Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications

Augmenting Exposure Therapy for Social Anxiety with tDCS

Purpose/Background: Exposure therapy is one of the most potent techniques available to treat social anxiety. However, studies suggest that exposure therapy only produces full remission in 20-50% of patients. Furthermore, laboratory conditioning and extinction studies suggest that fear responses toward individuals who differ from one\u27s own ethnicity/race may be more resistant to extinction. Because activation of the medial prefrontal cortex has been associated with facilitating fear reduction during exposure therapy, we expect that targeting activation of this region with a stimulation technique called transcranial direct current stimulation (tDCS) may improve outcomes from exposure therapy for social anxiety. The present study will therefore test the hypotheses that (1) fear responding at baseline will be greater toward an audience that does not match (vs matches) the participant\u27s own ethnicity, (2) pairing exposure therapy with active (vs sham) tDCS will facilitate alleviation of social anxiety symptoms, and (3) pairing exposure therapy with active (vs sham) tDCS facilitates extinction of fear response toward individuals who differ from the participant\u27s own ethnicity. Materials & Methods: We are recruiting Latino and non-Latino/Caucasian undergraduates with a fear of public speaking, the most commonly feared situation among individuals with social anxiety. Participants (N = 128) will receive either active/anodal (n = 64) or sham (n = 64) tDCS stimulation targeting the mPFC during an exposure therapy session delivered through virtual reality (VR). During exposure therapy, participants will complete six, 3-minute public speaking trials, alternating in a randomized order between audiences that are 75% matched to the participant\u27s ethnicity and 75% unmatched to the participant\u27s ethnicity. At one-month follow up, participants will complete two behavioral avoidance tests (BATs) parallel to therapy procedures, with one ethnic-matched trial and one ethnic-unmatched trial. Fear response during each BAT will be assessed behaviorally (duration of speech), physiologically (heart rate variability and electrodermal response), and subjectively (peak fear rating, on a 0 to 100 scale). At baseline and one-month follow-up, participants will also complete a battery of social anxiety questionnaires. Results: We will present methods and preliminary findings from the study. Results will include a preliminary examination of whether fear responding is greater toward individuals who differ from (vs match) the participant\u27s own ethnicity, whether pairing exposure therapy with active (vs sham) tDCS facilitates alleviation of social anxiety symptoms overall, and whether pairing exposure therapy with active (vs sham) tDCS facilitates alleviation of social anxiety responding toward individuals who differ from (vs match) the participant\u27s own ethnicity. Discussion/Conclusion: Findings point to key strategies to improve outcomes from exposure therapy for social anxiety, and could also have implications for improving response to exposure-based therapies for other anxiety disorders. Furthermore, if tDCS facilitates reductions in fear response toward ethnic/racial out-groups, minority/Latino individuals may experience better generalization of treatment effects for daily-life scenarios (in which they are surrounded by outgroup members), and ethnic/racial majority individuals will be better able to contribute to an inclusive social environment

Large-volume lava flow fields on Venus: Dimensions and morphology

Of all the volcanic features identified in Magellan images, by far the most extensive and really important are lava flow fields. Neglecting the widespread lava plains themselves, practically every C1-MIDR produced so far contains several or many discrete lava flow fields. These range in size from a few hundred square kilometers in area (like those fields associated with small volcanic edifices for example), through all sizes up to several hundred thousand square kilometers in extent (such as many rift related fields). Most of these are related to small, intermediate, or large-scale volcanic edifices, coronae, arachnoids, calderas, fields of small shields, and rift zones. An initial survey of 40 well-defined flow fields with areas greater than 50,000 sq km (an arbitrary bound) has been undertaken. Following Columbia River Basalt terminology, these have been termed great flow fields. This represents a working set of flow fields, chosen to cover a variety of morphologies, sources, locations, and characteristics. The initial survey is intended to highlight representative flow fields, and does not represent a statistical set. For each flow field, the location, total area, flow length, flow widths, estimated flow thicknesses, estimated volumes, topographic slope, altitude, backscatter, emissivity, morphology, and source has been noted. The flow fields range from about 50,000 sq km to over 2,500,000 sq km in area, with most being several hundred square kilometers in extent. Flow lengths measure between 140 and 2840 km, with the majority of flows being several hundred kilometers long. A few basic morphological types have been identified

