Extended Kelvin theorem in relativistic magnetohydrodynamics

We prove the existence of a generalization of Kelvin's circulation theorem in general relativity which is applicable to perfect isentropic magnetohydrodynamic flow. The argument is based on a new version of the Lagrangian for perfect magnetohydrodynamics. We illustrate the new conserved circulation with the example of a relativistic magnetohydrodynamic flow possessing three symmetries.Comment: Invited talk at IARD 2000, the Second International Conference on Relativistic Dynamics, Bar-Ilan University, Israel, 26-28 June, 2000. To appear in the proceedings in a special issue of Foundations of Physic

Fluorescence antibunching microscopy

Breaking the diffraction limit in microscopy by utilizing quantum properties of light has been the goal of intense research in the recent years. We propose a quantum superresolution technique based on non-classical emission statistics of fluorescent markers, routinely used as contrast labels for bio-imaging. The technique can be readily implemented using standard fluorescence microscopy equipment

Small-Sample Behavior of Novel Phase I Cancer Trial Designs

Novel dose-finding designs, using estimation to assign the best estimated maximum- tolerated-dose (MTD) at each point in the experiment, most commonly via Bayesian techniques, have recently entered large-scale implementation in Phase I cancer clinical trials. We examine the small-sample behavior of these "Bayesian Phase I" (BP1) designs, and also of non-Bayesian designs sharing the same main "long-memory" traits (hereafter: LMP1s). For all LMP1s examined, the number of cohorts treated at the true MTD (denoted here as n*) was highly variable between numerical runs drawn from the same toxicity-threshold distribution, especially when compared with "up-and-down" (U&D) short-memory designs. Further investigation using the same set of thresholds in permuted order, produced a nearly-identical magnitude of variability in n*. Therefore, this LMP1 behavior is driven by a strong sensitivity to the order in which toxicity thresholds appear in the experiment. We suggest that the sensitivity is related to LMP1's tendency to "settle" early on a specific dose level - a tendency caused by the repeated likelihood-based "winner-takes-all" dose assignment rule, which grants the early cohorts a disproportionately large influence upon experimental trajectories. Presently, U&D designs offer a simpler and more stable alternative, with roughly equivalent MTD estimation performance. A promising direction for combining the two approaches is briefly discussed (note: the '3+3' protocol is not a U&D design).Comment: Somewhat modified version of the version accepted pending final modifications at Clinical Trials. The supplement is in the bac

Dynamics of Perfectly Wetting Drops under Gravity

We study the dynamics of small droplets of polydimethylsiloxane (PDMS) silicone oil on a vertical, perfectly-wetting, silicon wafer. Interference videomicroscopy allows us to capture the dynamics of these droplets. We use droplets with a volumes typically ranging from 100 to 500 nanolitres (viscosities from 10 to 1000 centistokes) to understand long time derivations from classical solutions. Past researchers used one dimensional theory to understand the typical $t^{1/3}$ scaling for the position of the tip of the droplet in time $t$. We observe this regime in experiment for intermediate times and discover a two-dimensional, similarity solution of the shape of the droplet. However, at long times our droplets start to move more slowly down the plane than the $t^{1/3}$ scaling suggests and we observe deviations in droplet shape from the similarity solution. We match experimental data with simulations to show these deviations are consistent with retarded van der Waals forcing which should become significant at the small heights observed

Excitation Enhancement of a Quantum Dot Coupled to a Plasmonic Antenna

Plasmonic antennas are key elements to control the luminescence of quantum emitters. However, the antenna's influence is often hidden by quenching losses. Here, the luminescence of a quantum dot coupled to a gold dimer antenna is investigated. Detailed analysis of the multiply excited states quantifies the antenna's influence on the excitation intensity and the luminescence quantum yield separately

Theory of selective excitation in Stimulated Raman Scattering

A semiclassical model is used to investigate the possibility of selectively exciting one of two closely spaced, uncoupled Raman transitions. The duration of the intense pump pulse that creates the Raman coherence is shorter than the vibrational period of a molecule (impulsive regime of interaction). Pulse shapes are found that provide either enhancement or suppression of particular vibrational excitations.Comment: RevTeX4,10 pages, 5 figures, submitted to Phys.Rev.

A Large Blue Shift of the Biexciton State in Tellurium Doped CdSe Colloidal Quantum Dots

The exciton-exciton interaction energy of Tellurium doped CdSe colloidal quantum dots is experimentally investigated. The dots exhibit a strong Coulomb repulsion between the two excitons, which results in a huge measured biexciton blue shift of up to 300 meV. Such a strong Coulomb repulsion implies a very narrow hole wave function localized around the defect, which is manifested by a large Stokes shift. Moreover, we show that the biexciton blue shift increases linearly with the Stokes shift. This result is highly relevant for the use of colloidal QDs as optical gain media, where a large biexciton blue shift is required to obtain gain in the single exciton regime.Comment: 9 pages, 4 figure