1. Online tutorial on emergence and collective phenomena.
Here is an online tutorial entitled Emergence and Collective Phenomena in Equilibrium and Nonequilibrium Systems. The tutorial was provided as background material for the National Academy of Sciences Keck Futures Initiative workshop on Complexity (2008). A similar but more action-packed lecture is available from the Perimeter Institute.
2. Superfluidity in Helium 4
The video below is called Superfluid Helium. It was made and narrated by one of the co-discoverers of superfluidity, John F. Allen (1908-2001), while he was Professor of Physics at St. Andrews University, Scotland, and produced by Allen and J.G.M. Armitage. Ten years in the making, the movie is a masterpiece of ingenuity and pedagogy, and repays repeated viewing. I am pleased to be able to distribute the movie on this web page with express permission from Professor Stephen Lee, the Head of the School of Physics at the University of St. Andrews.
You can learn more about John F. Allen from these obituaries in the Guardian newspaper and Nature.
The history of superfluidity is fascinating and controversial, because of the three co-discoverers, only P. Kapitza received the Nobel Prize, in 1978. The citation reads "for his basic inventions and discoveries in the area of low-temperature physics", but many interpret the award as if it were for the discovery of superfluidity. Detailed reconstructions of the historical timeline are described in a pair of very interesting articles, one by S. Balibar, and the other by A. Griffin. Balibar's article also discusses something of the controversies associated with the development of the theory of superfluidity. Griffin has reviewed these and other aspects of the history of superfluidity and its connections to Bose-Einstein condensation and BCS superconductivity in a talk on the intriguing history of superfluidity.
Here are the original papers by Kapitza and by Allen and Misener, published back-to-back in Nature in 1938. Undisputed is the fact that Allen and Jones were the first to report on the discovery of the spectacular "fountain effect", first observed just a few days after the publication of the discovery of superfluidity.
3. Dynamics of quantum vortices
There is currently a resurgence of interest in the dynamics of quantum vortices. My former student, Patricio Jeraldo and I developed some fast computational algorithms for simulating superfluid hydrodynamics, and you can read about them in his Ph.D thesis. Some representative movies, using these unpublished cell dynamical system algorithms, can be seen below. Experimental observations and an accessible non-technical description can be viewed at this page, part of the APS backgrounder journal Physics.
Here are the animations made with data from numerical simulations of superfluid flows. The simulations were done using a cell dynamical system based model of the superfluid order parameter with dissipation. The scheme is similar in spirit to the Ginzburg-Pitaevskii equations for superfluids near the λ point.
Isosurfaces of minimum density are displayed in this kinematic simulation of a superfluid under the influence of a normal component described by an Arnold-Beltrami-Childress flow.
A vortex ring is stretched by a Gaussian vortex, the vortex string length increases until saturation. These are isosurfaces of minumum superfluid density.
Two vortex rings in the center of a box are affected by a normal component in the z direction (upwards). The rings also shrink because of dissipative effects. These are isosurfaces of minimum superfluid density
After a quench, the superfluid is “sheared” with a normal flow in the y-direction, witn maximum positive velocity at x=L/4, and maximum negative velocity at x=3L/4. These are isosurfaces of minimum superfluid density.
Vortex strings are transported by a flow which has its maximum speed at the center of the X-Z plane, with v=0 at the boundaries. The box has periodic boundary conditions, so it is not really a Pouiseille flow. These are isosurfaces of minimum superfluid density.
Updated by Nigel Goldenfeld, Jan 2018.
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