Size growth of red-sequence early-type galaxies in clusters in the last 10 Gyr

We carried out a photometric and structural analysis in the rest-frame $V$ band of a mass-selected ($\log M/M_\odot >10.7$) sample of red-sequence galaxies in 14 galaxy clusters, 6 of which are at $z>1.45$. To this end, we reduced/analyzed about 300 orbits of multicolor images taken with the Advanced Camera for Survey and the Wide Field Camera 3 on the Hubble Space Telescope. We uniformly morphologically classified galaxies from $z=0.023$ to $z=1.803$, and we homogeneously derived sizes (effective radii) for the entire sample. Furthermore, our size derivation allows, and therefore is not biased by, the presence of the usual variety of morphological structures seen in early-type galaxies, such as bulges, bars, disks, isophote twists, and ellipiticy gradients. By using such a mass-selected sample, composed of 244 red-sequence early-type galaxies, we find that the $\log$ of the galaxy size at a fixed stellar mass, $\log M/M_\odot= 11$ has increased with time at a rate of $0.023\pm0.002$ dex per Gyr over the last 10 Gyr, in marked contrast with the threefold increase found in the literature for galaxies in the general field over the same period. This suggests, at face value, that secular processes should be excluded as the primary drivers of size evolution because we observed an environmental environmental dependent size growth. Using spectroscopic ages of Coma early-type galaxies we also find that recently quenched early-type galaxies are a numerically minor population not different enough in size to alter the mean size at a given mass, which implies that the progenitor bias is minor, i.e., that the size evolution measured by selecting galaxies at the redshift of observation is indistinguishable from the one that compares ancestors and descendents.Comment: A&A 593, A2 (2016) after revision of the z=1.63 cluster name, mis-typed in previous version. No result of our paper is affected by having mis-typed the cluster nam

Improving Stochastic Estimator Techniques for Disconnected Diagrams

Disconnected diagrams are expected to be sensitive to the inclusion of dynamical fermions. We present a feasibility study for the observation of such effects on the nucleonic matrix elements of the axial vector current, using SESAM full QCD vacuum configurations with Wilson fermions on $16^3\times 32$ lattices, at $\beta =5.6$. Starting from the standard methods developed by the Kentucky and Tsukuba groups, we investigate the improvement from various refinements thereof.Comment: One author added. Contribution to Lattice 1997, 3 pages LaTex, to appear in Nucl. Phys. B (Proc. Suppl.

Touching the invisible: Localizing ultrasonic haptic cues

While mid-air gestures offer new possibilities to interact with or around devices, some situations, such as interacting with applications, playing games or navigating, may require visual attention to be focused on a main task. Ultrasonic haptic feedback can provide 3D spatial haptic cues that do not demand visual attention for these contexts. In this paper, we present an initial study of active exploration of ultrasonic haptic virtual points that investigates the spatial localization with and without the use of the visual modality. Our results show that, when providing haptic feedback giving the location of a widget, users perform 50% more accurately compared to providing visual feedback alone. When provided with a haptic location of a widget alone, users are more than 30% more accurate than when given a visual location. When aware of the location of the haptic feedback, active exploration decreased the minimum recommended widget size from 2cm2 to 1cm2 when compared to passive exploration from previous studies. Our results will allow designers to create better mid-air interactions using this new form of haptic feedback

Orbital Decay of the PSR J0045-7319/B Star Binary System: Age of Radio Pulsar and Initial Spin of Neutron Star

Recent timing observations of PSR J0045-7319 reveal that the neutron star/B star binary orbit is decaying on a time scale of |\Porb/\dot\Porb|=0.5 Myr, shorter than the characteristic age ($\tau_c=3$ Myr) of the pulsar (Kaspi et al.~1996a). We study mechanisms for the orbital decay. The standard weak friction theory based on static tide requires far too short a viscous time to explain the observed \dot\Porb. We show that dynamical tidal excitation of g-modes in the B star can be responsible for the orbital decay. However, to explain the observed short decay timescale, the B star must have some significant retrograde rotation with respect to the orbit --- The retrograde rotation brings lower-order g-modes, which couple much more strongly to the tidal potential, into closer ``resonances'' with the orbital motion, thus significantly enhancing the dynamical tide. A much less likely possibility is that the g-mode damping time is much shorter than the ordinary radiative damping time. The observed orbital decay timescale combined with a generic orbital evolution model based on dynamical tide can be used as a ``timer'', giving an upper limit of $1.4$ Myr for the age of the binary system since the neutron star formation. Thus the characteristic age of the pulsar is not a good age indicator. Assuming standard magnetic dipole braking for the pulsar and no significant magnetic field decay on a timescale \lo 1 Myr, the upper limit for the age implies that the initial spin of the neutron star at birth was close to its current value.Comment: AASTeX, 9 pages, 3 ps figures. ApJ Letters, in pres

Ramanujan's "Lost Notebook" and the Virasoro Algebra

By using the theory of vertex operator algebras, we gave a new proof of the famous Ramanujan's modulus 5 modular equation from his "Lost Notebook" (p.139 in \cite{R}). Furthermore, we obtained an infinite list of $q$-identities for all odd moduli; thus, we generalized the result of Ramanujan.Comment: To appear in Comm. Math. Phy

Spontaneous symmetry breaking in a nonlinear double-well structure

We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta-functions, a fully analytical solution is obtained for symmetric, antisymmetric and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on both direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta-functions. In the general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.Comment: submitted to Physical Review