Broken symmetries and pattern formation in two-frequency forced Faraday waves

We exploit the presence of approximate (broken) symmetries to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Specifically, we consider a two-frequency forcing function and trace the effects of time translation, time reversal and Hamiltonian structure for three illustrative examples: hexagons, two-mode superlattices, and two-mode rhomboids. By means of explicit parameter symmetries, we show how the size of various three-wave resonant interactions depends on the frequency ratio m:n and on the relative temporal phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.Comment: 4 pages, 6 figure

Super-lattice, rhombus, square, and hexagonal standing waves in magnetically driven ferrofluid surface

Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits various patterns including a superlattice and subharmonic rhombuses as well as conventional harmonic hexagons and subharmonic squares. The superlattice arises in a bicritical situation where harmonic and subharmonic modes collide. The rhombic pattern arises due to the non-monotonic dispersion relation of a ferrofluid

Pattern formation in 2-frequency forced parametric waves

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different 3--wave resonant interactions. They occur either as symmetry--breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by 4--wave interactions that arise when symmetry constraints rule out 3--wave resonances.Comment: The paper contains 34 pages and 53 figures and provides an extensive review of both the theoretical and experimental work peformed in this syste

Parametrically Excited Surface Waves: Two-Frequency Forcing, Normal Form Symmetries, and Pattern Selection

Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio m/n, where m and n are co-prime integers, there is the possibility that both harmonic and subharmonic waves may lose stability simultaneously, each with a different wavenumber. We focus on this situation and compare the case where the harmonic waves have a longer wavelength than the subharmonic waves with the case where the harmonic waves have a shorter wavelength. We show that in the former case a normal form transformation can be used to remove all quadratic terms from the amplitude equations governing the relevant resonant triad interactions. Thus the role of resonant triads in the pattern selection problem is greatly diminished in this situation. We verify our general results within the example of one-dimensional surface wave solutions of the Zhang-Vinals model of the two-frequency Faraday problem. In one-dimension, a 1:2 spatial resonance takes the place of a resonant triad in our investigation. We find that when the bifurcating modes are in this spatial resonance, it dramatically effects the bifurcation to subharmonic waves in the case of forcing frequencies are in ratio 1/2; this is consistent with the results of Zhang and Vinals. In sharp contrast, we find that when the forcing frequencies are in ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the presence of another spatially-resonant bifurcating mode.Comment: 22 pages, 6 figures, late

Amplitude measurements of Faraday waves

A light reflection technique is used to measure quantitatively the surface elevation of Faraday waves. The performed measurements cover a wide parameter range of driving frequencies and sample viscosities. In the capillary wave regime the bifurcation diagrams exhibit a frequency independent scaling proportional to the wavelength. We also provide numerical simulations of the full Navier-Stokes equations, which are in quantitative agreement up to supercritical drive amplitudes of 20%. The validity of an existing perturbation analysis is found to be limited to 2.5% overcriticaly.Comment: 7 figure

"It All Ended in an Unsporting Way": Serbian Football and the Disintegration of Yugoslavia, 1989-2006

Part of a wider examination into football during the collapse of Eastern European Communism between 1989 and 1991, this article studies the interplay between Serbian football and politics during the period of Yugoslavia's demise. Research utilizing interviews with individuals directly involved in the Serbian game, in conjunction with contemporary Yugoslav media sources, indicates that football played an important proactive role in the revival of Serbian nationalism. At the same time the Yugoslav conflict, twinned with a complex transition to a market economy, had disastrous consequences for football throughout the territories of the former Yugoslavia. In the years following the hostilities the Serbian game has suffered decline, major financial hardship and continuing terrace violence, resulting in widespread nostalgia for the pre-conflict era

Faraday instability on viscous ferrofluids in a horizontal magnetic field: Oblique rolls of arbitrary orientation

A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability threshold on the magnetic field is found at high frequencies of the vibrations. The reasons of the decrease of the critical acceleration amplitude caused by a horizontal magnetic field are discussed. It is revealed that the magnetic field can be used to select the first unstable pattern of Faraday waves. In particular, a rhombic pattern as a superposition of two different oblique rolls can occur. A scaling law is presented which maps all data into one graph for the tested range of viscosities, frequencies, magnetic fields and layer thicknesses.Comment: 8 pages, 6 figures, RevTex

