Invariant expectations and vanishing of bounded cohomology for exact groups

We study exactness of groups and establish a characterization of exact groups in terms of the existence of a continuous linear operator, called an invariant expectation, whose properties make it a weak counterpart of an invariant mean on a group. We apply this operator to show that exactness of a finitely generated group $G$ implies the vanishing of the bounded cohomology of $G$ with coefficients in a new class of modules, which are defined using the Hopf algebra structure of $\ell_1(G)$.Comment: Final version, to appear in the Journal of Topology and Analysi

Flightweight radiantly and actively cooled panel: Thermal and structural performance

A 2- by 4-ft flightweight panel was subjected to thermal/structural tests representative of design flight conditions for a Mach 6.7 transport and to off-design conditions simulating flight maneuvers and cooling system failures. The panel utilized Rene 41 heat shields backed by a thin layer of insulation to radiate away most of the 12 Btu/ft2-sec incident heating. A solution of ethylene glycol in water circulating through tubes in an aluminum-honeycomb-sandwich panel absorbed the remainder of the incident heating (0.8 Btu/sq ft-sec). The panel successfully withstood (1) 46.7 hr of radiant heating which included 53 thermal cycles and 5000 cycles of uniaxial inplane loading of + or - 1200 lfb/in; (2) simulated 2g-maneuver heating conditions and simulated cooling system failures without excessive temperatures on the structural panel; and (3) the extensive thermal/structural tests and the aerothermal tests reported in NASA TP-1595 without significant damage to the structural panel, coolant leaks, or hot-gas ingress to the structural panel

Creep motion of a domain wall in the two-dimensional random-field Ising model with a driving field

With Monte Carlo simulations, we study the creep motion of a domain wall in the two-dimensional random-field Ising model with a driving field. We observe the nonlinear fieldvelocity relation, and determine the creep exponent {\mu}. To further investigate the universality class of the creep motion, we also measure the roughness exponent {\zeta} and energy barrier exponent {\psi} from the zero-field relaxation process. We find that all the exponents depend on the strength of disorder.Comment: 5 pages, 4 figure

Relaxation-to-creep transition of domain-wall motion in two- dimensional random-field Ising model with ac driving field

With Monte Carlo simulations, we investigate the relaxation dynamics with a domain wall for magnetic systems at the critical temperature. The dynamic scaling behavior is carefully analyzed, and a dynamic roughening process is observed. For comparison, similar analysis is applied to the relaxation dynamics with a free or disordered surfaceComment: 5 pages, 5 figure

Laser induced magnetization switching in films with perpendicular anisotropy: a comparison between measurements and a multi-macrospin model

Thermally-assisted ultra-fast magnetization reversal in a DC magnetic field for magnetic multilayer thin films with perpendicular anisotropy has been investigated in the time domain using femtosecond laser heating. The experiment is set-up as an optically pumped stroboscopic Time Resolved Magneto-Optical Kerr Effect magnetometer. It is observed that a modest laser fluence of about 0.3 mJ/square-cm induces switching of the magnetization in an applied field much less than the DC coercivity (0.8 T) on the sub-nanosecond time-scale. This switching was thermally-assisted by the energy from the femtosecond pump-pulse. The experimental results are compared with a model based on the Landau Lifschitz Bloch equation. The comparison supports a description of the reversal process as an ultra-fast demagnetization and partial recovery followed by slower thermally activated switching due to the spin system remaining at an elevated temperature after the heating pulse.Comment: 8 pages, 10 figures, to be submitted to PR

Universality class of the depinning transition in the two-dimensional Ising model with quenched disorder

