240 research outputs found
Phase Diagrams for Sonoluminescing Bubbles
Sound driven gas bubbles in water can emit light pulses. This phenomenon is
called sonoluminescence (SL). Two different phases of single bubble SL have
been proposed: diffusively stable and diffusively unstable SL. We present phase
diagrams in the gas concentration vs forcing pressure state space and also in
the ambient radius vs gas concentration and vs forcing pressure state spaces.
These phase diagrams are based on the thresholds for energy focusing in the
bubble and two kinds of instabilities, namely (i) shape instabilities and (ii)
diffusive instabilities. Stable SL only occurs in a tiny parameter window of
large forcing pressure amplitude atm and low gas
concentration of less than of the saturation. The upper concentration
threshold becomes smaller with increasing forcing. Our results quantitatively
agree with experimental results of Putterman's UCLA group on argon, but not on
air. However, air bubbles and other gas mixtures can also successfully be
treated in this approach if in addition (iii) chemical instabilities are
considered. -- All statements are based on the Rayleigh-Plesset ODE
approximation of the bubble dynamics, extended in an adiabatic approximation to
include mass diffusion effects. This approximation is the only way to explore
considerable portions of parameter space, as solving the full PDEs is
numerically too expensive. Therefore, we checked the adiabatic approximation by
comparison with the full numerical solution of the advection diffusion PDE and
find good agreement.Comment: Phys. Fluids, in press; latex; 46 pages, 16 eps-figures, small
figures tarred and gzipped and uuencoded; large ones replaced by dummies;
full version can by obtained from: http://staff-www.uni-marburg.de/~lohse
Direct Visualization of Laser-Driven Focusing Shock Waves
Cylindrically or spherically focusing shock waves have been of keen interest
for the past several decades. In addition to fundamental study of materials
under extreme conditions, cavitation, and sonoluminescence, focusing shock
waves enable myriad applications including hypervelocity launchers, synthesis
of new materials, production of high-temperature and high-density plasma
fields, and a variety of medical therapies. Applications in controlled
thermonuclear fusion and in the study of the conditions reached in laser fusion
are also of current interest. Here we report on a method for direct real-time
visualization and measurement of laser-driven shock generation, propagation,
and 2D focusing in a sample. The 2D focusing of the shock front is the
consequence of spatial shaping of the laser shock generation pulse into a ring
pattern. A substantial increase of the pressure at the convergence of the
acoustic shock front is observed experimentally and simulated numerically.
Single-shot acquisitions using a streak camera reveal that at the convergence
of the shock wave in liquid water the supersonic speed reaches Mach 6,
corresponding to the multiple gigapascal pressure range 30 GPa
Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid
We observe critical phenomena in spherical collapse of radiation fluid. A
sequence of spacetimes is numerically computed, containing
models () that adiabatically disperse and models () that
form a black hole. Near the critical point (), evolutions develop a
self-similar region within which collapse is balanced by a strong,
inward-moving rarefaction wave that holds constant as a function of a
self-similar coordinate . The self-similar solution is known and we show
near-critical evolutions asymptotically approaching it. A critical exponent
is found for supercritical () models.Comment: 10 pages (LaTeX) (to appear in Phys. Rev. Lett.), TAR-039-UN
Self-similar imploding relativistic shock waves
Self-similar solutions to the problem of a strong imploding relativistic
shock wave are calculated. These solutions represent the relativistic
generalisation of the Newtonian Gouderley-Landau-Stanyukovich problem of a
strong imploding spherical shock wave converging to a centre. The solutions are
found assuming that the pre-shocked flow has a uniform density, and are
accurate for sufficiently large times after the formation of the shock wave.Comment: 22 pages, 4 figures. Minor corrections and a discussion of the
singular C_ characteristic added. Accepted for publication in Physics of
Fluid
First and second-type self-similar solutions of implosions and explosions containing ultra-relativistic shocks
We derive self similar solutions for ultra-relativistic shock waves
propagating into cold material of powerlaw density profile in radius rho ~
r^-k. We treat both implosions and explosions in three geometries: planar,
cylindrical and spherical. For spherical explosions these are the first type
solutions of Blandford and McKee for k<4 and the second type solutions found by
Best and Sari for k>5-sqrt(3/4). In addition we find new, hollow (with
evacuated interior), first type solutions that may be applicable for 4<k<17/4.
This ``sequence'' with increasing k of first type solutions, hollow first type
solutions, and then second type solutions is reminiscent of the
non-relativistic sequence. However, while in the non relativistic case there is
a range of k which corresponds to a ``gap'' - a range in with neither first
nor second type solutions which separates the hollow first type solutions and
the second type solutions, here there is an ``overlap'': a range of k for which
current considerations allow for both hollow first and second type solutions.
Further understanding is needed to determine which of the two solutions apply
in this overlap regime. We provide similar exploration for the other geometries
and for imploding configurations. Interestingly, we find a gap for imploding
spherical shocks and exploding planar shocks and an overlap for imploding
planar solutions. Cylindrical configurations have no hollow solutions and
exhibit direct transition from first type to second type solutions, without a
gap or an overlap region.Comment: Submitted to Physics of Fluids, March
Detonation Initiation via Imploding Shock Waves
An imploding annular shock wave driven by a jet of air was used to initiate detonations
inside a 76 mm diameter tube. The tube was filled with a test gas composed of either
stoichiometric ethylene-oxygen or propane-oxygen diluted with nitrogen. The strength of
the imploding shock wave and the sensitivity of the test gas were varied in an effort to
find the minimum shock strength required for detonation of each test mixture. The results
show that the minimum required shock strength increases with mixture sensitivity and
suggest that impractically large shock driver pressures are required to initiate detonations
in ethylene-air or propane-air mixtures when using this technique
Multidimensional Conservation Laws: Overview, Problems, and Perspective
Some of recent important developments are overviewed, several longstanding
open problems are discussed, and a perspective is presented for the
mathematical theory of multidimensional conservation laws. Some basic features
and phenomena of multidimensional hyperbolic conservation laws are revealed,
and some samples of multidimensional systems/models and related important
problems are presented and analyzed with emphasis on the prototypes that have
been solved or may be expected to be solved rigorously at least for some cases.
In particular, multidimensional steady supersonic problems and transonic
problems, shock reflection-diffraction problems, and related effective
nonlinear approaches are analyzed. A theory of divergence-measure vector fields
and related analytical frameworks for the analysis of entropy solutions are
discussed.Comment: 43 pages, 3 figure
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