Precision Measurements of Stretching and Compression in Fluid Mixing

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing. Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincare map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached.Comment: 5 pages, 5 figure

Quantum Gauge Equivalence in QED

We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in which the constraints are imposed on operator-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb and spatial axial gauges to what we call ``common form,'' in which all particle excitation modes have identical properties. We also show that, once that common form has been reached, QED in different gauges has a common time-evolution operator that defines time-translation for states that represent systems of electrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus of a gauge theory can be transformed from one gauge to another.Comment: Contribution for a special issue of Foundations of Physics honoring Fritz Rohrlich; edited by Larry P. Horwitz, Tel-Aviv University, and Alwyn van der Merwe, University of Denver (Plenum Publishing, New York); 40 pages, REVTEX, Preprint UCONN-93-3, 1 figure available upon request from author

Hammerhead, an ultrahigh resolution ePix camera for wavelength-dispersive spectrometers

Wavelength-dispersive spectrometers (WDS) are often used in synchrotron and FEL applications where high energy resolution (in the order of eV) is important. Increasing WDS energy resolution requires increasing spatial resolution of the detectors in the dispersion direction. The common approaches with strip detectors or small pixel detectors are not ideal. We present a novel approach, with a sensor using rectangular pixels with a high aspect ratio (between strips and pixels, further called "strixels"), and strixel redistribution to match the square pixel arrays of typical ASICs while avoiding the considerable effort of redesigning ASICs. This results in a sensor area of 17.4 mm x 77 mm, with a fine pitch of 25 $\mu$m in the horizontal direction resulting in 3072 columns and 176 rows. The sensors use ePix100 readout ASICs, leveraging their low noise (43 e$^-$, or 180 eV rms). We present results obtained with a Hammerhead ePix100 camera, showing that the small pitch (25 $\mu$m) in the dispersion direction maximizes performance for both high and low photon occupancies, resulting in optimal WDS energy resolution. The low noise level at high photon occupancy allows precise photon counting, while at low occupancy, both the energy and the subpixel position can be reconstructed for every photon, allowing an ultrahigh resolution (in the order of 1 $\mu$m) in the dispersion direction and rejection of scattered beam and harmonics. Using strixel sensors with redistribution and flip-chip bonding to standard ePix readout ASICs results in ultrahigh position resolution ($\sim$1 $\mu$m) and low noise in WDS applications, leveraging the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development complexity through sharing the ASIC, hardware, software and DAQ development with existing versions of ePix cameras.Comment: 8 pages, 6 figure

Regrowth-related defect formation and evolution in 1 MeV amorphized (001) Ge

Geimplanted with 1MeV Si⁺ at a dose of 1×10¹⁵cm⁻² creates a buried amorphous layer that, upon regrowth, exhibits several forms of defects–end-of-range (EOR), regrowth-related, and clamshell defects. Unlike Si, no planar {311} defects are observed. The minimal EOR defects are small dotlike defects and are very unstable, dissolving between 450 and 550°C. This is in contrast to Si, where the EOR defects are very stable. The amorphous layer results in both regrowth-related defects and clamshell defects, which were more stable than the EOR damage.This work is supported by Semiconductor Research Corporation Contract No. 00057787

Rain, power laws, and advection

Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws are generated by treating rain as a passive tracer undergoing advection in a velocity field generated by a two-dimensional system of point vortices.Comment: 7 pages, 4 figure

Clinical factors associated with the non-utilization of an anaesthesia incident reporting system

Background Incident reporting is a widely recommended method to measure undesirable events in anaesthesia. Under-utilization is a major weakness of voluntary incident reporting systems. Little is known about factors influencing reporting practices, particularly the clinical environment, anaesthesia team composition, severity of the incident, and perceived risk of litigation. The purpose of this study was to assess each of these, using an existing anaesthesia database. Methods We performed a retrospective cohort study and analysed 46 207 surgical patients. We used multivariate analysis to identify factors associated with the non-utilization of the reporting system. Results We found that in 7022 (15.1%) of the procedures performed, the incident reporting system was not used. Factors associated with the non-use of the system were regional anaesthesia/local anaesthesia, odds ratio (OR) 1.64 [95% confidence interval (CI) 1.03-2.62], emergency procedures OR 1.15 (95% CI: 1.05-1.27), and a consultant anaesthetist working without a trainee, OR 1.71 (95% CI: 1.03-2.82). In contrast, factors such as longer duration of surgery, OR 0.85 (95% CI: 0.76-0.94), the presence of a senior anaesthesia trainee, OR 0.86 (95% CI: 0.81-0.92), and the occurrence of severe complications with a high risk of litigation (i.e. death, nerve injuries) were less associated with a non-use of the reporting system, OR 0.65 (95% CI: 0.44-0.97). Team composition and time of day had no measurable impact on reporting practices. Conclusions Clinical factors play a significant role in the utilization of an anaesthesia incident reporting system and more particularly, severity of complications and higher liability risks which appear more as incentives than barriers to incident reportin

Slow decay of concentration variance due to no-slip walls in chaotic mixing

Chaotic mixing in a closed vessel is studied experimentally and numerically in different 2-D flow configurations. For a purely hyperbolic phase space, it is well-known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincare section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker's map, we introduce a 1-D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.Comment: 17 pages, 12 figure

Friction Drag on a Particle Moving in a Nematic Liquid Crystal

The flow of a liquid crystal around a particle does not only depend on its shape and the viscosity coefficients but also on the direction of the molecules. We studied the resulting drag force on a sphere moving in a nematic liquid crystal (MBBA) in a low Reynold's number approach for a fixed director field (low Ericksen number regime) using the computational artificial compressibility method. Taking the necessary disclination loop around the sphere into account, the value of the drag force anisotropy (F_\perp/F_\parallel=1.50) for an exactly computed field is in good agreement with experiments (~1.5) done by conductivity diffusion measurements. We also present data for weak anchoring of the molecules on the particle surface and of trial fields, which show to be sufficiently good for most applications. Furthermore, the behaviour of the friction close to the transition point nematic isotropic and for a rod-like and a disc-like liquid crystal will be given.Comment: 23 pages RevTeX, including 3 PS figures, 1 PS table and 1 PS-LaTeX figure; Accepted for publication in Phys. Rev.