Density-equalizing maps for simply-connected open surfaces

In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings with different properties can be achieved. For instance, area-preserving parameterizations of simply-connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored

Acoustic Spectroscopy of Superfluid 3He in Aerogel

We have designed an experiment to study the role of global anisotropic quasiparticle scattering on the dirty aerogel superfluid 3He system. We observe significant regions of two stable phases at temperatures below the superfluid transition at a pressure of 25 bar for a 98% aerogel.Comment: 2 pages, 2 figures, accepted for publication in proceedings of Low Temperature Conference 2

Specific Heat of Disordered 3^{3}He

Porous aerogel is a source of elastic scattering in superfluid 3He and modifies the properties of the superfluid, suppressing the transition temperature and order parameter. The specific heat jumps for the B-phase of superfluid 3He in aerogel have been measured as a function of pressure and interpreted using the homogeneous and inhomogeneous isotropic scattering models. The specific heat jumps for other p-wave states are estimated for comparison.Comment: Manuscript prepared for LT 2

Consequences of Mechanical and Radiative Feedback from Black Holes in Disc Galaxy Mergers

We study the effect of AGN mechanical and radiation feedback on the formation of bulge dominated galaxies via mergers of disc galaxies. The merging galaxies have mass-ratios of 1:1 to 6:1 and include pre-existing hot gaseous halos to properly account for the global impact of AGN feedback. Using smoothed particle hydrodynamics simulation code (GADGET-3) we compare three models with different AGN feedback models: (1) no black hole and no AGN feedback; (2) thermal AGN feedback; and (3) mechanical and radiative AGN feedback. The last model is motivated by observations of broad line quasars which show winds with initial velocities of $v_w \ge$ 10,000 km/s and also heating associated with the central AGN X-ray radiation. The primary changes in gas properties due to mechanical AGN feedback are lower thermal X-ray luminosity from the final galaxy - in better agreement with observations - and galactic outflows with higher velocity $\sim 1000$ km/s similar to recent direct observations of nearby merger remnants. The kinetic energy of the outflowing gas is a factor of $\sim$ 20 higher than in the thermal feedback case. All merger remnants with momentum-based AGN feedback with $v_w \sim 10,000$ km/s and $\epsilon_w=2 \times 10^{-3}$, independent of their progenitor mass-ratios, reproduce the observed relations between stellar velocity dispersion and black hole mass ($M_{\rm bh} - \sigma$) as well as X-ray luminosity ($L_X - \sigma$) with $10^{37.5}$ erg/s $\lesssim L_X (0.3-8~{\rm keV}) \lesssim 10^{39.2}$ erg/s for velocity dispersions in the range of 120 km/s $\lesssim \sigma \lesssim$ 190 km/s. In addition, the mechanical feedback produces a much greater AGN variability. We also show that gas is more rapidly and impulsively stripped from the galactic centres driving a moderate increase in galaxy size and decrease in central density with the mechanical AGN feedback model.Comment: 16 pages, 10 figures, resubmitted to MNRA