Two and three electrons in a quantum dot: 1/|J| - expansion

We consider systems of two and three electrons in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the electron plane of motion. We show that the energy levels corresponding to states with high angular momentum, J, and a low number of vibrational quanta may be systematically computed as power series in 1/|J|. These states are relevant in the high-B limit.Comment: LaTeX, 15 pages,6 postscript figure

Understanding the Radio Emission from ϵ\epsilon Eridani

Some solar-type stars are known to present faint, time-variable radio continuum emission whose nature is not clearly established. We report on Jansky Very Large Array observations of the nearby star $\epsilon$ Eridani at 10.0 and 33.0 GHz. We find that this star has flux density variations on scales down to days, hours and minutes. On 2020 Apr 15 it exhibited a radio pulse at 10.0 GHz with a total duration of about 20 minutes and a peak four times larger than the plateau of 40 $\mu$Jy present in that epoch. We were able to model the time behavior of this radio pulse in terms of the radiation from shocks ramming into the stellar wind. Such shocks can be produced by the wind interaction of violently expanding gas heated suddenly by energetic electrons from a stellar flare, similar to the observed solar flares. Because of the large temperature needed in the working surface to produce the observed emission, this has to be non thermal. It could be gyrosynchrotron or synchrotron emission. Unfortunately, the spectral index or polarization measurements from the radio pulse do not have enough signal-to-noise ratio to determine its nature.Comment: 7 pages, 4 figures. To appear in Astronomy & Astrophysic

Towards On-Chip Self-Referenced Frequency-Comb Sources Based on Semiconductor Mode-Locked Lasers.

Miniaturization of frequency-comb sources could open a host of potential applications in spectroscopy, biomedical monitoring, astronomy, microwave signal generation, and distribution of precise time or frequency across networks. This review article places emphasis on an architecture with a semiconductor mode-locked laser at the heart of the system and subsequent supercontinuum generation and carrier-envelope offset detection and stabilization in nonlinear integrated optics

Molecular cloud evolution. I. Molecular cloud and thin CNM sheet formation

We discuss molecular cloud formation by large-scale supersonic compressions in the diffuse warm neutral medium (WNM). Initially, a shocked layer forms, and within it, a thin cold layer. An analytical model and high-resolution 1D simulations predict the thermodynamic conditions in the cold layer. After $\sim 1$ Myr of evolution, the layer has column density \sim 2.5 \times 10^{19} \psc, thickness $\sim 0.03$ pc, temperature $\sim 25$ K and pressure $\sim 6650$ K \pcc. These conditions are strongly reminiscent of those recently reported by Heiles and coworkers for cold neutral medium sheets. In the 1D simulations, the inflows into the sheets produce line profiles with a central line of width \sim 0.5 \kms and broad wings of width \sim 1 \kms. 3D numerical simulations show that the cold layer develops turbulent motions and increases its thickness, until it becomes a fully three-dimensional turbulent cloud. Fully developed turbulence arises on times ranging from $\sim 7.5$ Myr for inflow Mach number \Mr = 2.4 to $> 80$ Myr for \Mr = 1.03. These numbers should be considered upper limits. The highest-density turbulent gas (HDG, n > 100 \pcc) is always overpressured with respect to the mean WNM pressure by factors 1.5--4, even though we do not include self-gravity. The intermediate-density gas (IDG, $10 < n [{\rm cm}^ {-3}] < 100$) has a significant pressure scatter that increases with \Mr, so that at \Mr = 2.4, a significant fraction of the IDG is at a higher pressure than the HDG. Our results suggest that the turbulence and at least part of the excess pressure in molecular clouds can be generated by the compressive process that forms the clouds themselves, and that thin CNM sheets may be formed transiently by this mechanism, when the compressions are only weakly supersonic.Comment: Accepted for publication in ApJ. For correct display of the tables, download the postscript version. Animations can be downloaded from http://www.astrosmo.unam.mx/~e.vazquez/turbulence/movies.htm

