5,203 research outputs found
Nonlinear Competition Between Small and Large Hexagonal Patterns
Recent experiments by Kudrolli, Pier and Gollub on surface waves,
parametrically excited by two-frequency forcing, show a transition from a small
hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We
show that generically the hexagons and the superlattice wave patterns bifurcate
simultaneously from the flat surface state as the forcing amplitude is
increased, and that the experimentally-observed transition can be described by
considering a low-dimensional bifurcation problem. A number of predictions come
out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let
Parametrically Excited Surface Waves: Two-Frequency Forcing, Normal Form Symmetries, and Pattern Selection
Motivated by experimental observations of exotic standing wave patterns in
the two-frequency Faraday experiment, we investigate the role of normal form
symmetries in the pattern selection problem. With forcing frequency components
in ratio m/n, where m and n are co-prime integers, there is the possibility
that both harmonic and subharmonic waves may lose stability simultaneously,
each with a different wavenumber. We focus on this situation and compare the
case where the harmonic waves have a longer wavelength than the subharmonic
waves with the case where the harmonic waves have a shorter wavelength. We show
that in the former case a normal form transformation can be used to remove all
quadratic terms from the amplitude equations governing the relevant resonant
triad interactions. Thus the role of resonant triads in the pattern selection
problem is greatly diminished in this situation. We verify our general results
within the example of one-dimensional surface wave solutions of the
Zhang-Vinals model of the two-frequency Faraday problem. In one-dimension, a
1:2 spatial resonance takes the place of a resonant triad in our investigation.
We find that when the bifurcating modes are in this spatial resonance, it
dramatically effects the bifurcation to subharmonic waves in the case of
forcing frequencies are in ratio 1/2; this is consistent with the results of
Zhang and Vinals. In sharp contrast, we find that when the forcing frequencies
are in ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the
presence of another spatially-resonant bifurcating mode.Comment: 22 pages, 6 figures, late
Charm as a domain wall fermion in quenched lattice QCD
We report a study describing the charm quark by a domain-wall fermion (DWF)
in lattice quantum chromodynamics (QCD). Our study uses a quenched gauge
ensemble with the DBW2 rectangle-improved gauge action at a lattice cutoff of
GeV. We calculate masses of heavy-light (charmed) and
heavy-heavy (charmonium) mesons with spin-parity and ,
leptonic decay constants of the charmed pseudoscalar mesons ( and ),
and the - mixing parameter. The charm quark mass is found to be
GeV. The mass splittings in
charmed-meson parity partners and are
degenerate within statistical errors, in accord with experiment, and they
satisfy a relation , also consistent with
experiment. A C-odd axial vector charmonium state, \chi_{c1}m_{h_{c}} = 3533(11)_{\rm stat.}\chi_{c1}) mass. However, in this regard, we emphasize
significant discrepancies in the calculation of hyperfine splittings on the
lattice. The leptonic decay constants of and mesons are found to be
MeV and
,
where the first error is statistical, the second a systematic due to chiral
extrapolation and the third error combination of other known systematics. The
- mixing bag parameter, which enters the
transition amplitude, is found to be .Comment: 49 pages, 15 figure
Dominant Topologies in Euclidean Quantum Gravity
The dominant topologies in the Euclidean path integral for quantum gravity
differ sharply according on the sign of the cosmological constant. For
, saddle points can occur only for topologies with vanishing first
Betti number and finite fundamental group. For , on the other hand,
the path integral is dominated by topologies with extremely complicated
fundamental groups; while the contribution of each individual manifold is
strongly suppressed, the ``density of topologies'' grows fast enough to
overwhelm this suppression. The value is thus a sort of boundary
between phases in the sum over topologies. I discuss some implications for the
cosmological constant problem and the Hartle-Hawking wave function.Comment: 14 pages, LaTeX. Minor additions (computability, relation to
``minimal volume'' in topology); error in eqn (3.5) corrected; references
added. To appear in Class. Quant. Gra
Sharper and Simpler Nonlinear Interpolants for Program Verification
Interpolation of jointly infeasible predicates plays important roles in
various program verification techniques such as invariant synthesis and CEGAR.
Intrigued by the recent result by Dai et al.\ that combines real algebraic
geometry and SDP optimization in synthesis of polynomial interpolants, the
current paper contributes its enhancement that yields sharper and simpler
interpolants. The enhancement is made possible by: theoretical observations in
real algebraic geometry; and our continued fraction-based algorithm that rounds
off (potentially erroneous) numerical solutions of SDP solvers. Experiment
results support our tool's effectiveness; we also demonstrate the benefit of
sharp and simple interpolants in program verification examples
Observation of the Askaryan Effect: Coherent Microwave Cherenkov Emission from Charge Asymmetry in High Energy Particle Cascades
We present the first direct experimental evidence for the charge excess in
high energy particle showers predicted nearly 40 years ago by Askaryan. We
directed bremsstrahlung photons from picosecond pulses of 28.5 GeV electrons at
the SLAC Final Focus Test Beam facility into a 3.5 ton silica sand target,
producing electromagnetic showers several meters long. A series of antennas
spanning 0.3 to 6 GHz were used to detect strong, sub-nanosecond radio
frequency pulses produced whenever a shower was present. The measured electric
field strengths are consistent with a completely coherent radiation process.
The pulses show 100% linear polarization, consistent with the expectations of
Cherenkov radiation. The field strength versus depth closely follows the
expected particle number density profile of the cascade, consistent with
emission from excess charge distributed along the shower. These measurements
therefore provide strong support for experiments designed to detect high energy
cosmic rays and neutrinos via coherent radio emission from their cascades.Comment: 10 pages, 4 figures. Submitted to Phys. Rev. Let
Mesons with Beauty and Charm: Spectroscopy
Applying knowledge of the interaction between heavy quarks derived from the
study of and bound states, we calculate the
spectrum of mesons. We compute transition rates for the
electromagnetic and hadronic cascades that lead from excited states to the
ground state, and briefly consider the prospects for
experimental observation of the spectrum.Comment: 32 pages + 2 uuencoded PostScript figures Fermilab-Pub-94/032-
Excited Charmed Mesons: Observations, Analyses and Puzzles
We review the status of recently observed positive parity charmed resonances,
both in the non-strange and in the strange sector. We describe the experimental
findings, the main theoretical analyses and the open problems deserving further
investigations.Comment: LaTeX, 25 pages, 5 figures. Invited revie
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