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

Faraday waves on a viscoelastic liquid

We investigate Faraday waves on a viscoelastic liquid. Onset measurements and a nonlinear phase diagram for the selected patterns are presented. By virtue of the elasticity of the material a surface resonance synchronous to the external drive competes with the usual subharmonic Faraday instability. Close to the bicriticality the nonlinear wave interaction gives rise to a variety of novel surface states: Localised patches of hexagons, hexagonal superlattices, coexistence of hexagons and lines. Theoretical stability calculations and qualitative resonance arguments support the experimental observations.Comment: 4 pages, 4figure

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

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

Comparative run-time performance of evolutionary algorithms on multi-objective interpolated continuous optimisation problems.

We propose a new class of multi-objective benchmark problems on which we analyse the performance of four well established multi-objective evolutionary algorithms (MOEAs) – each implementing a different search paradigm – by comparing run-time convergence behaviour over a set of 1200 problem instances. The new benchmarks are created by fusing previously proposed single-objective interpolated continuous optimisation problems (ICOPs) via a common set of Pareto non-dominated seeds. They thus inherit the ICOP property of having tunable fitness landscape features. The benchmarks are of intrinsic interest as they derive from interpolation methods and so can approximate general problem instances. This property is revealed to be of particular importance as our extensive set of numerical experiments indicates that choices pertaining to (i) the weighting of the inverse distance interpolation function and (ii) the problem dimension can be used to construct problems that are challenging to all tested multi-objective search paradigms. This in turn means that the new multi-objective ICOPs problems (MO-ICOPs) can be used to construct well-balanced benchmark sets that discriminate well between the run-time convergence behaviour of different solvers

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

Intracoronary Brachytherapy, a Promising Treatment Option for Diabetic Patients: Results from a European Multicenter Registry (RENO)

Despite advances in the interventional treatment of coronary disease, diabetics still have double the case fatality rate as nondiabetics. The purpose of this an

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

Precision alignment and integration of DESI's focal plane using a laser tracker

The recently commissioned Dark Energy Spectroscopic Instrument (DESI) will measure the expansion history of the Universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasars over 14000 sq deg will be measured during the life of the experiment. A new prime focus corrector for the KPNO Mayall telescope delivers light to 5000 fiber optic positioners. The fibers in turn feed ten broad-band spectrographs. We describe the use of a Faro Laser Tracker with custom hardware and software tools for alignment during integration of DESI’s focal plane. The focal plane is approximately one meter in diameter and consists primarily of ten radially symmetrical focal plane segments (“petals”) which were individually installed into the telescope. The nominal clearance between petals is 600 microns, and an alignment accuracy of 100 microns and 0.01 degrees was targeted. Alignment of the petals to their targeted locations on the telescope was accomplished by adjusting a purpose-built alignment structure with 14 degrees of freedom using feedback from the laser tracker, which measured the locations of retroreflectors attached to both the petal and the telescope and whose positions relative to key features were precisely known. These measurements were used to infer the locations of aligning features in both structures, which were in turn used to calculate the adjustments necessary to bring the system into alignment. Once alignment was achieved to within acceptable tolerances, each petal was installed while monitoring building movement due to wind and thermal variations