Few-anyon systems in a parabolic dot

The energy levels of two and three anyons in a two-dimensional parabolic quantum dot and a perpendicular magnetic field are computed as power series in 1/|J|, where J is the angular momentum. The particles interact repulsively through a coulombic (1/r) potential. In the two-anyon problem, the reached accuracy is better than one part in 10^5. For three anyons, we study the combined effects of anyon statistics and coulomb repulsion in the ``linear'' anyonic states.Comment: LaTeX, 6 pages, 4 postscript figure

Clustering Improves the Goemans–Williamson Approximation for the Max-Cut Problem

MAX−CUT is one of the well-studied NP-hard combinatorial optimization problems. It can be formulated as an Integer Quadratic Programming problem and admits a simple relaxation obtained by replacing the integer “spin” variables xi by unitary vectors v⃗ i. The Goemans–Williamson rounding algorithm assigns the solution vectors of the relaxed quadratic program to a corresponding integer spin depending on the sign of the scalar product v⃗ i⋅r⃗ with a random vector r⃗ . Here, we investigate whether better graph cuts can be obtained by instead using a more sophisticated clustering algorithm. We answer this question affirmatively. Different initializations of k-means and k-medoids clustering produce better cuts for the graph instances of the most well known benchmark for MAX−CUT. In particular, we found a strong correlation of cluster quality and cut weights during the evolution of the clustering algorithms. Finally, since in general the maximal cut weight of a graph is not known beforehand, we derived instance-specific lower bounds for the approximation ratio, which give information of how close a solution is to the global optima for a particular instance. For the graphs in our benchmark, the instance specific lower bounds significantly exceed the Goemans–Williamson guarantee

Portability vs. Precedent: IMUs vs. 3D Motion Capture for Collecting Kinematic Data in Dancers

The emergence of portable kinematic data collection systems (Inertial Measurement Units - IMUs) have become a potential alternative to 3D video motion capture systems for real-world application. However, there remains little research on the application of IMU technology for the evaluation of dancers’ biomechanical movement. PURPOSE: To assess the validity of the Noraxon IMU system compared with the Cortex 3D video motion capture system for kinematic data collection during a sauté. METHODS: 10 healthy, advanced female dancers were equipped with both a Noraxon IMU (200Hz) system and reflective markers used with a 12-camera Motion Analysis system (Cortex, 250 Hz) for simultaneous data collection. Participants completed an independent After a 10-minute warmup, each participant performed one trial of 10 stationary sautés while barefoot, with feet in second position and arms in fifth position in time with music at 95 bpm. The middle 5 jumps of each participant’s trial were processed and analyzed with Visual3D and MATLAB for the Cortex data, and through Noraxon’s reporting system for the Noraxon data. All results were compared through SPSS with repeated-measures ANOVAs. RESULTS: A main effect of measurement system was found for peak joint angles in the sagittal ((6,4)=0.009, p \u3c 0.001), frontal ((9,1)=0.12, p \u3c 0.001), and transverse ((9,1)=0.009, p \u3c 0.001) planes. Pairwise comparisons revealed significant differences in peak hip flexion, hip extension, knee flexion, knee extension, ankle plantar flexion, ankle dorsiflexion, hip adduction, knee adduction, ankle inversion, hip internal rotation, hip external rotation, knee internal rotation, knee external rotation, and ankle internal rotation. No significant main effect was found between measurement systems for sagittal, frontal, and transverse plane joint excursions ((9,1)=0.12, p=0.253). CONCLUSION: Significant differences in most peak joint angles indicate that Noraxon IMUs do not have strong validity for capturing absolute joint angles compared to 3D video motion capture. However, joint excursion measurements were similar, indicating that Noraxon IMUs may be valid for measuring the total amount of motion during a particular movement. Additional analysis is warranted for further understanding of this technology