Rapid sympathetic cooling to Fermi degeneracy on a chip

Neutral fermions present new opportunities for testing many-body condensed matter systems, realizing precision atom interferometry, producing ultra-cold molecules, and investigating fundamental forces. However, since their first observation, quantum degenerate Fermi gases (DFGs) have continued to be challenging to produce, and have been realized in only a handful of laboratories. In this Letter, we report the production of a DFG using a simple apparatus based on a microfabricated magnetic trap. Similar approaches applied to Bose-Einstein Condensation (BEC) of 87Rb have accelerated evaporative cooling and eliminated the need for multiple vacuum chambers. We demonstrate sympathetic cooling for the first time in a microtrap, and cool 40K to Fermi degeneracy in just six seconds -- faster than has been possible in conventional magnetic traps. To understand our sympathetic cooling trajectory, we measure the temperature dependence of the 40K-87Rb cross-section and observe its Ramsauer-Townsend reduction.Comment: 5 pages, 4 figures (v3: new collision data, improved atom number calibration, revised text, improved figures.

ProtoDESI: First On-Sky Technology Demonstration for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) is under construction to measure the expansion history of the universe using the baryon acoustic oscillations technique. The spectra of 35 million galaxies and quasars over 14,000 square degrees will be measured during a 5-year survey. A new prime focus corrector for the Mayall telescope at Kitt Peak National Observatory will deliver light to 5,000 individually targeted fiber-fed robotic positioners. The fibers in turn feed ten broadband multi-object spectrographs. We describe the ProtoDESI experiment, that was installed and commissioned on the 4-m Mayall telescope from August 14 to September 30, 2016. ProtoDESI was an on-sky technology demonstration with the goal to reduce technical risks associated with aligning optical fibers with targets using robotic fiber positioners and maintaining the stability required to operate DESI. The ProtoDESI prime focus instrument, consisting of three fiber positioners, illuminated fiducials, and a guide camera, was installed behind the existing Mosaic corrector on the Mayall telescope. A Fiber View Camera was mounted in the Cassegrain cage of the telescope and provided feedback metrology for positioning the fibers. ProtoDESI also provided a platform for early integration of hardware with the DESI Instrument Control System that controls the subsystems, provides communication with the Telescope Control System, and collects instrument telemetry data. Lacking a spectrograph, ProtoDESI monitored the output of the fibers using a Fiber Photometry Camera mounted on the prime focus instrument. ProtoDESI was successful in acquiring targets with the robotically positioned fibers and demonstrated that the DESI guiding requirements can be met.Comment: Accepted versio

The surprising Far-UV spectrum of the polar BY Camelopardalis

We report on the first far-UV observations of the asynchronous polar BY Cam made by the Far-Ultraviolet Spectroscopic Explorer (FUSE). The source is known to exhibit the most extreme NV/CIV emission resonance line ratio observed among polars. The FUSE observations reveal a OVI resonance line weaker than in the prototype of polars, AM Her, with the absence of a detectable narrow component. The OVI broad line is detected with an equivalent width of the same order as in AM Her, the blueward doublet component is clearly present but the redward component is strongly affected by H2 absorption. The presence of a strong NIII line and weak CIII lines also confirms the peculiar CNO line flux. We compare the resonance CNO line intensities with the predictions of the CLOUDY plasma code coupled to a geometrical model of the accretion column. Varying the temperature and/or intensity of the ionising spectrum is unable to reproduce the observed broad line ratios. A solution is obtained by significantly altering the element abundances with a strong depletion of C, overabundance of N and a weak underabundance of O. This confirms previous suggestions of non-solar abundances which may result from redistribution in the accreted material following nova outbursts and/or the secondary nuclear evolution. A very significant H2 absorption is observed in front of the source, a possible indication for either the existence of a dense interstellar cloud or of circumstellar material.Comment: 6 pages, 4 Postscript figures, accepted by Astronomy and Astrophysics, uses aa.st