The Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.

Transiting Exoplanets with JWST

The era of exoplanet characterization is upon us. For a subset of exoplanets -- the transiting planets -- physical properties can be measured, including mass, radius, and atmosphere characteristics. Indeed, measuring the atmospheres of a further subset of transiting planets, the hot Jupiters, is now routine with the Spitzer Space Telescope. The James Webb Space Telescope (JWST) will continue Spitzer's legacy with its large mirror size and precise thermal stability. JWST is poised for the significant achievement of identifying habitable planets around bright M through G stars--rocky planets lacking extensive gas envelopes, with water vapor and signs of chemical disequilibrium in their atmospheres. Favorable transiting planet systems, are, however, anticipated to be rare and their atmosphere observations will require tens to hundreds of hours of JWST time per planet. We review what is known about the physical characteristics of transiting planets, summarize lessons learned from Spitzer high-contrast exoplanet measurements, and give several examples of potential JWST observations.Comment: 22 pages, 11 figures. In press in "Astrophysics in the Next Decade: JWST and Concurrent Facilities, Astrophysics & Space Science Library, Thronson, H. A., Tielens, A., Stiavelli, M., eds., Springer: Dordrecht (2008)." The original publication will be available at http://www.springerlink.co

Tidal Evolution of Close Binary Asteroid Systems

We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less than five times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function, based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system, e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate, semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent.Comment: 40 pages, 2 tables, 8 figure

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

The Effects of Sugars Intake and Frequency of Ingestion on Dental Caries Increment in a Three-year Longitudinal Study

A three-year longitudinal study was carried out with a group of children, initially aged 11-15, residing in non-fluoridated rural communities in south-central Michigan. This report analyzes the relation between caries increment and consumption of sugars from all sources to see if accepted relationships have changed with the caries decline in the United States. There were 499 children who provided three or more 24-hour dietary recall interviews, and who received dental examinations at baseline and after three years. Caries increment averaged 2.91 DMFS over the three years, with 81 % of new lesions on pit-and-fissure surfaces. Consumption of sugars from all sources averaged 156 g per day for males and 127 g per day for females, an average of 52 kg per person per year. Sugars constituted one-quarter of total caloric intake for both boys and girls, and the average number of eating occasions per day was 4.3. Children who consumed a higher proportion of their total energy intake as sugars had a higher increment of approximal caries, though there was little relation to pit-and-fissure caries. The average number of daily eating occasions was not related to caries increment, nor was the average number of sugary snacks (defined as foods with 15% or more of sugars) consumed between meals, but the average consumption of between-meal sugars was related to the approximal caries increment. When children were categorized by high caries increment compared with no caries increment, a tendency toward more frequent snacks was seen in the high-caries children. In an age of generally declining caries, it was concluded that higher average daily consumption of sugars, and higher between-meal consumption of sugars, was still a risk factor for children susceptible to approximal caries. Overall frequency of eating and frequency of ingestion of sugary foods between meals, however, were both poorly related to approximal caries increment. Pit-and-fissure caries could not be related to any aspect of sugars consumption.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67206/2/10.1177_00220345880670111201.pd

Microflares and the Statistics of X-ray Flares

This review surveys the statistics of solar X-ray flares, emphasising the new views that RHESSI has given us of the weaker events (the microflares). The new data reveal that these microflares strongly resemble more energetic events in most respects; they occur solely within active regions and exhibit high-temperature/nonthermal emissions in approximately the same proportion as major events. We discuss the distributions of flare parameters (e.g., peak flux) and how these parameters correlate, for instance via the Neupert effect. We also highlight the systematic biases involved in intercomparing data representing many decades of event magnitude. The intermittency of the flare/microflare occurrence, both in space and in time, argues that these discrete events do not explain general coronal heating, either in active regions or in the quiet Sun.Comment: To be published in Space Science Reviews (2011

Measurements of differential production cross sections for a Z boson in association with jets in pp collisions at root s=8 TeV

Peer reviewe