A non-singular boundary element method for modelling bubble dynamics in viscoelastic fluids

When a cavity forms near a solid boundary a liquid jet can form directed towards the boundary, causing the generation of high pressures at the wall (potentially causing damage) and the formation of a toroidal bubble. In this paper several recent developments in the boundary element modelling of the dynamics of cavitation bubbles in viscoelastic fluids are presented. The standard formulation of the boundary element method (BEM) is in terms of a boundary integral equation with a singular kernel. A reformulation of the BEM in terms of a non-singular kernel is shown to provide enhanced stability. In situations when a liquid jet forms and impacts the far side of the bubble there is a transition to a toroidal form. This topological singularity in bubble geometry is modelled by placing a vortex ring inside the bubble to account for the circulation in the fluid and the discontinuity in potential following jet impact. The bubble dynamics are dependent on the initial stand-off distance from the boundary as well as the viscous and elastic properties of the fluid. It is shown that, while the viscosity of the fluid inhibits jet formation, the dynamics are particularly dependent on the relative strength of viscous, elastic and inertial forces. In particular, if the Deborah number is large enough elastic effects effectively negate fluid viscosity and behaviour similar to the inviscid case is recovered in terms of liquid jet formation

High Harmonic Generation in SF6_{6}: Raman-excited Vibrational Quantum Beats

In a recent experiment (N. Wagner et al., PNAS v103, p13279) on SF$_{6}$, a high-harmonic generating laser pulse is preceded by a pump pulse which stimulates Raman-active modes in the molecule. Varying the time delay between the two pulses modulates high harmonic intensity, with frequencies equal to the vibration frequencies of the Raman-active modes. We propose an explanation of this modulation as a quantum interference between competing pathways that occur via adjacent vibrational states of the molecule. The Raman and high harmonic processes act as beamsplitters, producing vibrational quantum beats among the Raman-active vibrational modes that are excited by the first pulse. We introduce a rigorous treatment of the electron-ion recombination process and the effect of the ionic Coulomb field in the electron propagation outside the molecule, improving over the widely-used three-step model.Comment: submitted to PR

Monitoring changes in genetic diversity

DNA is the most elemental level of biodiversity, drives the process of speciation, and underpins other levels of biodiversity, including functional traits, species and ecosystems. Until recently biodiversity indicators have largely overlooked data from the molecular tools that are available for measuring variation at the DNA level. More direct analysis of trends in genetic diversity are now feasible and are ready to be incorporated into biodiversity monitoring. This chapter explores the current state-of-the-art in genetic monitoring, with an emphasis on new molecular tools and the richness of data they provide to supplement existing approaches. We also briefly consider proxy approaches that may be useful for many-species, global scale monitoring cases

Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment

Intrinsic thermal vibrations of suspended doubly clamped single-wall carbon nanotubes

We report the observation of thermally driven mechanical vibrations of suspended doubly clamped carbon nanotubes, grown by chemical vapor deposition (CVD). Several experimental procedures are used to suspend carbon nanotubes. The vibration is observed as a blurring in images taken with a scanning electron microscope. The measured vibration amplitudes are compared with a model based on linear continuum mechanics.Comment: pdf including figures, see: http://www.unibas.ch/phys-meso/Research/Papers/2003/NT-Thermal-Vibrations.pd

Transients in Power Systems

Power system engineering largely focuses on steady state analysis. The main areas of power system engineering are power flow studies and fault studies - both steady state technologies. But the world is largely transient, and power systems are always subject to time varying and short lived signals. This technical report concerns several important topics in transient analyses of power systems. The leading chapter deals with a new analytical tool-wavelets-for power system transients. Flicker and electric are furnace transients are discussed in Chapters I1 and IV. Chapter 111 deals with transients from shunt capacitor switching. The concluding chapters deal with transformer inrush current and non simultaneous pole closures of circuit breakers. This report was prepared by the students in EE532 at Purdue University. When I first came to Purdue in 1965, Professor El-Abiad was asking for student term projects which were turned into technical reports. I have \u27borrowed\u27 this idea and for many years we have produced technical reports from the power systems courses. The students get practice in writing reports, and the reader is able to get an idea of the coverage of our courses. I think that the students have done a good job on the subject of transients in power systems

Incorporating Oxygen Isotopes of Oxidized Reactive Nitrogen in the Regional Atmospheric Chemistry Mechanism, version 2 (ICOIN-RACM2)

The oxygen isotope anomaly (Δ17O = δ17O − 0.52 × δ18O &gt; 0) has proven to be a robust tool for probing photochemical cycling and atmospheric formation pathways of oxidized reactive nitrogen (NOy). Several studies have developed modeling techniques to implicitly model Δ17O of NOy molecules based on numerous assumptions that may not always be valid. Thus, these models may be oversimplified and limit our ability to compare model Δ17O values of NOy with observations. In this work, we introduce a novel method for explicitly tracking Δ17O transfer and propagation into NOy and odd oxygen (Ox), integrated into the Regional Atmospheric Chemistry Mechanism, version 2 (RACM2). Termed ICOIN-RACM2 (InCorporating Oxygen Isotopes of NOy in RACM2), this new model includes the addition of 55 new species and 729 replicate reactions to represent the propagation of Δ17O derived from O3 into NOy and Ox. Employing this mechanism within a box model, we simulate Δ17O for various NOy and Ox molecules for chamber experiments with varying initial nitrogen oxides (NOx = NO + NO2) and α-pinene conditions, revealing response shifts in Δ17O linked to distinct oxidant conditions. Furthermore, diel cycles are simulated under two summertime scenarios, representative of an urban and rural site, revealing pronounced Δ17O diurnal patterns for several NOy components and substantial Δ17O differences associated with pollution levels (urban vs. rural). Overall, the proposed mechanism offers the potential to assess NOy oxidation chemistry in chamber studies and air quality campaigns through Δ17O model comparisons against observations. The integration of this mechanism into a 3-D atmospheric chemistry transport model is expected to notably enhance our capacity to model and anticipate Δ17O across landscapes, consequently refining model representations of atmospheric chemistry and tropospheric oxidation capacity.</p