Coupled normal fluid and superfluid profiles of turbulent helium II in channels

We perform fully coupled two--dimensional numerical simulations of plane channel helium II counterflows with vortex--line density typical of experiments. The main features of our approach are the inclusion of the back reaction of the superfluid vortices on the normal fluid and the presence of solid boundaries. Despite the reduced dimensionality, our model is realistic enough to reproduce vortex density distributions across the channel recently calculated in three--dimensions. We focus on the coarse--grained superfluid and normal fluid velocity profiles, recovering the normal fluid profile recently observed employing a technique based on laser--induced fluorescence of metastable helium molecules.Comment: 26 pages, 8 Figures, accepted for publication in Phys. Rev.

Complex singularities and PDEs

In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of the 2D KP equation, and to Navier-Stokes equation for high Reynolds number incompressible flows in the case of interaction with rigid boundaries

The saturation of decaying counterflow turbulence in helium II

We are concerned with the problem of the decay of a tangle of quantized vortices in He II generated by a heat current. Direct application of Vinen's equation yields the temporal scaling of vortex line density $L \sim t^{-1}$. Schwarz and Rozen [Phys. Rev. Lett. {\bf 66}, 1898 (1991); Phys. Rev. B {\bf 44}, 7563 (1991)] observed a faster decay followed by a slower decay. More recently, Skrbek and collaborators [Phys. Rev. E {\bf 67}, 047302 (2003)] found an initial transient followed by the same classical $t^{-3/2}$ scaling observed in the decay of grid-generated turbulence. We present a simple theoretical model which, we argue, contains the essential physical ingredients, and accounts for these apparently contradictory results.Comment: 19 pages, 5 figure

Radiation hardened transistor characteristics for applications at LHC and beyond

The high radiation environment at the LHC will require the use of radiation hardened microelectronics for the readout of inner detectors. Two such technologies are a Harris bulk CMOS process and the DMILL mixed technology process. Transistors have been fabricated in both of these and have been tested before and after irradiation to 10 Mrads, the total dose expected in the innermost silicon microstrip layers. Several processing runs of Harris transistors have been carried out and samples from one have also been irradiated to 100 Mrads. A preamplifier-shaper circuit, to be used for readout of the CMS microstrip tracker, has been tested and the noise performance is compared with individual transistors

Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions

Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

Quantification of Myocardial Perfusion in Human Subjects Using 82Rb and Wavelet-Based Noise Reduction

Quantification of myocardial perfusion with 82Rb has been difficult to achieve because of the low signal-to-noise ratio of the dynamic data curves. This study evaluated the accuracy of flow estimates after the application of a novel multidimensional wavelet-based noise-reduction protocol. Methods: Myocardial perfusion was estimated using 82Rb and a two-compartment model from dynamic PET scans on 11 healthy volunteers at rest and after hyperemic stress with dipyridamole. Midventricular planes were divided into eight regions of interest, and a wavelet transform protocol was applied to images and time–activity curves. Flow estimates without and with the wavelet approach were compared with those obtained using H215O. Results: Over a wide flow range (0.45–2.75 mL/g/min), flow achieved with the wavelet approach correlated extremely closely with values obtained with H215O (y = 1.03 x -0.12; n = 23 studies, r = 0.94, P < 0.001). If the wavelet noise-reduction technique was not used, the correlation was less strong (y = 1.11 x + 0.24; n = 23 studies, r = 0.79, P < 0.001). In addition, the wavelet approach reduced the regional variation from 75% to 12% and from 62% to 11% (P < 0.001 for each comparison) for resting and stress studies, respectively. Conclusion: The use of a wavelet protocol allows near-optimal noise reduction, markedly enhances the physiologic flow signal within the PET images, and enables accurate measurement of myocardial perfusion with 82Rb in human subjects over a wide range of flows

Turbulent superfluid profiles in a counterflow channel

We have developed a two-dimensional model of quantised vortices in helium II moving under the influence of applied normal fluid and superfluid in a counterflow channel. We predict superfluid and vortex-line density profiles which could be experimentally tested using recently developed visualization techniques.Comment: 3 double figures, 9 page

Analytic solutions and Singularity formation for the Peakon b--Family equations

Using the Abstract Cauchy-Kowalewski Theorem we prove that the $b$-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to $H^s$ with $s > 3/2$, and the momentum density $u_0 - u_{0,{xx}}$ does not change sign, we prove that the solution stays analytic globally in time, for $b\geq 1$. Using pseudospectral numerical methods, we study, also, the singularity formation for the $b$-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity approaches the real axis, estimating the rate of decay of the Fourier spectrum