Stability of Periodic, Traveling-Wave Solutions to the Capillary-Whitham Equation

Recently, the Whitham and capillary-Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions to both and study their stability. We present plots of a representative sampling of solutions for a range of wavelengths, wave speeds, wave heights, and surface tension values. Finally, we discuss the role these parameters play in the stability of the solutions

A Comparison of Frequency Downshift Models of Wave Trains on Deep Water

Frequency downshift (FD) in wave trains on deep water occurs when a measure of the frequency, typically the spectral peak or the spectral mean, decreases as the waves travel down a tank or across the ocean. Many FD models rely on wind or wave breaking. We consider seven models that do not include these effects and compare their predictions with four sets of experiments that also do not include these effects. The models are the (i) nonlinear Schr\"odinger equation (NLS), (ii) dissipative NLS equation (dNLS), (iii) Dysthe equation, (iv) viscous Dysthe equation (vDysthe), (v) Gordon equation (Gordon) (which has a free parameter), (vi) Islas-Schober equation (IS) (which has a free parameter), and (vii) a new model, the dissipative Gramstad-Trulsen (dGT) equation. The dGT equation has no free parameters and addresses some of the difficulties associated with the Dysthe and vDysthe equations. We compare a measure of overall error and the evolution of the spectral amplitudes, mean, and peak. We find: (i) The NLS and Dysthe equations do not accurately predict the measured spectral amplitudes. (ii) The Gordon equation, which is a successful model of FD in optics, does not accurately model FD in water waves, regardless of the choice of free parameter. (iii) The dNLS, vDysthe, dGT, and IS (with optimized free parameter) models all do a reasonable job predicting the measured spectral amplitudes, but none captures all spectral evolutions. (iv) The vDysthe, dGT, and IS (with optimized free parameter) models do the best at predicting the observed evolution of the spectral peak and the spectral mean. (v) The IS model, optimized over its free parameter, has the smallest overall error for three of the four experiments. The vDysthe equation has the smallest overall error in the other experiment

Markerless View Independent Gait Analysis with Self-camera Calibration

We present a new method for viewpoint independent markerless gait analysis. The system uses a single camera, does not require camera calibration and works with a wide range of directions of walking. These properties make the proposed method particularly suitable for identification by gait, where the advantages of completely unobtrusiveness, remoteness and covertness of the biometric system preclude the availability of camera information and use of marker based technology. Tests on more than 200 video sequences with subjects walking freely along different walking directions have been performed. The obtained results show that markerless gait analysis can be achieved without any knowledge of internal or external camera parameters and that the obtained data that can be used for gait biometrics purposes. The performance of the proposed method is particularly encouraging for its appliance in surveillance scenarios

Observation of a possible superflare on Proxima Centauri

We report the observation on UT 2017 July 1 of an unusually powerful flare detected in near-infrared continuum photometry of Proxima Centauri. During a campaign monitoring the star for possible exoplanet transits, we identified an increase in Sloan i' flux leading to an observed peak at BJD 2457935.996 that was at least 10 per cent over pre-flare flux in this band. It was followed by a two-component rapid decline in the first 100 s that became a slower exponential decay with time constant of 1350 s. A smaller flare event 1300 s after the first added an incremental peak flux increase of 1 per cent of pre-flare flux. Since the onset of the flare was not fully time resolved at a cadence of 62 s, its actual peak value is unknown but greater than the time average over a single exposure of 20 s. The i' band is representative of broad optical and near-IR continuum flux over which the integrated energy of the flare is 100 times the stellar luminosity. This meets the criteria that established the concept of superflares on similar stars. The resulting implied ultraviolet flux and space weather could have had an extreme effect on the atmospheres of planets within the star's otherwise habitable zone

The Origin of the Brightest Cluster Galaxies

Most clusters and groups of galaxies contain a giant elliptical galaxy in their centres which far outshines and outweighs normal ellipticals. The origin of these brightest cluster galaxies is intimately related to the collapse and formation of the cluster. Using an N-body simulation of a cluster of galaxies in a hierarchical cosmological model, we show that galaxy merging naturally produces a massive, central galaxy with surface brightness and velocity dispersion profiles similar to observed BCG's. To enhance the resolution of the simulation, 100 dark halos at $z=2$ are replaced with self-consistent disk+bulge+halo galaxy models following a Tully-Fisher relation using 100000 particles for the 20 largest galaxies and 10000 particles for the remaining ones. This technique allows us to analyze the stellar and dark matter components independently. The central galaxy forms through the merger of several massive galaxies along a filament early in the cluster's history. Galactic cannibalism of smaller galaxies through dynamical friction over a Hubble time only accounts for a small fraction of the accreted mass. The galaxy is a flattened, triaxial object whose long axis aligns with the primordial filament and the long axis of the cluster galaxy distribution agreeing with observed trends for galaxy-cluster alignment.Comment: Revised and accepted in ApJ, 25 pages, 10 figures, online version available at http://www.cita.utoronto.ca/~dubinski/bcg

Color Transformations for the 2MASS Second Incremental Data Release

Transformation equations are presented to convert colors and magnitudes measured in the AAO, ARNICA, CIT, DENIS, ESO, LCO (Persson standards), MSSSO, SAAO, and UKIRT photometric systems to the photometric system inherent to the 2MASS Second Incremental Data Release. The transformations have been derived by comparing 2MASS photometry with published magnitudes and colors for stars observed in these systems. Transformation equations have also been derived indirectly for the Bessell & Brett (1988) and Koornneef (1983) homogenized photometric systems.Comment: To appear in AJ, May 200