Retrieving Neptune's aerosol properties from Keck OSIRIS observations. I. Dark regions

We present and analyze three-dimensional data cubes of Neptune from the OSIRIS integral-field spectrograph on the 10-m Keck telescope, from July 2009. These data have a spatial resolution of 0.035"/pixel and spectral resolution of R~3800 in the H and K broad bands. We focus our analysis on regions of Neptune's atmosphere that are near-infrared dark- that is, free of discrete bright cloud features. We use a forward model coupled to a Markov chain Monte Carlo algorithm to retrieve properties of Neptune's aerosol structure and methane profile above ~4 bar in these near-infrared dark regions. Using a set of high signal-to-noise spectra in a cloud-free band from 2-12N, we find that Neptune's cloud opacity is dominated by a compact, optically thick cloud layer with a base near 3 bar and composed of low albedo, forward scattering particles, with an assumed characteristic size of ~1$\mu$m. Above this cloud, we require a vertically extended haze of smaller (~0.1 $\mu$m) particles, which reaches from the upper troposphere (~0.6 bar) into the stratosphere. The particles in this haze are brighter and more isotropically scattering than those in the deep cloud. When we extend our analysis to 18 cloud-free locations from 20N to 87S, we observe that the optical depth in aerosols above 0.5 bar decreases by a factor of 2-3 or more at mid- and high-southern latitudes relative to low latitudes. We also consider Neptune's methane (CH$_4$) profile, and find that our retrievals indicate a strong preference for a low methane relative humidity at pressures where methane is expected to condense. Our preferred solution at most locations is for a methane relative humidity below 10% near the tropopause in addition to methane depletion down to 2.0-2.5 bar. We tentatively identify a trend of lower CH$_4$ columns above 2.5 bar at mid- and high-southern latitudes over low latitudes.Comment: Published in Icarus: 15 September 201

Computing the Similarity Between Moving Curves

In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically the Fr\'echet distance between surfaces. While the Fr\'echet distance between surfaces is not even known to be computable, we show for variants arising in the context of moving curves that they are polynomial-time solvable or NP-complete depending on the restrictions imposed on how the moving curves are matched. We achieve the polynomial-time solutions by a novel approach for computing a surface in the so-called free-space diagram based on max-flow min-cut duality

Implementing an apparent-horizon finder in three dimensions

Locating apparent horizons is not only important for a complete understanding of numerically generated spacetimes, but it may also be a crucial component of the technique for evolving black-hole spacetimes accurately. A scheme proposed by Libson et al., based on expanding the location of the apparent horizon in terms of symmetric trace-free tensors, seems very promising for use with three-dimensional numerical data sets. In this paper, we generalize this scheme and perform a number of code tests to fully calibrate its behavior in black-hole spacetimes similar to those we expect to encounter in solving the binary black-hole coalescence problem. An important aspect of the generalization is that we can compute the symmetric trace-free tensor expansion to any order. This enables us to determine how far we must carry the expansion to achieve results of a desired accuracy. To accomplish this generalization, we describe a new and very convenient set of recurrence relations which apply to symmetric trace-free tensors.Comment: 14 pages (RevTeX 3.0 with 3 figures

Proving Nontermination via safety

We show how the problem of nontermination proving can be reduced to a question of underapproximation search guided by a safety prover. This reduction leads to new nontermination proving implementation strategies based on existing tools for safety proving. Our preliminary implementation beats existing tools. Furthermore, our approach leads to easy support for programs with unbounded nondeterminism

Reduction of Two-Dimensional Dilute Ising Spin Glasses

The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large systems. Low-temperature domain-wall excitations are studied to determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found, consistent with previous results obtained on undiluted lattices. This comparison demonstrates the validity of the reduction method for bond-diluted spin systems and provides strong support for similar studies proclaiming accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see http://www.physics.emory.edu/faculty/boettcher

Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D ±J\pm J Random-Bond Ising Model

The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$ are studied. We are able to consider large samples of up to $320^2$ spins by using sophisticated matching algorithms. We study $L \times L$ systems, but we also consider $L \times M$ samples, for different aspect ratios $R = L / M$. We find that the scaling behavior of the ground-state energy and its sample-to-sample fluctuations inside the spin-glass region ($p_c \le p \le 1 - p_c$) are characterized by simple scaling functions. In particular, the fluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glass region the average domain-wall energy converges to a finite nonzero value as the sample size becomes infinite, holding $R$ fixed. Here, large finite-size effects are visible, which can be explained for all $p$ by a single exponent $\omega\approx 2/3$, provided higher-order corrections to scaling are included. Finally, we confirm the validity of aspect-ratio scaling for $R \to 0$: the distribution of the domain-wall energies converges to a Gaussian for $R \to 0$, although the domain walls of neighboring subsystems of size $L \times L$ are not independent.Comment: 11 pages with 15 figures, extensively revise

Thermal barrier coating life prediction model

The objectives of this program are to determine the predominant modes of degradation of a plasma sprayed thermal barrier coating system, and then to develop and verify life prediction models accounting for these degradation modes. The program is divided into two phases, each consisting of several tasks. The work in Phase 1 is aimed at identifying the relative importance of the various failure modes, and developing and verifying life prediction model(s) for the predominant model for a thermal barrier coating system. Two possible predominant failure mechanisms being evaluated are bond coat oxidation and bond coat creep. The work in Phase 2 will develop design-capable, causal, life prediction models for thermomechanical and thermochemical failure modes, and for the exceptional conditions of foreign object damage and erosion

Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p\in[0,1]$ of antiferromagnetic and $(1-p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to 700. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at $p_c \sim 0.103$ compared to the concentration $p_n\sim 0.109$ at the Nishimory point, which means that the phase diagram of the model exhibits a reentrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.Comment: 7 pages, 12 figures, revTe

Results from the Palo Verde neutrino oscillation experiment

The ν̅e flux and spectrum have been measured at a distance of about 800 m from the reactors of the Palo Verde Nuclear Generating Station using a segmented Gd-loaded liquid scintillator detector. Correlated positron-neutron events from the reaction ν̅ep→e+n were recorded for a period of 200 d including 55 d with one of the three reactors off for refueling. Backgrounds were accounted for by making use of the reactor-on and reactor-off cycles, and also with a novel technique based on the difference between signal and background under reversal of the e+ and n portions of the events. A detailed description of the detector calibration, background subtraction, and data analysis is presented here. Results from the experiment show no evidence for neutrino oscillations. ν̅e→ν̅x oscillations were excluded at 90% C.L. for Δm2>1.12×10-3 eV2 for full mixing and sin22θ>0.21 for large Δm2. These results support the conclusion that the observed atmospheric neutrino oscillations do not involve νe