51,670 research outputs found
Global existence for a translating near-circular Hele-Shaw bubble with surface tension
This paper concerns global existence for arbitrary nonzero surface tension of
bubbles in a Hele-Shaw cell that translate in the presence of a pressure
gradient. When the cell width to bubble size is sufficiently large, we show
that a unique steady translating near-circular bubble symmetric about the
channel centerline exists, where the bubble translation speed in the laboratory
frame is found as part of the solution. We prove global existence for symmetric
sufficiently smooth initial conditions close to this shape and show that the
steady translating bubble solution is an attractor within this class of
disturbances. In the absence of side walls, we prove stability of the steady
translating circular bubble without restriction on symmetry of initial
conditions. These results hold for any nonzero surface tension despite the fact
that a local planar approximation near the front of the bubble would suggest
Saffman Taylor instability.
We exploit a boundary integral approach that is particularly suitable for
analysis of nonzero viscosity ratio between fluid inside and outside the
bubble. An important element of the proof was the introduction of a weighted
Sobolev norm that accounts for stabilization due to advection of disturbances
from the front to the back of the bubble
Acoustic Attenuation by Two-dimensional Arrays of Rigid Cylinders
In this Letter, we present a theoretical analysis of the acoustic
transmission through two-dimensional arrays of straight rigid cylinders placed
parallelly in the air. Both periodic and completely random arrangements of the
cylinders are considered. The results for the sound attenuation through the
periodic arrays are shown to be in a remarkable agreement with the reported
experimental data. As the arrangement of the cylinders is randomized, the
transmission is significantly reduced for a wider range of frequencies. For the
periodic arrays, the acoustic band structures are computed by the plane-wave
expansion method and are also shown to agree with previous results.Comment: 4 pages, 3 figure
Collisional stability of fermionic Feshbach molecules
Using a Feshbach resonance, we create ultracold fermionic molecules starting
from a Bose-Fermi atom gas mixture. The resulting mixture of atoms and weakly
bound molecules provides a rich system for studying few-body collisions because
of the variety of atomic collision partners for molecules; either bosonic,
fermionic, or distinguishable atoms. Inelastic loss of the molecules near the
Feshbach resonance is dramatically affected by the quantum statistics of the
colliding particles and the scattering length. In particular, we observe a
molecule lifetime as long as 100 ms near the Feshbach resonance.Comment: 4 pages, 4 figures, 1 tabl
Systematic study of Optical Feshbach Resonances in an ideal gas
Using a narrow intercombination line in alkaline earth atoms to mitigate
large inelastic losses, we explore the Optical Feshbach Resonance (OFR) effect
in an ultracold gas of bosonic Sr. A systematic measurement of three
resonances allows precise determinations of the OFR strength and scaling law,
in agreement with coupled-channels theory. Resonant enhancement of the complex
scattering length leads to thermalization mediated by elastic and inelastic
collisions in an otherwise ideal gas. OFR could be used to control atomic
interactions with high spatial and temporal resolution.Comment: Significant changes to text and figure presentation to improve
clarity. Extended supplementary material. 4 pages, 4 figures; includes
supplementary material 8 pages, 4 figures. Submitted to Physical Review
Letter
Real-time cavity QED with single atoms
We report the first measurement of the real-time evolution of the complex field amplitude brought on by single atom transits. We show the variation in time of both quadrature amplitudes (simultaneously recorded) of the light transmitted through the cavity, as well the resultant optical phase for a single atom transit event. In this particular measurement, the cavity and laser were both detuned by 10 MHz from the Cs resonance
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