Splash wave and crown breakup after disc impact on a liquid surface

In this paper we analyze the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash --giving rise to what is known as the crown splash-- if the impact Weber number exceeds a threshold value \Weber_{crit}\simeq 140. We explain this threshold by defining a local Bond number $Bo_{tip}$ based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when $Bo_{tip}\gtrsim 1$, revealing that the rim disrupts due to a Rayleigh-Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-number-dependent self-similar structure for every Weber number. From this we demonstrate that \Bond_{tip}\propto\Weber, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for $We_{crit}\simeq 140$. Next, including the effect of air, we have developed a theory which predicts the time-varying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affect the velocity of propagation of the splash wave as well as the time-varying force on the disc, $F_D$. The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, what sets the length scale of the splash drops ejected when We>\Weber_{crit}

The intensity JND comes from Poisson neural noise: Implications for image coding

While the problems of image coding and audio coding have frequently been assumed to have similarities, specific sets of relationships have remained vague. One area where there should be a meaningful comparison is with central masking noise estimates, which define the codec's quantizer step size. In the past few years, progress has been made on this problem in the auditory domain (Allen and Neely, J. Acoust. Soc. Am., {\bf 102}, 1997, 3628-46; Allen, 1999, Wiley Encyclopedia of Electrical and Electronics Engineering, Vol. 17, p. 422-437, Ed. Webster, J.G., John Wiley \& Sons, Inc, NY). It is possible that some useful insights might now be obtained by comparing the auditory and visual cases. In the auditory case it has been shown, directly from psychophysical data, that below about 5 sones (a measure of loudness, a unit of psychological intensity), the loudness JND is proportional to the square root of the loudness \DL(\L) \propto \sqrt{\L(I)}. This is true for both wideband noise and tones, having a frequency of 250 Hz or greater. Allen and Neely interpret this to mean that the internal noise is Poisson, as would be expected from neural point process noise. It follows directly that the Ekman fraction (the relative loudness JND), decreases as one over the square root of the loudness, namely \DL/\L \propto 1/\sqrt{\L}. Above {\L} = 5 sones, the relative loudness JND \DL/\L \approx 0.03 (i.e., Ekman law). It would be very interesting to know if this same relationship holds for the visual case between brightness \B(I) and the brightness JND \DB(I). This might be tested by measuring both the brightness JND and the brightness as a function of intensity, and transforming the intensity JND into a brightness JND, namely \DB(I) = \B(I+ \DI) - \B(I) \approx \DI \frac{d\B}{dI}. If the Poisson nature of the loudness relation (below 5 sones) is a general result of central neural noise, as is anticipated, then one would expect that it would also hold in vision, namely that \DB(\B) \propto \sqrt{\B(I)}. %The history of this problem is fascinating, starting with Weber and Fechner. It is well documented that the exponent in the S.S. Stevens' power law is the same for loudness and brightness (Stevens, 1961) \nocite{Stevens61a} (i.e., both brightness \B(I) and loudness \L(I) are proportional to $I^{0.3}$). Furthermore, the brightness JND data are more like Riesz's near miss data than recent 2AFC studies of JND measures \cite{Hecht34,Gescheider97}

Angular Momentum Loss from Cool Stars: An Empirical Expression and Connection to Stellar Activity

We show here that the rotation period data in open clusters allow the empirical determination of an expression for the rate of loss of angular momentum from cool stars on the main sequence. One significant component of the expression, the dependence on rotation rate, persists from prior work; others do not. The expression has a bifurcation, as before, that corresponds to an observed bifurcation in the rotation periods of coeval open cluster stars. The dual dependencies of this loss rate on stellar mass are captured by two functions, $f(B-V)$ and $T(B-V)$, that can be determined from the rotation period observations. Equivalent masses and other [UBVRIJHK] colors are provided in Table 1. Dimensional considerations, and a comparison with appropriate calculated quantities suggest interpretations for $f$ and $T$, both of which appear to be related closely (but differently) to the calculated convective turnover timescale, $\tau_c$, in cool stars. This identification enables us to write down symmetrical expressions for the angular momentum loss rate and the deceleration of cool stars, and also to revive the convective turnover timescale as a vital connection between stellar rotation and stellar activity physics.Comment: 20 pages, 9 color figures; this version includes corrections listed in the associated journal erratu

The route toward a diode-pumped 1-W erbium 3-µm fiber laser

A rate-equation analysis of the erbium 3-um ZBLAN fiber laser is performed. The computer calculation includes the longitudinal spatial resolution of the host material. It considers ground-state bleaching, excited-state absorption (ESA), interionic processes, lifetime quenching by co-doping, and stimulated emission at 2.7 um and 850 nm. State-of-the-art technology including double-clad diode pumping is assumed in the calculation. Pump ESA is identified as the major problem of this laser. With high Er3+ concentration, suitable Pr3+ co-doping, and low pump density, ESA is avoided and a diode-pumped erbium 3-um ZBLAN laser is predicted which is capable of emitting a transversely single-mode output power of 1.0 W when pumped with 7-W incident power at 800 nm. The corresponding output intensity which is relevant for surgical applications will be in the range of 1.8 MW/cm2. Compared to Ti:sapphire-pumped cascade-lasing regimes, the proposed approach represents a strong decrease of the requirements on mirror coatings, cavity alignment, and especially pump intensity. Of the possible drawbacks investigated in the simulation, only insufficient lifetime quenching is found to have a significant influence on laser performance

Few-body correlations in the QCD phase diagram

From the viewpoint of statistical physics, nuclear matter is a strongly correlated many-particle system. Several regimes of the QCD phase diagram should exhibit strong correlations. Here I focus on three- and four-body correlations that might be important in the phase diagram.Comment: 3 pages, 4 figures, contribution to QNP200