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 $P_a \sim 1.2 - 1.5$atm and low gas concentration of less than $0.4\%$ 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

Fusion yield: Guderley model and Tsallis statistics

The reaction rate probability integral is extended from Maxwell-Boltzmann approach to a more general approach by using the pathway model introduced by Mathai [Mathai A.M.:2005, A pathway to matrix-variate gamma and normal densities, Linear Algebra and Its Applications}, 396, 317-328]. The extended thermonuclear reaction rate is obtained in closed form via a Meijer's G-function and the so obtained G-function is represented as a solution of a homogeneous linear differential equation. A physical model for the hydrodynamical process in a fusion plasma compressed and laser-driven spherical shock wave is used for evaluating the fusion energy integral by integrating the extended thermonuclear reaction rate integral over the temperature. The result obtained is compared with the standard fusion yield obtained by Haubold and John in 1981.[Haubold, H.J. and John, R.W.:1981, Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave, Plasma Physics, 23, 399-411]. An interpretation for the pathway parameter is also given.Comment: 17 pages, LaTe

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

Diet-Independent Remodeling of Cellular Membranes Precedes Seasonally Changing Body Temperature in a Hibernator

Polyunsaturated fatty acids (PUFA) have a multitude of health effects. Their incorporation into membrane phospholipids (PL) is generally believed to depend directly on dietary influx. PL influence transmembrane protein activity and thus can compensate temperature effects; e.g. PL n-6 PUFA are thought to stabilize heart function at low body temperature (Tb), whereas long chain (>C18) n-3 PUFA may boost oxidative capacity. We found substantial remodeling of membranes in free-living alpine marmots which was largely independent of direct dietary supply. Organ PL n-6 PUFA and n-6 to n-3 ratios were highest at onset and end of hibernation after rapid increases during a brief transitional period prior to hibernation. In contrast, longer chain PL n-3 PUFA content was low at end of summer but maximal at end of hibernation. After termination of hibernation in spring, these changes in PL composition were rapidly reversed. Our results demonstrate selective trafficking of PUFA within the body, probably governed by a circannual endogenous rhythm, as hibernating marmots were in winter burrows isolated for seven months from food and external cues signaling the approaching spring. High concentrations of PL n-6 PUFA throughout hibernation are in line with their hypothesized function of boosting SERCA 2a activity at low Tb. Furthermore, we found increasing rate of rewarming from torpor during winter indicating increasing oxidative capacity that could be explained by the accumulation of long-chain PL n-3 PUFA. It may serve to minimize the time necessary for rewarming despite the increasing temperature range to be covered, because rewarming is a period of highest metabolic rate and hence production of reactive oxygen species. Considering the importance of PUFA for health our results may have important biomedical implications, as seasonal changes of Tb and associated remodeling of membranes are not restricted to hibernators but presumably common among endothermic organisms

Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit “time”-stepping applied to preconditioned Euler equations. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41714/1/10444_2005_Article_BF02123476.pd

Novel reptilian uncoupling proteins: molecular evolution and gene expression during cold acclimation

Many animals upregulate metabolism in response to cold. Uncoupling proteins (UCPs) increase proton conductance across the mitochondrial membrane and can thereby alleviate damage from reactive oxygen species that may form as a result of metabolic upregulation. Our aim in this study was to determine whether reptiles (Crocodylus porosus) possess UCP genes. If so, we aimed to place reptilian UCP genes within a phylogenetic context and to determine whether the expression of UCP genes is increased during cold acclimation. We provide the first evidence that UCP2 and UCP3 genes are present in reptiles. Unlike in other vertebrates, UCP2 and UPC3 are expressed in liver and skeletal muscle of the crocodile, and both are upregulated in liver during cold acclimation but not in muscle. We identified two transcripts of UCP3, one of which produces a truncated protein similar to the UCP3S transcript in humans, and the resulting protein lacks the predicted nucleotide-binding regulatory domain. Our molecular phylogeny suggests that uncoupling protein 1 (UCP1) is ancestral and has been lost in archosaurs. In birds, UCP3 may have assumed a similar function as UCP1 in mammals, which has important ramifications for understanding endothermic heat production