With Monte Carlo methods, we investigate the universality class of the depinning transition in the two-dimensional Ising model with quenched random fields. Based on the short-time dynamic approach, we accurately determine the depinning transition field and both static and dynamic critical exponents. The critical exponents vary significantly with the form and strength of the random fields, but exhibit independence on the updating schemes of the Monte Carlo algorithm. From the roughness exponents $\zeta, \zeta_{loc}$ and $\zeta_s$, one may judge that the depinning transition of the random-field Ising model belongs to the new dynamic universality class with $\zeta \neq \zeta_{loc}\neq \zeta_s$ and $\zeta_{loc} \neq 1$. The crossover from the second-order phase transition to the first-order one is observed for the uniform distribution of the random fields, but it is not present for the Gaussian distribution.Comment: 16 pages, 16 figures, 3 table

Depleted Galaxy Cores and Dynamical Black Hole Masses

Shallow cores in bright, massive galaxies are commonly thought to be the result of scouring of stars by mergers of binary supermassive black holes. Past investigations have suggested correlations between the central black hole mass and the stellar light or mass deficit in the core, using proxy measurements of $M_{\rm BH}$ or stellar mass-to-light ratios ($\Upsilon$). Drawing on a wealth of dynamical models which provide both $M_{\rm BH}$ and $\Upsilon$, we identify cores in 23 galaxies, of which 20 have direct, reliable measurements of $M_{\rm BH}$ and dynamical stellar mass-to-light ratios ($\Upsilon_{\star,{\rm dyn}}$). These cores are identified and measured using Core-S\'ersic model fits to surface brightness profiles which extend out to large radii (typically more than the effective radius of the galaxy); for approximately one fourth of the galaxies, the best fit includes an outer (\sersic) envelope component. We find that the core radius is most strongly correlated with the black hole mass and that it correlates better with total galaxy luminosity than it does with velocity dispersion. The strong core-size-- $M_{\rm BH}$ correlation enables estimation of black hole masses (in core galaxies) with an accuracy comparable to the $M_{\rm BH}$--$\sigma$ relation (rms scatter of 0.30 dex in $\log M_{\rm BH}$), without the need for spectroscopy. The light and mass deficits correlate more strongly with galaxy velocity dispersion than they do with black hole mass. Stellar mass deficits span a range of 0.2--39 \mbh, with almost all (87%) being $< 10 \, M_{\rm BH}$; the median value is 2.2 $M_{\rm BH}$.Comment: Proof-corrected version, AJ, 146, 160, http://stacks.iop.org/1538-3881/146/16

The supermassive black hole in NGC4486a detected with SINFONI at the VLT

The near-infrared integral field spectrograph SINFONI at the ESO VLT opens a new window for the study of central supermassive black holes. With a near-IR spatial resolution similar to HST optical and the ability to penetrate dust it provides the possibility to explore the low-mass end of the M-sigma relation (sigma<120km/s) where so far very few black hole masses were measured with stellar dynamics. With SINFONI we observed the central region of the low-luminosity elliptical galaxy NGC4486a at a spatial resolution of ~0.1arcsec in the K band. The stellar kinematics was measured with a maximum penalised likelihood method considering the region around the CO absorption band heads. We determined a black hole mass of M_BH=1.25^{+0.75}_{-0.79} x 10^7 M_sun (90% C.L.) using the Schwarzschild orbit superposition method including the full 2-dimensional spatial information. This mass agrees with the predictions of the M-sigma relation, strengthening its validity at the lower sigma end.Comment: 7 pages, 7 figures. Accepted by MNRA

Co-evolution of strategy and structure in complex networks with dynamical linking

Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. We provide analytic results for the limiting cases where linking dynamics is much faster than evolutionary dynamics and vice-versa, and show how the individual capacity of forming new links or severing inconvenient ones maps into the problem of strategy evolution in a well-mixed population under a different game. For intermediate ranges, we investigate numerically the detailed interplay determined by these two time-scales and show that the scope of validity of the analytical results extends to a much wider ratio of time scales than expected

Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

Based on the Hamiltonian equation of motion of the $\phi^4$ theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we numerically determine the transition field, and the static and dynamic critical exponents. The results show that the fundamental Hamiltonian equation of motion belongs to a universality class very different from those effective equations of motion.Comment: 6 pages, 7 figures, have been accept by EP