Surface Curvature Effects on Reflectance from Translucent Materials

Most of the physically based techniques for rendering translucent objects use the diffusion theory of light scattering in turbid media. The widely used dipole diffusion model (Jensen et al. 2001) applies the diffusion-theory formula derived for a planar interface to objects of arbitrary shapes. This paper presents first results of our investigation of how surface curvature affects the diffuse reflectance from translucent materials.Comment: 10 pages, 2 figures. The first version of this paper was published in the Communication Papers Proceedings of 18th International Conference on Computer Graphics, Visualization and Computer Vision 2010 - WSCG201

Extensions of differential representations of SL(2) and tori

Linear differential algebraic groups (LDAGs) measure differential algebraic dependencies among solutions of linear differential and difference equations with parameters, for which LDAGs are Galois groups. The differential representation theory is a key to developing algorithms computing these groups. In the rational representation theory of algebraic groups, one starts with SL(2) and tori to develop the rest of the theory. In this paper, we give an explicit description of differential representations of tori and differential extensions of irreducible representation of SL(2). In these extensions, the two irreducible representations can be non-isomorphic. This is in contrast to differential representations of tori, which turn out to be direct sums of isotypic representations.Comment: 21 pages; few misprints corrected; Lemma 4.6 adde

Mapping extragalactic dark matter structures through gamma-rays

If dark matter is composed of neutralinos, the gamma-ray radiation produced in their annihilation offers an attractive possibility for dark matter detection. This process may contribute significantly to the extragalactic gamma-ray background (EGB) radiation, which is being measured by the FERMI satellite with unprecedented sensitivity. Using the high-resolution Millennium-II simulation of cosmic structure formation we have produced the first full-sky maps of the expected contribution of dark matter annihilation to the EGB radiation. Our maps include a proper normalization of the signal according to a specific supersymmetric model based on minimal supergravity. The new simulated maps allow a study of the angular power spectrum of the gamma-ray background from dark matter annihilation, which has distinctive features associated with the nature of the annihilation process. Our results are in broad agreement with analytic models for the gamma-ray background, but they also include higher-order correlations not readily accessible in analytic calculations and, in addition, provide detailed spectral information for each pixel. In particular, we find that color maps combining different energies can reveal the cosmic large-scale structure at low and intermediate redshifts.Comment: 7 pages, 5 figures, 2009 Fermi Symposium, eConf Proceedings C09112

Dynamical Friction and Galaxy Merging Timescales

The timescale for galaxies within merging dark matter halos to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging timescales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies, and the statistical properties of satellite galaxies within dark matter halos. In this paper, we study the merging timescales of extended dark matter halos using N-body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging timescales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for $M_sat/M_host \approx 0.1$ and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of $\sim 3.3$ for $M_sat/M_host\approx 0.01$. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the timescale for an extended satellite to sink from the virial radius of a host halo down to the halo's center for a wide range of $M_sat/M_host$ and orbits. Including a central bulge in each galaxy changes the merging timescale by \la 10%. To highlight one concrete application of our results, we show that merging timescales often used in the literature overestimate the growth of stellar mass by satellite accretion by $\approx 40$, with the extra mass gained in low mass ratio mergers.Comment: 10 pages, 7 figures; MNRAS, in press. Minor revisions, including results from additional simulations with baryonic components; conclusions unchange

Dynamics of the Magellanic Clouds in a LCDM Universe

We examine Milky Way-Magellanic Cloud systems selected from the Millennium-II Simulation in order to place the orbits of the Magellanic Clouds in a cosmological context. Our analysis shows that satellites massive enough to be LMC analogs are typically accreted at late times. Moreover, those that are accreted at early times and survive to the present have orbital properties that are discrepant with those observed for the LMC. The high velocity of the LMC, coupled with the dearth of unbound orbits seen in the simulation, argues that the mass of the MW's halo is unlikely to be less than 2 x 10^12 Msun. This conclusion is further supported by statistics of halos hosting satellites with masses, velocities, and separations comparable to those of the LMC. We further show that: (1) LMC and SMC-mass objects are not particularly uncommon in MW-mass halos; (2) the apparently high angular momentum of the LMC is not cosmologically unusual; and (3) it is rare for a MW halo to host a LMC-SMC binary system at z=0, but high speed binary pairs accreted at late times are possible. Based on these results, we conclude that the LMC was accreted within the past four Gyr and is currently making its first pericentric passage about the MW.Comment: 14 pages, 13 figures; MNRAS, in press. Minor revisions, conclusions unchange