Microscopic Theory of Spontaneous Decay in a Dielectric

The local field correction to the spontanous dacay rate of an impurity source atom imbedded in a disordered dielectric is calculated to second order in the dielectric density. The result is found to differ from predictions associated with both "virtual" and "real" cavity models of this decay process. However, if the contributions from two dielectric atoms at the same position are included, the virtual cavity result is reproduced.Comment: 12 Page

Evidence of a mis-aligned secondary bar in the Large Magellanic Cloud

Evidence of a mis-aligned secondary bar, within the primary bar of the Large Magellanic Cloud (LMC) is presented. The density distribution and the de-reddened mean magnitudes ($I_0$) of the red clump stars in the bar obtained from the OGLE II data are used for this study. The bar region which predominantly showed wavy pattern in the line of sight in \citet{a03} was located. These points in the X-Z plane delineate an S-shaped pattern, clearly indicating a mis-aligned bar. This feature is statistically significant and does not depend on the considered value of $I_0$ for the LMC center. The rest of the bar region were not found to show the warp or the wavy pattern. The secondary bar is found to be considerably elongated in the Z-direction, with an inclination of 66$^o$.5 $\pm$ 0$^o$.9, whereas the undisturbed part of the primary bar is found to have an inclination of 15$^o$.1 $\pm$ 2$^o$.7, such that the eastern sides are closer to us with respect to the western sides of both the bars. The PA$_{maj}$ of the secondary bar is found to be 108$^o$.4 $\pm$ 7$^o$.3. The streaming motions found in the H I velocity map close to the LMC center could be caused by the secondary bar. The recent star formation and the gas distribution in LMC could be driven by the mis-aligned secondary bar.Comment: 10 pages, to appear in ApJ Letter

Generalizing Boolean Satisfiability II: Theory

This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-Loveland inference procedure to this broader setting, and show that earlier computational improvements are either subsumed or left intact by the new method. The third paper in this series discusses ZAPs implementation and presents experimental performance results

Generalizing Boolean Satisfiability III: Implementation

This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances

Re-examination of the possible tidal stream in front of the LMC

It has recently been suggested that the stars in a vertical extension of the red clump feature seen in LMC color-magnitude diagrams could belong to a tidal stream of material located in front of that galaxy. If this claim is correct, this foreground concentration of stars could contribute significantly to the rate of gravitational microlensing events observed in the LMC microlensing experiments. Here we present radial velocity measurements of stars in this so-called ``vertical red clump'' (VRC) population. The observed stellar sample, it transpires, has typical LMC kinematics. It is shown that it is improbable that an intervening tidal stream should have the same distribution of radial velocities as the LMC, which is consistent with an earlier study that showed that the VRC feature is more likely a young stellar population in the main body of that galaxy. However, the kinematic data do not discriminate against the possibility that the VRC is an LMC halo population.Comment: 10 pages, 3 figures, 1 table. Accepted for publication in ApJ

Fast Monte Carlo Algorithms for Permutation Groups

AbstractWe introduce new, elementary Monte Carlo methods to speed up and greatly simplify the manipulation of permutation groups (given by a list of generators). The methods are of a combinatorial character, using only elementary group theory. The key idea is that under certain conditions, "random subproducts" of the generators successfully emulate truly random elements of a group. We achieve a nearly optimal O(n3 logcn) asymptotic running time for membership testing, where n is the size of the permutation domain. This is an improvement of two orders of magnitude compared to known elementary algorithms and one order of magnitude compared to algorithms which depend on heavy use of group theory. An even greater asymptotic speedup is achieved for normal closures, a key ingredient in group-theoretic computation, now constructible in Monte Carlo time O(n2 logcn), i.e., essentially linear time (as a function of the input length). Some of the new techniques are sufficiently general to allow polynomial-time implementations in the very general model of "black box groups" (group operations are performed by an oracle). In particular, the normal closure algorithm has a number of applications to matrix-group computation. It should be stressed that our randomized algorithms are not heuristic: the probability of error is guaranteed not to exceed a bound ϵ > 0, prescribed by the user. The cost of this requirement is a factor of |log ϵ| in the running time

A comparison between Pa alpha and H alpha emission: The relation between HII region mean reddening, local gas density and metallicity

We measure reddenings to HII regions in NGC 2903, NGC 1512, M51, NGC 4449 and NGC 6946 from Hubble Space Telescope Pa alpha and H alpha images. Extinctions range from A_V ~ 5 - 0 depending upon the galaxy. For the galaxies with HST images in both lines, NGC 2903, NGC 1512 and M51, the Pa alpha and H alpha emission are almost identical in morphology which implies that little emission from bright HII regions is hidden from view by regions of comparatively high extinction. The scatter in the measured extinctions is only +- 0.5 mag. We compare the reddenings we measure in five galaxies using the Pa alpha to H alpha ratios to those measured previously from the Balmer decrement in the LMC and as a function of radius in M101 and M51. We find that luminosity weighted mean extinctions of these ensembles of HI regions are correlated with gas surface density and metallicity. The correlation is consistent with the mean extinction depending on dust density where the dust to gas mass ratio scales with the metallicity. This trend is expected if HII regions tend to be located near the mid-plane of a gas disk and emerge from their parent molecular clouds soon after birth. In environments with gas densities below a few hundred Msol/pc^2 star formation rates estimated from integrated line fluxes and mean extinctions are likely to be fairly accurate.Comment: accepted for publication in A

Minimal chordal sense of direction and circulant graphs

A sense of direction is an edge labeling on graphs that follows a globally consistent scheme and is known to considerably reduce the complexity of several distributed problems. In this paper, we study a particular instance of sense of direction, called a chordal sense of direction (CSD). In special, we identify the class of k-regular graphs that admit a CSD with exactly k labels (a minimal CSD). We prove that connected graphs in this class are Hamiltonian and that the class is equivalent to that of circulant graphs, presenting an efficient (polynomial-time) way of recognizing it when the graphs' degree k is fixed

A Survey of Women in Academia and the role of a Multidisciplinary Professional Society

The Society of Women Engineers (SWE) is a global professional society of over 30,000 members with a mission to “Stimulate women to achieve full potential in careers as engineers and leaders, expand the image of the engineering profession as a positive force in improving the quality of life, and demonstrate the value of diversity”1. SWE is an organization that is deeply rooted in industry. The founding members were employed by firms that are a result of the industrial revolution, and thus the focus of its membership is on those that work for industry, consultants, and often themselves. This focus has unintentionally left a large population of its membership, the academic population, underrepresented and misunderstood. Early discussion at the board level in the mid 2000’s indicated a willingness for a paradigm shift. However, the representation of academics on the board and other leadership roles has been lacking. This can be attributed to the lower numbers of this group relative to the whole, as well as the requirements of tenure that do not support the time and dedication to such an endeavor. A small but influential group of members, including a former board member, and a few involved at various levels of the society have been working toward increasing opportunities for women in academia (WIA). Some of the initiatives have been the societal support of the WIA committee, the addition of professional development opportunities targeting women in academic careers, providing recognition and awards, and aiding in networking opportunities. These all lead toward career advancement, making SWE more attractive to women engineers in the academe. To further our understanding of available opportunities and those opportunities that will make membership and active participation more attractive to members in academia, a survey was developed. Information gathered by the survey include demographics, perceived needs, and potential contributions the individual could make in furthering the creation of professional development opportunities for this population. This work is intended to share the results of this survey, using descriptive statistics, further developing our understanding of this underserved population within SWE