Giant Quantum Reflection of Neon Atoms from a Ridged Silicon Surface

The specular reflectivity of slow, metastable neon atoms from a silicon surface was found to increase markedly when the flat surface was replaced by a grating structure with parallel narrow ridges. For a surface with ridges that have a sufficiently narrow top, the reflectivity was found to increase more than two orders of magnitude at the incident angle of 10 mRad from the surface. The slope of the reflectivity vs the incident angle near zero was found to be nearly an order of magnitude smaller than that of a flat surface. A grating with 6.5% efficiency for the first-order diffraction was fabricated by using the ridged surface structure.Comment: 5 pages, 4 figures. To be published in J. Phys. Soc. Jp

Theory of resistor networks: The two-point resistance

The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for regular lattices in one, two, and three dimensions under various boundary conditions including that of a Moebius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyze large-size expansions of two-and-higher dimensional lattices.Comment: 30 pages, 5 figures now included; typos in Example 1 correcte

Large Scale Spectral Clustering Using Approximate Commute Time Embedding

Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for large scale systems. Recently, many methods have been proposed to accelerate the computational time of spectral clustering. These approximate methods usually involve sampling techniques by which a lot information of the original data may be lost. In this work, we propose a fast and accurate spectral clustering approach using an approximate commute time embedding, which is similar to the spectral embedding. The method does not require using any sampling technique and computing any eigenvector at all. Instead it uses random projection and a linear time solver to find the approximate embedding. The experiments in several synthetic and real datasets show that the proposed approach has better clustering quality and is faster than the state-of-the-art approximate spectral clustering methods

Critical scaling in standard biased random walks

The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented with Monte Carlo simulations. We show that, for appropriate step sizes, the model displays a critical phenomenon, at $p=p_c$. Its scaling properties as well as the main features of the fragmented coverage occurring in the vicinity of the critical point are shown. In particular, in the limit $p\to p_c$, the distribution of fragment lengths is scale-free, with nontrivial exponents. Moreover, the spatial distribution of cracks (unvisited sites) defines a fractal set over the spanned interval. Thus, from the perspective of the covered territory, a very rich critical phenomenology is revealed in a simple one-dimensional standard model.Comment: 4 pages, 4 figure

Upper bounds on subglacial channel development for interior regions of the Greenland Ice Sheet

AbstractWe use a simple numerical model to test whether surface water influx to the bed of the interior Greenland ice sheet has the potential to cause significant subglacial channel growth similar to that observed near the ice-sheet margin and at alpine glaciers. We examine the effects on channel growth from (1) rapid supraglacial lake drainage events and (2) sustained water input into moulins. By assuming that all drainage occurs through subglacial channels and by prescribing favorable pressure conditions at the domain inlet, the model can provide upper bounds on channel growth. Our results indicate that R-channels do not grow significantly within the limited period of high pressure associated with lake drainage events. Subsequent channel growth only occurs with sustained pressures above overburden. Rapid closure of channels at low pressures suggests channels in the interior are unlikely to draw significant quantities of water from nearby distributed networks. These results indicate that other drainage mechanisms such as turbulent sheets or linked-cavity networks are likely to be of greater importance for interior subglacial drainage than the growth of channels.</jats:p

Patterns of Individual Shopping Behavior

Much of economic theory is built on observations of aggregate, rather than individual, behavior. Here, we present novel findings on human shopping patterns at the resolution of a single purchase. Our results suggest that much of our seemingly elective activity is actually driven by simple routines. While the interleaving of shopping events creates randomness at the small scale, on the whole consumer behavior is largely predictable. We also examine income-dependent differences in how people shop, and find that wealthy individuals are more likely to bundle shopping trips. These results validate previous work on mobility from cell phone data, while describing the unpredictability of behavior at higher resolution.Comment: 4 pages, 5 figure

Far-UV Emissions of the Sun in Time: Probing Solar Magnetic Activity and Effects on Evolution of Paleo-Planetary Atmospheres

