Circular Coloring of Random Graphs: Statistical Physics Investigation

Circular coloring is a constraints satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study circular coloring of random graphs using the cavity method. We identify two very interesting properties of this problem. For sufficiently many color and sufficiently low temperature there is a spontaneous breaking of the circular symmetry between colors and a phase transition forwards a ferromagnet-like phase. Our second main result concerns 5-circular coloring of random 3-regular graphs. While this case is found colorable, we conclude that the description via one-step replica symmetry breaking is not sufficient. We observe that simulated annealing is very efficient to find proper colorings for this case. The 5-circular coloring of 3-regular random graphs thus provides a first known example of a problem where the ground state energy is known to be exactly zero yet the space of solutions probably requires a full-step replica symmetry breaking treatment.Comment: 19 pages, 8 figures, 3 table

Quantized superfluid vortex dynamics on cylindrical surfaces and planar annuli

Superfluid vortex dynamics on an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference, the simplest being $\pm \hbar/(2MR)$, with $M$ the mass of the superfluid particles and $R$ the radius of the cylinder. A generalization to a finite cylinder automatically includes these quantum-mechanical effects through the pairing of the single vortex and its image in either the top or bottom end of the surface. The dynamics of a single vortex on this surface provides a hydrodynamic analog of Laughlin pumping. The interaction energy for two vortices on an infinite cylinder is proportional to the classical stream function $\chi({\bf r}_{12})$, and it crosses over from logarithmic to linear when the intervortex separation ${\bf r}_{12}$ becomes larger than the cylinder radius. An Appendix summarizes the connection to an earlier study of Ho and Huang for one or more vortices on an infinite cylinder. A second Appendix reviews the topologically equivalent planar annulus, where such quantized vortex motion has no offset, but Laughlin pumping may be more accessible to experimental observation.Comment: 16 pages, 7 figures; published version, with thoroughly revised Appendice

Using Spectral Analysis Techniques to Identify Characteristic Scales in Digital Elevation Models

Meandering river floodplains exhibit periodic structures which can be seen in features such as meander bends, point bars, and oxbow lakes. To improve our understanding and better analyze floodplain landscapes created by the dynamics of meandering rivers, characteristic scales need to be identified. Although methods that involve manual measurements of certain floodplain features are of utility, they are limited in their application and are typically very time intensive. Spectral analysis techniques represent an improved approach. For this research, two separate 2D spectral analysis techniques were used: the Fourier transform and the continuous wavelet transform. By using an appropriate theoretical red-noise background spectrum for the landscape, the spectral analysis techniques could provide a power spectrum which is then used to clearly identify the global and local characteristic scales. The results from the analysis of synthetic test images demonstrated such capability of both methodologies, and indicated that both performed similarly although the wavelet transform provides spatial information in addition to scale. The methodologies were then applied to simulated meandering river floodplain of meandering river where two ranges of characteristic scales were identified that corresponded to bend-scale and meander-train scale features. The characteristic meander-scale features also correlated with the surface metrics focal mean, the average elevation within a given area, and rugosity, the ratio between surface area of a given area and the surface area of a completely flat surface. The results show that the spectral analysis techniques can identify characteristic scale of a meander-river floodplain and that the relationship to the surface metrics indicate that it provides information to the topographic structure of the floodplain

Bose polarons at finite temperature and strong coupling

A mobile impurity coupled to a weakly interacting Bose gas, a Bose polaron, displays several interesting effects. While a single attractive quasiparticle is known to exist at zero temperature, we show here that the spectrum splits into two quasiparticles at finite temperatures for sufficiently strong impurity-boson interaction. The ground state quasiparticle has minimum energy at Tc, the critical temperature for Bose-Einstein condensation, and it becomes overdamped when T»Tc. The quasiparticle with higher energy instead exists only below Tc, since it is a strong mixture of the impurity with thermally excited collective Bogoliubov modes. This phenomenology is not restricted to ultracold gases, but should occur whenever a mobile impurity is coupled to a medium featuring a gapless bosonic mode with a large population for finite temperature.Peer ReviewedPostprint (author's final draft

Testing evolutionary tracks of Pre-Main Sequence stars: the case of HD113449

Evolutionary tracks are of key importance for the understanding of star formation. Unfortunately, tracks published by various groups differ so that it is fundamental to have observational tests. In order to do this, we intend to measure the masses of the two components of the Pre-Main Sequence binary HD113449 by combining radial velocity measurements taken with HARPS, with infrared interferometric data using AMBER on the VLTI. The spectroscopic orbit that has already been determined, combined with the first AMBER measurement, allows us to obtain a very first estimation of the inclination of the binary system and from this the masses of the two stars. More AMBER measurements of HD 113449 are needed to improve the precision on the masses: in the ESO period P82 two new measurements are scheduled.Comment: 4 pages, 3 figures; to appear in proceedings of Cool Star 15 conference, St.Andrews 200

Radiometric Assessment of ICESat-2 over Vegetated Surfaces

The ice, cloud, and land elevation satellite-2 (ICESat-2) is providing global elevation measurements to the science community. ICESat-2 measures the height of the Earth’s surface using a photon counting laser altimeter, ATLAS (advanced topographic laser altimetry system). As a photon counting system, the number of reflected photons per shot, or radiometry, is a function primarily of the transmitted laser energy, solar elevation, surface reflectance, and atmospheric scattering and attenuation. In this paper, we explore the relationship between detected scattering and attenuation in the atmosphere against the observed radiometry for three general forest types, as well as the radiometry as a function of day versus night. Through this analysis, we found that ATLAS strong beam radiometry exceeds the pre-launch design cases for boreal and tropical forests but underestimates the predicted radiometry over temperate forests by approximately half a photon. The weak beams, in contrast, exceed all pre-launch conditions by a factor of two to six over all forest types. We also observe that the signal radiometry from day acquisitions is lower than night acquisitions by 10% and 40% for the strong and weak beams, respectively. This research also found that the detection ratio between each beam-pair was lower than the predicted 4:1 values. This research also presents the concept of ICESat-2 radiometric profiles; these profiles provide a path for calculating vegetation structure. The results from this study are intended to be informative and perhaps serve as a benchmark for filtering or analysis of the ATL08 data products over vegetated surfaces

Life cycle assessment of carbon concrete composites: a circular economy path beyond climate mitigation?

Sustainable construction and materials play an ever-important role to stay within our planetary boundaries. In support, innovative carbon concrete composites (CCC) promise significant raw material savings by integral design. We aim to illustrate current environmental hotspots and a feasible recycling scenario of CCC that meets circularity requirements. We modelled a cradle-to-grave life cycle assessment for two potential building structural applications (sandwich wall, ceiling reinforcement) made of CCC. We based our recycling scenario on previously conducted large-scale experiments. Results show a relative larger energy intensity and abiotic depletion of fossil fuels for variants of CCC but lower global warming. Yet, recycling is, second to embodied emissions of basic materials, the driving force of total environmental impacts. The presented recycling path (demolition, pyrolysis for carbon fabric, reuse in fiber fleece) offers less "green credentials" than steel