Geodesics in Heat

We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The method represents a significant breakthrough in the practical computation of distance on a wide variety of geometric domains, since the resulting linear systems can be prefactored once and subsequently solved in near-linear time. In practice, distance can be updated via the heat method an order of magnitude faster than with state-of-the-art methods while maintaining a comparable level of accuracy. We provide numerical evidence that the method converges to the exact geodesic distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where more regularity is required

Stability, Adsorption and Diffusion of CH4, CO2 and H2 in Clathrate Hydrates

We present a study of the adsorption and diffusion of CH4, CO2 and H2 molecules in clathrate hydrates using ab initio van der Waals density functional formalism [Dion et al. Phys. Rev. Lett. 92, 246401 (2004)]. We find that the adsorption energy is dominated by van der Waals interactions and that, without them, gas hydrates would not be stable. We calculate the maximum adsorption capacity as well as the maximum hydrocarbon size that can be adsorbed.The relaxation of the host lattice is essential for a good description of the diffusion activation energies, which are estimated to be of the order of 0.2, 0.4, and 1.0 eV for H2, CO2, and CH4, respectively.Comment: 4 pages, 4 figures, 3 table

Riparian trees and aridland streams of the southwestern United States: An assessment of the past, present, and future

Riparian ecosystems are vital components of aridlands within the southwestern United States. Historically, surface flows influenced population dynamics of native riparian trees. Many southwestern streams has been altered by regulation, however, and will be further affected by greenhouse warming. Our analysis of stream gage data revealed that decreases in volume of annual discharge and mean peak discharge and a shift to earlier peak discharge will occur in the Southern Rockies region of Colorado, New Mexico, and Utah. These changes will likely decrease rates of reproduction and survival of cottonwood (Populus fremontii and Populus deltoides ssp. wislizenii), Goodding\u27s willow (Salix gooddingii), and boxelder (Acer negundo), which rely on surface flows to stimulate germination and recharge groundwater aquifers. Streams in the Central Highlands of Arizona and New Mexico will likely see reductions in annual discharge volume, which could limit reproduction and survival of the above taxa and Arizona sycamore (Platanus wrightii). These effects may be exacerbated by demands of expanding urban areas and agricultural operations, but could also be ameliorated by increasing water use efficiency and environmental mitigation. These factors must be considered, along with climate projections, when planning for conservation of riparian trees and the animal communities they support

Riparian trees and aridland streams of the southwestern United States: An assessment of the past, present, and future

Riparian ecosystems are vital components of aridlands within the southwestern United States. Historically, surface flows influenced population dynamics of native riparian trees. Many southwestern streams has been altered by regulation, however, and will be further affected by greenhouse warming. Our analysis of stream gage data revealed that decreases in volume of annual discharge and mean peak discharge and a shift to earlier peak discharge will occur in the Southern Rockies region of Colorado, New Mexico, and Utah. These changes will likely decrease rates of reproduction and survival of cottonwood (Populus fremontii and Populus deltoides ssp. wislizenii), Goodding\u27s willow (Salix gooddingii), and boxelder (Acer negundo), which rely on surface flows to stimulate germination and recharge groundwater aquifers. Streams in the Central Highlands of Arizona and New Mexico will likely see reductions in annual discharge volume, which could limit reproduction and survival of the above taxa and Arizona sycamore (Platanus wrightii). These effects may be exacerbated by demands of expanding urban areas and agricultural operations, but could also be ameliorated by increasing water use efficiency and environmental mitigation. These factors must be considered, along with climate projections, when planning for conservation of riparian trees and the animal communities they support

Phantom energy from graded algebras

We construct a model of phantom energy using the graded Lie algebra SU(2/1). The negative kinetic energy of the phantom field emerges naturally from the graded Lie algebra, resulting in an equation of state with w<-1. The model also contains ordinary scalar fields and anti-commuting (Grassmann) vector fields which can be taken as two component dark matter. A potential term is generated for both the phantom fields and the ordinary scalar fields via a postulated condensate of the Grassmann vector fields. Since the phantom energy and dark matter arise from the same Lagrangian the phantom energy and dark matter of this model are coupled via the Grassman vector fields. In the model presented here phantom energy and dark matter come from a gauge principle rather than being introduced in an ad hoc manner.Comment: 8 pages no figures; references added and discussion on condensate of vector grassman fields added. To be published MPL

The Asymptotic Giant Branch and the Tip of the Red Giant Branch as Probes of Star Formation History: The Nearby Dwarf Irregular Galaxy KKH 98

We investigate the utility of the asymptotic giant branch (AGB) and the red giant branch (RGB) as probes of the star formation history (SFH) of the nearby (D=2.5 Mpc) dwarf irregular galaxy, KKH 98. Near-infrared (IR) Keck Laser Guide Star Adaptive Optics (AO) images resolve 592 IR bright stars reaching over 1 magnitude below the Tip of the Red Giant Branch. Significantly deeper optical (F475W and F814W) Hubble Space Telescope images of the same field contain over 2500 stars, reaching to the Red Clump and the Main Sequence turn-off for 0.5 Gyr old populations. Compared to the optical color magnitude diagram (CMD), the near-IR CMD shows significantly tighter AGB sequences, providing a good probe of the intermediate age (0.5 - 5 Gyr) populations. We match observed CMDs with stellar evolution models to recover the SFH of KKH 98. On average, the galaxy has experienced relatively constant low-level star formation (5 x 10^-4 Mo yr^-1) for much of cosmic time. Except for the youngest main sequence populations (age < 0.1 Gyr), which are typically fainter than the AO data flux limit, the SFH estimated from the the 592 IR bright stars is a reasonable match to that derived from the much larger optical data set. Differences between the optical and IR derived SFHs for 0.1 - 1 Gyr populations suggest that current stellar evolution models may be over-producing the AGB by as much as a factor of three in this galaxy. At the depth of the AO data, the IR luminous stars are not crowded. Therefore these techniques can potentially be used to determine the stellar populations of galaxies at significantly further distances.Comment: 15 pages, 14 figs, accepted for publication in Ap

One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes

We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and is normalized by a size-dependent constant. The exponent $\alpha$ of the power law is taken in the range $0 \le \alpha <1$. The oscillator frequency distribution is symmetric about its mean (taken to be zero), and is non-increasing on $[0,\infty)$. In the continuum limit, the local density of oscillators evolves in time following the continuity equation that expresses the conservation of the number of oscillators of each frequency under the dynamics. This equation admits as a stationary solution the unsynchronized state uniform both in phase and over the space of the lattice. We perform a linear stability analysis of this state to show that when it is unstable, different spatial Fourier modes of fluctuations have different stability thresholds beyond which they grow exponentially in time with rates that depend on the Fourier modes. However, numerical simulations show that at long times, all the non-zero Fourier modes decay in time, while only the zero Fourier mode (i.e., the "mean-field" mode) grows in time, thereby dominating the instability process and driving the system to a synchronized state. Our theoretical analysis is supported by extensive numerical simulations.Comment: 7 pages, 4 figures. v2: new simulation results added, close to the published versio