Evolution of an elliptical bubble in an accelerating extensional flow

Mathematical models that describe the dynamical behavior of a thin gas bubble embedded in a glass fiber during a fiber drawing process have been discussed and analyzed. The starting point for the mathematical modeling was the equations presented in [1] for a glass fiber with a hole undergoing extensional flow. These equations were reconsidered here with the additional reduction that the hole, i.e. the gas bubble, was thin as compared to the radius of the fiber and of finite extent. The primary model considered was one in which the mass of the gas inside the bubble was fixed. This fixed-mass model involved equations for the axial velocity and fiber radius, and equations for the radius of the bubble and the gas pressure inside the bubble. The model equations assumed that the temperature of the furnace of the drawing tower was known. The governing equations of the bubble are hyperbolic and predict that the bubble cannot extend beyond the limiting characteristics specified by the ends of the initial bubble shape. An analysis of pinch-off was performed, and it was found that pinch-off can occur, depending on the parameters of the model, due to surface tension when the bubble radius is small. In order to determine the evolution of a bubble, a numerical method of solution was presented. The method was used to study the evolution of two different initial bubble shapes, one convex and the other non-convex. Both initial bubble shapes had fore-aft symmetry, and it was found that the bubbles stretched and elongated severely during the drawing process. For the convex shape, fore-aft symmetry was lost in the middle of the drawing process, but the symmetry was re-gained by the end of the drawing tower. A small amount of pinch-off was observed at each end for this case, so that the final bubble length was slightly shorter than its theoretical maximum length. For the non-convex initial shape, pinch-off occurred in the middle of the bubble resulting in two bubbles by the end of the fiber draw. The two bubbles had different final pressures and did not have fore-aft symmetry. An extension of the fixed-mass model was considered in which the gas in the bubble was allowed to diffuse into the surrounding glass. The governing equations for this leaky-mass model were developed and manipulated into a form suitable for a numerical treatment

Conditions for one-dimensional supersonic flow of quantum gases

One can use transsonic Bose-Einstein condensates of alkali atoms to establish the laboratory analog of the event horizon and to measure the acoustic version of Hawking radiation. We determine the conditions for supersonic flow and the Hawking temperature for realistic condensates on waveguides where an external potential plays the role of a supersonic nozzle. The transition to supersonic speed occurs at the potential maximum and the Hawking temperature is entirely determined by the curvature of the potential

Dissipative Transport of a Bose-Einstein Condensate

We investigate the effects of impurities, either correlated disorder or a single Gaussian defect, on the collective dipole motion of a Bose-Einstein condensate of $^7$Li in an optical trap. We find that this motion is damped at a rate dependent on the impurity strength, condensate center-of-mass velocity, and interatomic interactions. Damping in the Thomas-Fermi regime depends universally on the disordered potential strength scaled to the condensate chemical potential and the condensate velocity scaled to the peak speed of sound. The damping rate is comparatively small in the weakly interacting regime, and the damping in this case is accompanied by strong condensate fragmentation. \textit{In situ} and time-of-flight images of the atomic cloud provide evidence that this fragmentation is driven by dark soliton formation.Comment: 14 pages, 20 figure

Quantum phase space picture of Bose-Einstein Condensates in a double well: Proposals for creating macroscopic quantum superposition states and a study of quantum chaos

We present a quantum phase space model of Bose-Einstein condensate (BEC) in a double well potential. In a two-mode Fock-state analysis we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase space information is extracted from the stationary quantum states using the Husimi distribution function. It is shown that the quantum states are localized on the known classical phase space orbits of a nonrigid physical pendulum, and thus the novel phase space characteristics of a nonrigid physical pendulum such as the $\pi$ motions are seen to be a property of the exact quantum states. Low lying states are harmonic oscillator like libration states while the higher lying states are Schr\"odinger cat-like superpositions of two pendulum rotor states. To study the dynamics in phase space, a comparison is made between a displaced quantum wavepacket and the trajectories of a swarm of points in classical phase space. For a driven double well, it is shown that the classical chaotic dynamics is manifest in the dynamics of the quantum states pictured using the Husimi distribution. Phase space analogy also suggests that a $\pi$ phase displaced wavepacket put on the unstable fixed point on a separatrix will bifurcate to create a superposition of two pendulum rotor states - a Schr\"odinger cat state (number entangled state) for BEC. It is shown that the choice of initial barrier height and ramping, following a $\pi$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.Comment: revised version, 13 pages, 13 figure

