Vortex Penetration into a Type II Superconductor due to a Mesoscopic External Current

Applying the London theory we study curved vortices produced by an external current near and parallel to the surface of a type II superconductor. By minimizing the energy functional we find the contour describing the hard core of the flux line, and predict the threshold current for entrance of the first vortex. We assume that the vortex entrance is allowed due to surface defects, despite the Bean-Livingston barrier. Compared to the usual situation with a homogeneous magnetic field, the main effect of the present geometry is that larger magnetic fields can be applied locally before vortices enter the superconducting sample. It is argued that this effect can be further enhanced in anisotropic superconductors.Comment: 9 pages, 14 figure

On the expansion rate of Margulis expanders

In this note we determine exactly the expansion rate of an infinite 4-regular expander graph which is a variant of an expander due to Margulis. The vertex set of this graph consists of all points in the plane. The point (x, y) is adjacent to the points S(x, y), S −1 (x, y), T(x, y), T −1 (x, y) where S(x, y) = (x, x+y) and T(x, y) = (x+y, y). We show that the expansion rate of this 4-regular graph is 2. The main technical result asserts that for any compact planar set A of finite positive measure, |S(A) ∪ S −1 (A) ∪ T(A) ∪ T −1 (A) ∪ A| |A| where |B | is the Lebesgue measure of B. The proof is completely elementary and is based on symmetrization- a classical method in the area of isoperimetric problems. We also use symmetrization to prove a similar result for a directed version of the same graph.

The geometry of graphs and some of its algorithmic applications

In this paper we explore some implications of view-ing graphs as geometric objects. This approach of-fers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect the met-ric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the dis-tances between their geometric images. In this paper we develop efficient algorithms for em-bedding graphs low-dimensionally with a small distor-tion. Further algorithmic applications include: 0 A simple, unified approach to a number of prob-lems on multicommodity flows, including the Leighton-Rae Theorem [29] and some of its ex-tensions. 0 For graphs embeddable in low-dimensional spaces with a small distortion, we can find low-diameter decompositions (in the sense of [4] and [34]). The parameters of the decomposition depend only on the dimension and the distortion and not on the size of the graph. 0 In graphs embedded this way, small balanced separators can be found efficiently. Faithful low-dimensional representations of statisti-cal data allow for meaningful and efficient cluster-ing, which is one of the most basic tasks in pattern-recognition. For the (mostly heuristic) methods use

Myopia control utilizing low-dose atropine as an isolated therapy or in combination with other optical measures: A retrospective cohort study

PURPOSE: To assess the additive potency of low-dose atropine combined with optical measures designed to decrease myopia progression. MATERIALS AND METHODS: This retrospective study included 104 myopic children aged 5–12 over 4 years, divided into five groups: daily instillation of 0.01% atropine and distance single-vision spectacles (A), 0.01% atropine and progressive addition lenses (A + PAL), 0.01% atropine and soft contact lens with peripheral blur (A + CL). Two control groups were included, prescribed bifocal spectacles or single vision (SV) spectacles. Cycloplegic spherical equivalence refraction was measured biannually, including 1 year after cessation of treatment. RESULTS: A significant decrease in myopia progression was noted during the 2nd and 3rd years of atropine treatment: A −0.55 ± 0.55D, −0.15 ± 0.15, −0.12 ± 0.12D were 1st, 2nd, 3rd years, respectively, A + PAL −0.47 ± 0.37D, −0.10 ± 0.25D, and −0.11 ± 0.25D were 1st, 2nd, 3rd years, respectively, A + CL −0.36 ± 0.43D, −0.13 ± 0.29D, and −0.10 ± 0.27D were 1st, 2nd, 3rd years, respectively. Myopia progression over 3 years, respectively, was −0.82 ± 0.50D, −0.70 ± 0.69D, −0.59 ± 0.66D in the bifocal group and −1.20 ± 1.28D, −0.72 ± 0.62D, −0.65 ± 0.47D in the SV group. One year after cessation of atropine treatment, myopia progression was − 0.32 ± 0.31D in A, −0.23 ± 0.28D in A + PAL, and −0.18 ± 0.35D in A + CL. CONCLUSION: Atropine 0.01% presented as effective at decelerating myopia progression, more prominent in the 2nd and 3rd years of treatment. Combining atropine 0.01% with optical modalities exhibited a trend for added efficacy over monotherapy. A + CL exhibited the least rebound effect 1 year after cessation of treatment

Debt, Structural Adjustment and Deforestation: A Cross-National Study

We present cross-national models that examine the determinants of deforestation from 1990 to 2005 for a sample of sixty-two poor nations. We test dependency theory hypotheses that both debt and structural adjustment affect forests. We find substantial support for this theoretical perspective. The results indicate that both factors increase deforestation. We also find support for world polity theory that international non-governmental organization density decreases deforestation. We conclude with a brief discussion of the findings, policy implications, and possible directions for future research