An Alternative Method to Deduce Bubble Dynamics in Single Bubble Sonoluminescence Experiments

In this paper we present an experimental approach that allows to deduce the important dynamical parameters of single sonoluminescing bubbles (pressure amplitude, ambient radius, radius-time curve) The technique is based on a few previously confirmed theoretical assumptions and requires the knowledge of quantities such as the amplitude of the electric excitation and the phase of the flashes in the acoustic period. These quantities are easily measurable by a digital oscilloscope, avoiding the cost of expensive lasers, or ultrafast cameras of previous methods. We show the technique on a particular example and compare the results with conventional Mie scattering. We find that within the experimental uncertainties these two techniques provide similar results.Comment: 8 pages, 5 figures, submitted to Phys. Rev.

Isoperimetric Inequalities in Simplicial Complexes

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gunder and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes

Sonoluminescence as a QED vacuum effect. I: The Physical Scenario

Several years ago Schwinger proposed a physical mechanism for sonoluminescence in terms of changes in the properties of the quantum-electrodynamic (QED) vacuum state. This mechanism is most often phrased in terms of changes in the Casimir Energy: changes in the distribution of zero-point energies and has recently been the subject of considerable controversy. The present paper further develops this quantum-vacuum approach to sonoluminescence: We calculate Bogolubov coefficients relating the QED vacuum states in the presence of a homogeneous medium of changing dielectric constant. In this way we derive an estimate for the spectrum, number of photons, and total energy emitted. We emphasize the importance of rapid spatio-temporal changes in refractive indices, and the delicate sensitivity of the emitted radiation to the precise dependence of the refractive index as a function of wavenumber, pressure, temperature, and noble gas admixture. Although the physics of the dynamical Casimir effect is a universal phenomenon of QED, specific experimental features are encoded in the condensed matter physics controlling the details of the refractive index. This calculation places rather tight constraints on the possibility of using the dynamical Casimir effect as an explanation for sonoluminescence, and we are hopeful that this scenario will soon be amenable to direct experimental probes. In a companion paper we discuss the technical complications due to finite-size effects, but for reasons of clarity in this paper we confine attention to bulk effects.Comment: 25 pages, LaTeX 209, ReV-TeX 3.2, eight figures. Minor revisions: Typos fixed, references updated, minor changes in numerical estimates, minor changes in some figure

Recent Developments in Geothermal Drilling Fluids

In the past, standard drilling muds have been used to drill most geothermal wells. However, the harsh thermal and chemical environment and the unique geothermal formations have led to such problems as excessive thickening of the fluid, formation damage, and lost circulation. This paper describes three recent development efforts aimed at solving some of these drilling fluid problems. Each of the efforts is at a different stage of development. The Sandia aqueous foam studies are still in the laboratory phase, NL Baroid's polymeric deflocculant is soon to be field tested, and the Mudtech high-temperature mud was field tested several months ago. Low density and the capability to suspend particles at low relative velocities are two factors which make foam an attractive drilling fluid. The stability of these foams and their material properties at high temperatures are presently unknown and this lack of information has precluded their use as a geothermal drilling fluid. The aqueous foam studies being conducted at Sandia are aimed at screening available surfactants for temperature and chemical stability. Approximately 100 surfactants have been tested at temperatures of 260 and 310 C (500 and 590 F), and several of these candidates appear very promising. NL Baroid has developed a polymeric deflocculant for water-based muds which shows promise in retarding thermal degradation effects and associated gelation. Formulations containing this new polymer have shown good rheological properties up to 260 C (500 F) in laboratory testing. A high-temperature mud consisting primarily of sepiolite, bentonite, and brown coal has been developed by Mudtech, Inc. A field test of this mud was conducted in a geothermal well in the Imperial Valley of California in May 1980. The fluid exhibited good hole-cleaning characteristics and good rheological properties throughout the test

Analysis of an exhaustive search algorithm in random graphs and the n^{c\log n} -asymptotics

We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual G_{n,p} -model where each possible edge appears independently with the same probability p. The expected cost turns out to be of the less common asymptotic order n^{c\log n}, which we explore from several different perspectives. Also we collect many instances where such an order appears, from algorithmics to analysis, from probability to algebra. The limiting distribution of the cost required by the algorithm under a purely idealized random model is proved to be normal. The approach we develop is of some generality and is amenable for other graph algorithms.Comment: 35 page

Heart failure subtypes and thromboembolic risk in patients with atrial fibrillation::The PREFER in AF - HF substudy

BACKGROUND AND OBJECTIVES: To assess thromboembolic and bleeding risks in patients with heart failure (HF) and atrial fibrillation (AF) according to HF type. METHODS: We analyzed 6170 AF patients from the Prevention of thromboembolic events - European Registry in Atrial Fibrillation (PREFER in AF), and categorized patients into: HF with reduced left-ventricular ejection fraction (HFrEF; LVEF60%), and no HF. Outcomes were ischemic stroke, major adverse cardiovascular and cerebral events (MACCE) and major bleeding occurring within 1-year. RESULTS: The annual incidence of stroke was linearly and inversely related to LVEF, increasing by 0.054% per each 1% of LVEF decrease (95% CI: 0.013%-0.096%; p=0.031). Patients with HFHpEF had the highest CHA2DS2-VASc score, but significantly lower stroke incidence than other HF groups (0.65%, compared to HFLpEF 1.30%; HFmrEF 1.71%; HFrEF 1.75%; trend p=0.014). The incidence of MACCE was also lower in HFHpEF (2.0%) compared to other HF groups (range: 3.8-4.4%; p=0.001). Age, HF type, and NYHA class were independent predictors of thromboembolic events. Conversely, major bleeding did not significantly differ between groups (p=0.168). CONCLUSION: Our study in predominantly anticoagulated patients with AF shows that, reduction in LVEF is associated with higher thromboembolic, but not higher bleeding risk. HFHpEF is a distinct and puzzling group, featuring the highest CHA2DS2-VASc score but the lowest residual risk of thromboembolic events, which warrants further investigation