Spin picture of the one-dimensional Hubbard model: Two-fluid structure and phase dynamics

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schroedinger equations, whereas near half-filling the model is described by two coupled Josephson junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed point equation of the simpler among them, we show that the standard one-band ground state phase space is found.Comment: 10 pages, 1 figure, to appear on Phys. Rev.

Correlation functions and emission time sequence of light charged particles from projectile-like fragment source in E/A = 44 and 77 MeV 40Ar + 27Al collisions

Two-particle correlation functions, involving protons, deuterons, tritons, and alpha-particles, have been measured at very forward angles (0.7 deg < theta_lab < 7 deg), in order to study projectile-like fragment (PLF) emission in E/A = 44 and 77 MeV 40Ar + 27Al collisions. Peaks, originating from resonance decays, are larger at E/A = 44 than at 77 MeV. This reflects the larger relative importance of independently emitted light particles, as compared to two-particle decay from unstable fragments, at the higher beam energy. The time sequence of the light charged particles, emitted from the PLF, has been deduced from particle-velocity-gated correlation functions (discarding the contribution from resonance decays). Alpha-particles are found to have an average emission time shorter than protons but longer than tritons and deuterons.Comment: 18 pages, 5 figures, submitted to Nuclear Physics

Quantized Roentgen Effect in Bose-Einstein Condensates

A classical dielectric moving in a charged capacitor can create a magnetic field (Roentgen effect). A quantum dielectric, however, will not produce a magnetization, except at vortices. The magnetic field outside the quantum dielectric appears as the field of quantized monopoles

Assessing protocol adherence in a clinical trial with ordered treatment regimens: Quantifying the pragmatic, randomized optimal platelet and plasma ratios (PROPPR) trial experience

AbstractBackgroundMedication dispensing errors are common in clinical trials, and have a significant impact on the quality and validity of a trial. Therefore, the definition, calculation and evaluation of such errors are important for supporting a trial’s conclusions. A variety of medication dispensing errors can occur. In this paper, we focus on errors in trials where the intervention includes multiple therapies that must be given in a pre-specified order that varies across treatment arms and varies in duration.MethodsThe Pragmatic, Randomized Optimal Platelet and Plasma Ratios (PROPPR) trial was a Phase III multi-site, randomized trial to compare the effectiveness and safety of 1:1:1 transfusion ratios of plasma and platelets to red blood cells with a 1:1:2 ratio. In this trial, these three types of blood products were to be transfused in a pre-defined order that differed by treatment arm. In this paper, we present approaches from the PROPPR trial that we used to define and calculate the occurrence of out of order blood transfusion errors. We applied the proposed method to calculate protocol adherence to the specified order of transfusion in each treatment arm.ResultsUsing our proposed method, protocol adherence was greater in the 1:1:1 group than in the 1:1:2 group (96% vs 93%) (p<0.0001), although out of order transfusion errors in both groups were low. Final transfusion ratios of plasma to platelets to red blood cells for the 1:1:1 ratio group was 0.93:1.32:1, while the transfusion ratio for the 1:1:2 ratio group was 0.48:0.48:1.ConclusionsOverall, PROPPR adherence to blood transfusion order pre-specified in the protocol was high, and the required order of transfusions for the 1:1:2 group was more difficult to achieve. The approaches proposed in this manuscript were useful in evaluating the PROPPR adherence and are potentially useful for other trials where a specific treatment orders with varying durations must be maintained