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Register a new userViscosity of liquid He-4 and quantum of circulation: Why and how are they related?
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The relationship between the apparently unrelated physical quantities -- kinematic viscosity of liquid He-4, $ u$, and quantum of circulation, $kappa=2pi hbar/m_4$, where $hbar$ is the Planck constant and $m_4$ denotes the mass of the $^4$He atom -- is examined in the vicinity of the superfluid transition occurring due to Bose-Einstein condensation. A model is developed, leading to the surprisingly simple relation $ u approx kappa/6$. We critically examine the available experimental data for $^4$He relevant to this simple relation and predict the kinematic viscosity for the stretched liquid $^4$He along the $lambda$-line at negative pressures.
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We perform a comprehensive analysis of the spectral statistics of the molecular resonances in $^{166}$Er and $^{168}$Er observed in recent ultracold collision experiments [Frisch et al., Nature {bf 507}, 475 (2014)] with the aim of determining the chaoticity of this system. We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. The analysis of the short-range fluctuations as a function of the magnetic field points to a steady increase of chaoticity until $B sim 30$ G. The repulsion parameter decreases for higher magnetic fields, an effect that can be interpreted as due to missing resonances. The analysis of long-range fluctuations allows us to be more quantitative and estimate a $20-25%$ fraction of missing levels. Finally, a study of the distribution of resonance widths provides additional evidence supporting missing resonances of small width compared with the experimental magnetic field resolution. We conclude that further measurements with increased resolution will be necessary to give a final answer to the problem of missing resonances and the agreement with RMT.
We obtain the von Karman-Howarth relation for the stochastically forced three-dimensional Hall-Vinen-Bekharvich-Khalatnikov (3D HVBK) model of superfluid turbulence in Helium ($^4$He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analyitcal studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) $P(gamma)$, of the ratio $gamma$ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as $P(gamma) sim gamma^3$, for $gamma ll 1$, and $P(gamma) sim gamma^{-3}$, for $gamma gg 1$. Furthermore, we show that the PDF $P(theta)$, of the angle $theta$ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: $P(theta)sim theta$ for $theta ll theta_*$ and $P(theta)sim theta^{-4}$ for $theta_* ll theta ll 1$, where $theta_*$ is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, and the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature $T$, by using the experimentally determined mutual-friction coefficients for superfluid Helium $^4$He, so our results are of direct relevance to superfluid turbulence in this system.
The mayfly nymph breathes under water through an oscillating array of wing-shaped tracheal gills. As the nymph grows, the kinematics of these gills change abruptly from rowing to flapping. The classical fluid dynamics approach to consider the mayfly nymph as a pumping device fails in giving clear reasons to this switch. In order to understand the whys and the hows of this switch between the two distinct kinematics, we analyze the problem under a Lagrangian viewpoint. We consider that a good Lagrangian transport that distributes and spreads water and dissolved oxygen well between and around the gills is the main goal of the gill motion. Using this Lagrangian approach we are able to provide the reason behind the switch from rowing to flapping that the mayfly nymph experiences as it grows. More precisely, recent and powerful tools from this Lagrangian approach are applied to in-sillico mayfly nymph experiments, where body shape, as well as, gill shapes, structures and kinematics are matched to those from in-vivo. In this letter, we show both qualitatively and quantitatively how the change of kinematics enables a better attraction, stirring and confinement of water charged of dissolved oxygen inside the gills area. From the computational velocity field we reveal attracting barriers to transport, i.e. attracting Lagrangian coherent structures, that form the transport skeleton between and around the gills. In addition, we quantify how well the fluid particles and consequently dissolved oxgen is spread and stirred inside the gills area.
The fact that superfluid helium always leaks out of an open container is usually explained by the phenomenon of wetting. In the present paper it is demonstrated that this explanation is unconvincing. The fact can be readily explained from the viewpoint of the interpretation of superfluidity proposed earlier by the author according to which superfluidity is an equilibrium state of liquid helium where the symmetry is spontaneously broken because of an intrinsic superflow. Experiments on the thickness of moving helium films that have given rise to much controversy are discussed as well. Some experiments concerning the phenomena considered in the paper are proposed.
It is shown that, contrary to an existing claim, the near equality between the lifetime of the sun and the timescale of biological evolution on earth does not necessarily imply that extraterrestrial civilizations are exceedingly rare. Furthermore, on the basis of simple assumptions it is demonstrated that a near equality between these two timescales may be the most probable relation. A calculation of the cosmic history of carbon production which is based on the recently determined history of the star formation rate suggests that the most likely time for intelligent civilizations to emerge in the universe, was when the universe was already older then about 10 billion years (for an assumed current age of about 13 billion years).
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