Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate -but fast - methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained. The error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed. The total error introduced in a multilevel implementation is also investigated numerically.published_or_final_versio

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Dissipation in intercluster plasma

We discuss dissipative processes in strongly gyrotropic, nearly collisionless plasma in clusters of galaxies (ICM). First, we point out that Braginsky theory, which assumes that collisions are more frequent that the system's dynamical time scale, is inapplicable to fast, sub-viscous ICM motion. Most importantly, the electron contribution to collisional magneto-viscosity dominates over that of ions for short-scale Alfvenic motions. Thus, if a turbulent cascade develops in the ICM and propagates down to scales $\leq 1$ kpc, it is damped collisionally not on ions, but on electrons. Second, in high beta plasma of ICM, small variations of the magnetic field strength, of relative value $\sim 1/\beta$, lead to development of anisotropic pressure instabilities (firehose, mirror and cyclotron). Unstable wave modes may provide additional resonant scattering of particles, effectively keeping the plasma in a state of marginal stability. We show that in this case the dissipation rate of a laminar, subsonic, incompressible flows scales as inverse of plasma beta parameter. We discuss application to the problem of ICM heating.Comment: 4 pages, accepted by ApJ Let

Exterior optical cloaking and illusions by using active sources: a boundary element perspective

Recently, it was demonstrated that active sources can be used to cloak any objects that lie outside the cloaking devices [Phys. Rev. Lett. \textbf{103}, 073901 (2009)]. Here, we propose that active sources can create illusion effects, so that an object outside the cloaking device can be made to look like another object. invisibility is a special case in which the concealed object is transformed to a volume of air. From a boundary element perspective, we show that active sources can create a nearly "silent" domain which can conceal any objects inside and at the same time make the whole system look like an illusion of our choice outside a virtual boundary. The boundary element method gives the fields and field gradients (which can be related to monopoles and dipoles) on continuous curves which define the boundary of the active devices. Both the cloaking and illusion effects are confirmed by numerical simulations

On the Abundance of Circumbinary Planets

We present here the first observationally based determination of the rate of occurrence of circumbinary planets. This is derived from the publicly available Kepler data, using an automated search algorithm and debiasing process to produce occurrence rates implied by the seven systems already known. These rates depend critically on the planetary inclination distribution: if circumbinary planets are preferentially coplanar with their host binaries, as has been suggested, then the rate of occurrence of planets with $R_p>6R_\oplus$ orbiting with $P_p<300$\ d is $10.0 ^{+18}_{-6.5}$\% (95\% confidence limits), higher than but consistent with single star rates. If on the other hand the underlying planetary inclination distribution is isotropic, then this occurrence rate rises dramatically, to give a lower limit of 47\%. This implies that formation and subsequent dynamical evolution in circumbinary disks must either lead to largely coplanar planets, or proceed with significantly greater ease than in circumstellar disks. As a result of this investigation we also show that giant planets (${>}10R_\oplus$) are significantly less common in circumbinary orbits than their smaller siblings, and confirm that the proposed shortfall of circumbinary planets orbiting the shorter period binaries in the Kepler sample is a real effect.Comment: Accepted for publication in MNRAS (1st August 2014). 12 pages. Update to match final version, including clarifications and new figures. Results are unchange

The Radiology Fellowship Application and Selection Process in the United States: Experiences and Perceptions from Both Sides

Objective. Our purpose was to investigate radiology fellowship directors\u27 and recent fellows\u27 experiences and perceptions with regard to the fellowship application and selection process and to compare these experiences and perceptions. Materials and Methods. Institutional review board approval was obtained. We conducted an online survey of the memberships of three radiology subspecialty societies between October 2009 and December 2009 to learn about radiologists\u27 views regarding various aspects of radiology fellowships. Results. In the process of selecting fellows, program directors and recent fellows consider performance during the radiology residency and the quality or prestige of the residency program as the most important objective factors, and the personal interview, letters of recommendation, and personality as the most important subjective factors. 25% of the program directors were in the match, and 41% of the recent fellows were in the match. Most (48%) of program directors favored a match, but most (56%) of the recent fellows disfavored participating in a match. Both program directors and recent fellows expressed satisfaction with the fellowship application and selection process. Conclusion. There was no majority support for a fellowship match among program directors and recent fellows and less support among recent fellows. Recent fellows appear more satisfied with the current selection and application process than program directors

Clinical Use of Cinacalcet in MEN1 Hyperparathyroidism

Background. Management of multiple-endocrine neoplasia type 1- (MEN1-) associated hyperparathyroidism is associated with high recurrence rates and high surgical morbidity due to multiple neck explorations. Cinacalcet, a calcimimetic agent licensed for the treatment of secondary hyperparathyroidism and parathyroid carcinoma, may provide a medical alternative for the management of these complex patients. Methods. A prospective audit was performed of eight patients; three males and five females, aged 20–38 at diagnosis. Two patients commenced cinacalcet as primary treatment and six had previous surgery. Six patients had complications of hyperparathyroidism: renal calculi, renal dysfunction, and reduced bone mineral density. All were commenced on cinacalcet 30 mg bd for MEN1 associated hyperparathyroidism; doses were subsequently reduced to 30 mg od in four patients. Results. Significant reductions were observed in serum calcium and PTH measurements. Serum calcium reduced by a median of 0.35 mmol/L (P = .012 Wilcoxon Signed Rank). Serum PTH levels decreased by a median of 5.05 pmol/L (P = .012). There was no change in urine calcium. Duration ranged from 10–35 months with maintenance of control. Cinacalcet was well tolerated by six patients; one experienced nausea and one experienced diarrhoea. Conclusion. Cinacalcet is an effective and well-tolerated medical treatment for the management of complex primary hyperparathyroidism

Properties of Regge Trajectories

Early Chew-Frautschi plots show that meson and baryon Regge trajectoies are approximately linear and non-intersecting. In this paper, we reconstruct all Regge trajectories from the most recent data. Our plots show that meson trajectories are non-linear and intersecting. We also show that all current meson Regge trajectories models are ruled out by data.Comment: 30 pages, latex, 18 figures, to be published in Physical Review

Calderón Preconditioned PMCHWT Equations for Analyzing Penetrable Objects in Layered Medium

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