetime. At the disk we discuss the energy-momentum tensor,
i.e. the angular velocities of the dust streams and the energy density of the
disk. The solutions have ergospheres in strongly relativistic situations. The
ultrarelativistic limit of the solution in which the central redshift diverges
is discussed in detail: In the case of two counter-rotating dust components in
the disk, the solutions describe a disk with diverging central density but
finite mass. In the case of a disk made up of one component, the exterior of
the disks can be interpreted as the extreme Kerr solution.Comment: 30 pages, 20 figures; to appear in Phys. Rev.
- …