We present and analyze FUSE observations of six solar analogs. These are single, main-sequence G0-5 strs selected as proxies for the Sun at several stages of its main-sequence lifetime. The emission features in the FUSE 920-1180 A wavelength range allow for a critical probe of the hot plasma over three decades in temperature. Using the flux ratio CIII 1176/977 as diagnostics, we investigate the dependence of the electron pressure of the transition region as a function of the rotation period, age and magnetic activity. The results from these solar proxies indicate that the electron pressure of the stellar ~10^5-K plasma decreases by a factor of about 70 between the young, fast-rotating magnetically active star and the old, slow-rotating inactive star. Also, the observations indicate that the average surface fluxes of emission features strongly decrease with increasing stellar age and longer rotation period. The emission flux evolution with age or rotation period is well fitted by power laws, which become steeper from cooler chromospheric (10^4 K) to hotter coronal (10^7 K) plasma. The relationship for the integrated (920-1180 A) FUSE flux indicates that the solar far-ultraviolet emissions were about twice the present value 2.5 Gyr ago and about 4 times the present value 3.5 Gyr ago. Note also that the FUSE/FUV flux of the Zero-Age Main Sequence Sun could have been higher by as much as 50 times. Our analysis suggests that the strong FUV emissions of the young Sun may have played a crucial role in the developing planetary system, in particular through the photoionization, photochemical evolution and possible erosion of the planetary atmospheres. (abridged)Comment: 15 pages, 8 figures, accepted for publication in Ap

A transiting companion to the eclipsing binary KIC002856960

We present an early result from an automated search of Kepler eclipsing binary systems for circumbinary companions. An intriguing tertiary signal has been discovered in the short period eclipsing binary KIC002856960. This third body leads to transit-like features in the light curve occurring every 204.2 days, while the two other components of the system display eclipses on a 6.2 hour period. The variations due to the tertiary body last for a duration of \sim1.26 days, or 4.9 binary orbital periods. During each crossing of the binary orbit with the tertiary body, multiple individual transits are observed as the close binary stars repeatedly move in and out of alignment with the tertiary object. We are at this stage unable to distinguish between a planetary companion to a close eclipsing binary, or a hierarchical triply eclipsing system of three stars. Both possibilities are explored, and the light curves presented.Comment: Accepted into A&A Letters (5 pages & 3 figures

Nonthermal Hard X-ray Emission and Iron Kalpha Emission from a Superflare on II Pegasi

We report on an X-ray flare detected on the active binary system II~Pegasi with the Swift telescope. The trigger had a 10-200 keV luminosity of 2.2$\times10^{32}$ erg s$^{-1}$-- a superflare, by comparison with energies of typical stellar flares on active binary systems. The trigger spectrum indicates a hot thermal plasma with T$\sim$180 $\times10^{6}$K. X-ray spectral analysis from 0.8--200 keV with the X-Ray Telescope and BAT in the next two orbits reveals evidence for a thermal component (T$>$80 $\times10^{6}$K) and Fe K 6.4 keV emission. A tail of emission out to 200 keV can be fit with either an extremely high temperature thermal plasma (T$\sim3\times10^{8}$K) or power-law emission. Based on analogies with solar flares, we attribute the excess continuum emission to nonthermal thick-target bremsstrahlung emission from a population of accelerated electrons. We estimate the radiated energy from 0.01--200 keV to be $\sim6\times10^{36}$ erg, the total radiated energy over all wavelengths $\sim10^{38}$ erg, the energy in nonthermal electrons above 20 keV $\sim3\times10^{40}$ erg, and conducted energy $<5\times10^{43}$ erg. The nonthermal interpretation gives a reasonable value for the total energy in electrons $>$ 20 keV when compared to the upper and lower bounds on the thermal energy content of the flare. This marks the first occasion in which evidence exists for nonthermal hard X-ray emission from a stellar flare. We investigate the emission mechanism responsible for producing the 6.4 keV feature, and find that collisional ionization from nonthermal electrons appears to be more plausible than the photoionization mechanism usually invoked on the Sun and pre-main sequence stars.Comment: 41 pages, 7 figures, accepted for publication in the Astrophysical Journa