6,261 research outputs found
Exact shock solution of a coupled system of delay differential equations: a car-following model
In this paper, we present exact shock solutions of a coupled system of delay
differential equations, which was introduced as a traffic-flow model called
{\it the car-following model}. We use the Hirota method, originally developed
in order to solve soliton equations. %While, with a periodic boundary
condition, this system has % a traveling-wave solution given by elliptic
functions. The relevant delay differential equations have been known to allow
exact solutions expressed by elliptic functions with a periodic boundary
conditions. In the present work, however, shock solutions are obtained with
open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure
High Density Mesoscopic Atom Clouds in a Holographic Atom Trap
We demonstrate the production of micron-sized high density atom clouds of
interest for meso- scopic quantum information processing. We evaporate atoms
from 60 microK, 3x10^14 atoms/cm^3 samples contained in a highly anisotropic
optical lattice formed by interfering di racted beams from a holographic phase
plate. After evaporating to 1 microK by lowering the con ning potential, in
less than a second the atom density reduces to 8x10^13 cm^- 3 at a phase space
density approaching unity. Adiabatic recompression of the atoms then increases
the density to levels in excess of 1x10^15 cm^-3. The resulting clouds are
typically 8 microns in the longest dimension. Such samples are small enough to
enable mesoscopic quantum manipulation using Rydberg blockade and have the high
densities required to investigate new collision phenomena.Comment: 4 pages, 4 figures, submitted to PR
Systematic derivation of a rotationally covariant extension of the 2-dimensional Newell-Whitehead-Segel equation
An extension of the Newell-Whitehead-Segel amplitude equation covariant under
abritrary rotations is derived systematically by the renormalization group
method.Comment: 8 pages, to appear in Phys. Rev. Letters, March 18, 199
Non-destructive spatial heterodyne imaging of cold atoms
We demonstrate a new method for non-destructive imaging of laser-cooled
atoms. This spatial heterodyne technique forms a phase image by interfering a
strong carrier laser beam with a weak probe beam that passes through the cold
atom cloud. The figure of merit equals or exceeds that of phase-contrast
imaging, and the technique can be used over a wider range of spatial scales. We
show images of a dark spot MOT taken with imaging fluences as low as 61 pJ/cm^2
at a detuning of 11 linewidths, resulting in 0.0004 photons scattered per atom.Comment: text+3 figures, submitted to Optics Letter
Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation
We consider an extended Korteweg-de Vries (eKdV) equation, the usual
Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity.
We investigate the statistical behaviour of flat-top solitary waves described
by an eKdV equation in the presence of weak dissipative disorder in the linear
growth/damping term. With the weak disorder in the system, the amplitude of
solitary wave randomly fluctuates during evolution. We demonstrate numerically
that the probability density function of a solitary wave parameter
which characterizes the soliton amplitude exhibits loglognormal divergence near
the maximum possible value.Comment: 8 pages, 4 figure
First measurements of the flux integral with the NIST-4 watt balance
In early 2014, construction of a new watt balance, named NIST-4, has started
at the National Institute of Standards and Technology (NIST). In a watt
balance, the gravitational force of an unknown mass is compensated by an
electromagnetic force produced by a coil in a magnet system. The
electromagnetic force depends on the current in the coil and the magnetic flux
integral. Most watt balances feature an additional calibration mode, referred
to as velocity mode, which allows one to measure the magnetic flux integral to
high precision. In this article we describe first measurements of the flux
integral in the new watt balance. We introduce measurement and data analysis
techniques to assess the quality of the measurements and the adverse effects of
vibrations on the instrument.Comment: 7 pages, 8 figures, accepted for publication in IEEE Trans. Instrum.
Meas. This Journal can be found online at
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=1
Raman solitons in transient SRS
We report the observation of Raman solitons on numerical simulations of
transient stimulated Raman scattering (TSRS) with small group velocity
dispersion. The theory proceeds with the inverse scattering transform (IST) for
initial-boundary value problems and it is shown that the explicit theoretical
solution obtained by IST for a semi-infinite medium fits strikingly well the
numerical solution for a finite medium. We understand this from the rapid
decrease of the medium dynamical variable (the potential of the scattering
theory). The spectral transform reflection coefficient can be computed directly
from the values of the input and output fields and this allows to see the
generation of the Raman solitons from the numerical solution. We confirm the
presence of these nonlinear modes in the medium dynamical variable by the use
of a discrete spectral analysis.Comment: LaTex file, to appear in Inverse Problem
Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier
In quantum mechanics some properties are maximally incompatible, such as the
position and momentum of a particle or the vertical and horizontal projections
of a 2-level spin. Given any definite state of one property the other property
is completely random, or unbiased. For N-level systems, the 6-level ones are
the smallest for which a tomographically efficient set of N+1 mutually unbiased
bases (MUBs) has not been found. To facilitate the search, we numerically
extend the classification of unbiased bases, or Hadamards, by incrementally
adjusting relative phases in a standard basis. We consider the non-unitarity
caused by small adjustments with a second order Taylor expansion, and choose
incremental steps within the 4-dimensional nullspace of the curvature. In this
way we prescribe a numerical integration of a 4-parameter set of Hadamards of
order 6.Comment: 5 pages, 2 figure
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