Narrow-escape-time problem: the imperfect trapping case

We present a master equation approach to the \emph{narrow escape time} (NET) problem, i.e. the time needed for a particle contained in a confining domain with a single narrow opening, to exit the domain for the first time. We introduce a finite transition probability, $\nu$, at the narrow escape window allowing the study of the imperfect trapping case. Ranging from 0 to $\infty$, $\nu$ allowed the study of both extremes of the trapping process: that of a highly deficient capture, and situations where escape is certain ("perfect trapping" case). We have obtained analytic results for the basic quantity studied in the NET problem, the \emph{mean escape time} (MET), and we have studied its dependence in terms of the transition (desorption) probability over (from) the surface boundary, the confining domain dimensions, and the finite transition probability at the escape window. Particularly we show that the existence of a global minimum in the NET depends on the `imperfection' of the trapping process. In addition to our analytical approach, we have implemented Monte Carlo simulations, finding excellent agreement between the theoretical results and simulations.Comment: 9 page

Molecular collisions. 16: Comparison of GPS with classical trajectory calculations of rotational inelasticity for the Ar-N2 system

Comparison of generalized phase shift treatment with classical trajectory calculations of rotational inelasticity cross sections of Ar-N2 scatterin

Nova Geminorum 1912 and the Origin of the Idea of Gravitational Lensing

Einstein's early calculations of gravitational lensing, contained in a scratch notebook and dated to the spring of 1912, are reexamined. A hitherto unknown letter by Einstein suggests that he entertained the idea of explaining the phenomenon of new stars by gravitational lensing in the fall of 1915 much more seriously than was previously assumed. A reexamination of the relevant calculations by Einstein shows that, indeed, at least some of them most likely date from early October 1915. But in support of earlier historical interpretation of Einstein's notes, it is argued that the appearance of Nova Geminorum 1912 (DN Gem) in March 1912 may, in fact, provide a relevant context and motivation for Einstein's lensing calculations on the occasion of his first meeting with Erwin Freundlich during a visit in Berlin in April 1912. We also comment on the significance of Einstein's consideration of gravitational lensing in the fall of 1915 for the reconstruction of Einstein's final steps in his path towards general relativity.Comment: 31 p

Shaping our literate lives: Examining the role of literacy experiences in shaping positive literacy identities of doctoral students

The purpose of this study was to examine the ways in which literacy histories and present literacy experiences of doctoral students shaped their literacy identities. Data were collected through surveys, interviews, and visual identity representations. This paper focuses on the literacy stories of two doctoral students with positive literacy identities. Findings suggest that participants valued literacy as a social learning experience from an early age through higher education. These social experiences with reading and writing can take many forms and can be embraced in various home and school contexts. Additionally, these findings highlight the need for schools to create and nurture such experiences across all grade levels, through multiple forums, which may lead to positive literacy identities

A Coupled Remote Sensing and Simplified Surface Energy Balance Approach to Estimate Actual Evapotranspiration from Irrigated Fields

Accurate crop performance monitoring and production estimation are critical for timely assessment of the food balance of several countries in the world. Since 2001, the Famine Early Warning Systems Network (FEWS NET) has been monitoring crop performance and relative production using satellite-derived data and simulation models in Africa, Central America, and Afghanistan where ground-based monitoring is limited because of a scarcity of weather stations. The commonly used crop monitoring models are based on a crop water-balance algorithm with inputs from satellite-derived rainfall estimates. These models are useful to monitor rainfed agriculture, but they are ineffective for irrigated areas. This study focused on Afghanistan, where over 80 percent of agricultural production comes from irrigated lands. We developed and implemented a Simplified Surface Energy Balance (SSEB) model to monitor and assess the performance of irrigated agriculture in Afghanistan using a combination of 1-km thermal data and 250-m Normalized Difference Vegetation Index (NDVI) data, both from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor. We estimated seasonal actual evapotranspiration (ETa) over a period of six years (2000-2005) for two major irrigated river basins in Afghanistan, the Kabul and the Helmand, by analyzing up to 19 cloud-free thermal and NDVI images from each year. These seasonal ETa estimates were used as relative indicators of year-to-year production magnitude differences. The temporal water-use pattern of the two irrigated basins was indicative of the cropping patterns specific to each region. Our results were comparable to field reports and to estimates based on watershed-wide crop water-balance model results. For example, both methods found that the 2003 seasonal ETa was the highest of all six years. The method also captured water management scenarios where a unique year-to-year variability was identified in addition to water-use differences between upstream and downstream basins. A major advantage of the energy-balance approach is that it can be used to quantify spatial extent of irrigated fields and their water-use dynamics without reference to source of water as opposed to a water-balance model which requires knowledge of both the magnitude and temporal distribution of rainfall and irrigation applied to fields

Superdiffusion in Decoupled Continuous Time Random Walks

Continuous time random walk models with decoupled waiting time density are studied. When the spatial one jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized superdiffusive regime is established. This is verified by showing that the square width of the probability distribution (appropriately defined)grows as $t^{2/\gamma}$ with $0<\gamma\leq2$ when $t\to \infty$. An important connection of our results and those of Tsallis' nonextensive statistics is shown. The normalized q-expectation value of $x^2$ calculated with the corresponding probability distribution behaves exactly as $t^{2/\gamma}$ in the asymptotic limit.Comment: 9 pages (.tex file), 1 Postscript figures, uses revtex.st