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The onset of turbulent flow around an oscillating sphere in superfluid $^4$He is known to occur at a critical velocity $v_c \sim \sqrt{\kappa\omega}$ where $\kappa$ is the circulation quantum and $\omega$ is the oscillation frequency. But it is also well known that initially in a first up-sweep of the oscillation amplitude, $v_c$ can be considerably exceeded before the transition occurs, thus leading to a strong hysteresis in the velocity sweeps. The velocity amplitude $v_c^* > v_c$ where the transition finally occurs is related to the density $L_0$ of the remanent vortices in the superfluid. Moreover, at temperatures below ca. 0.5 K and in a small interval of velocity amplitudes between $v_c$ and a velocity that is about 2% larger, the flow pattern is found to be unstable, switching intermittently between potential flow and turbulence. From time series recorded at constant temperature and driving force the distribution of the excess velocities $\Delta v = v_c^* - v_c$ is obtained and from that the failure rate. Below 0.1 K we also can determine the distribution of the lifetimes of the phases of potential flow. Finally, the frequency dependence of these results is discussed., Comment: 8 pages,6 figures

We investigate the statistical properties of single phase slip events observed in vortex nucleation experiments in He-4 by the groups in Berkeley and Paris. From the cumulative distribution function of the events we calculate the slip rate as a function of flow velocity. The critical velocity is defined as the mean velocity and its statistical width as the standard deviation. From the slip rate and from the observed linear temperature dependence of the critical velocity we obtain the energy barrier for vortex nucleation which is a quadratic function of the flow velocity. A comparison with the statistical properties of the laminar to turbulent transition in the flow around an oscillating sphere shows strikingly different behaviour., Comment: 10 pages, 5 figures

The damping of the oscillations of a small permanent magnet (spherical shape, radius 0.1 mm) levitating between two parallel YBCO surfaces is measured as a function of oscillation amplitude and temperature. The losses in the samples (epitaxial thin films, bulk granular and bulk melt-textured) are analyzed in terms of oscillating shielding currents flowing through trapped flux lines whose motion gives rise to electric fields. We find dissipation to originate from different mechanisms of flux dynamics. At small amplitudes there is a linear regime described by a surface resistance varying from 10^-9 Ohm for bulk samples down to 10^-13 Ohm for the thin films at low temperatures. With increasing amplitude various nonlinear regimes are observed, firstly collective pinning with diverging energy barriers, secondly in bulk samples above 85 K hysteretic damping, and finally in thin films exponentially large losses which can be described by pinning energies vanishing linearly at large currents., Comment: 9 pages, 12 figures

The damping of the oscillations of a small permanent magnet (spherical shape, radius 0.1 mm) levitating between two parallel epitaxial YBCO films is measured as a function of oscillation amplitude and temperature. At small amplitudes the dissipation is found to be orders of magnitude lower than in bulk YBCO, Q-factors exceeding one million at low temperatures. With increasing amplitude the dissipation becomes exponentially large, exceeding the bulk values at large drives. We describe our results by calculating the ac shielding currents flowing through trapped flux whose motion gives rise to electric fields. We find dissipation to originate from different mechanisms of flux dynamics., Comment: LaTeX (revtex, aps, prl, multicol, epsfig); 4 pages 5 figures included