Building Community in the Asynchronous Environment; Perspectives Across the Campus

Technology and circumstances have opened doors to online education, and there are many reasons why students opt for online education. While online education offers the comfort of convenience, it also brings in several concerns of feeling alone, sitting in front of a device, and attempting to complete coursework with little support synchronously. Throughout this interactive session, you will have the opportunity to hear from different perspectives on how we have brought the classroom to the living room by enhancing our online offerings while building a sense of community

ZNF804A genotype modulates neural activity during working memory for faces

Copyright © 2013 S. Karger AG, Basel.Peer reviewedPublisher PD

Bounding and approximating parabolas for the spectrum of Heisenberg spin systems

We prove that for a wide class of quantum spin systems with isotropic Heisenberg coupling the energy eigenvalues which belong to a total spin quantum number S have upper and lower bounds depending at most quadratically on S. The only assumption adopted is that the mean coupling strength of any spin w.r.t. its neighbours is constant for all N spins. The coefficients of the bounding parabolas are given in terms of special eigenvalues of the N times N coupling matrix which are usually easily evaluated. In addition we show that the bounding parabolas, if properly shifted, provide very good approximations of the true boundaries of the spectrum. We present numerical examples of frustrated rings, a cube, and an icosahedron.Comment: 8 pages, 3 figures. Submitted to Europhysics Letter

Gigantic transmission band edge resonance in periodic stacks of anisotropic layers

We consider Fabry-Perot cavity resonance in periodic stacks of anisotropic layers with misaligned in-plane anisotropy at the frequency close to a photonic band edge. We show that in-plane dielectric anisotropy can result in a dramatic increase in field intensity and group delay associated with the transmission resonance. The field enhancement appears to be proportional to forth degree of the number N of layers in the stack. By contrast, in common periodic stacks of isotropic layers, those effects are much weaker and proportional to N^2. Thus, the anisotropy allows to drastically reduce the size of the resonance cavity with similar performance. The key characteristic of the periodic arrays with the gigantic transmission resonance is that the dispersion curve omega(k)at the photonic band edge has the degenerate form Delta(omega) ~ Delta(k)^4, rather than the regular form Delta(omega) ~ Delta(k)^2. This can be realized in specially arranged stacks of misaligned anisotropic layers. The degenerate band edge cavity resonance with similar outstanding properties can also be realized in a waveguide environment, as well as in a linear array of coupled multimode resonators, provided that certain symmetry conditions are in place.Comment: To be submitted to Phys. Re

The statistical mechanics of combinatorial optimization problems with site disorder

We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several different domains and various problems in one dimension such as the so called descent problem. We first motivate our method by analyzing these problems using the annealed approximation, then the limit of a large number of points we develop a formalism to carry out the quenched calculation. This formalism does not require the replica method and its predictions are found to agree with Monte Carlo simulations. In addition our method reproduces an exact mathematical result for the Maximum traveling salesman problem in two dimensions and suggests its generalization to higher dimensions. The general approach may provide an alternative method to study certain systems with quenched disorder.Comment: 21 pages RevTex, 8 figure

Finding the Center of Mass of a Soft Spring

This article shows how to use calculus to find the center of mass position of a soft cylindrical helical spring that is suspended vertically. The spring is non-uniformly stretched by the action of gravity. A general expression for the vertical position of the center of mass is obtained.Comment: LaTeX, 7 pages, 2 figures. Minor changes to agree with published versio

The declining representativeness of the British party system, and why it matters

In a recent article, Michael Laver has explained ‘Why Vote-Seeking Parties May Make Voters Miserable’. His model shows that, while ideological convergence may boost congruence between governments and the median voter, it can reduce congruence between the party system and the electorate as a whole. Specifically, convergence can increase the mean distance between voters and their nearest party. In this article we show that this captures the reality of today’s British party system. Policy scale placements in British Election Studies from 1987 to 2010 confirm that the pronounced convergence during the past decade has left the Conservatives and Labour closer together than would be optimal in terms of minimising the policy distance between the average voter and the nearest major party. We go on to demonstrate that this comes at a cost. Respondents who perceive themselves as further away from one of the major parties in the system tend to score lower on satisfaction with democracy. In short, vote-seeking parties have left the British party system less representative of the ideological diversity in the electorate, and thus made at least some British voters miserable