Newtonian and General Relativistic Models of Spherical Shells - II

A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by inversion transformations of spheres and of the finite shells. We also present a family of double shells with finite thickness. All potential-density pairs are analytical and can be stated in terms of elementary functions. For the above-mentioned structures, we study the circular orbits of test particles and their stability with respect to radial perturbations. All examples presented are found to be stable. A particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian families of spheres and shells. The matter of these structures is anisotropic, and the degree of anisotropy is a function of the radius.Comment: 22 pages, 7 figures, accepted for publication in MNRA

A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations

The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye for general second order elliptic problems on triangular meshes. The goal of this paper is to conduct a computational investigation for the weak Galerkin method for various model problems with more general finite element partitions. The numerical results confirm the theory established by Wang and Ye. The results also indicate that the weak Galerkin method is efficient, robust, and reliable in scientific computing.Comment: 19 page

Charge distribution in two-dimensional electrostatics

We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)=\sum_i |z_i|^2-\sum_{i<j} ln|z_i-z_j|^2$. We interpret the equilibrium distributions in terms of a shell model and compare predictions of the model with the results of numerical simulations for systems with up to 100 particles.Comment: LaTe

Caustics of Compensated Spherical Lens Models

We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect.Comment: 21 pages, 5 ps figures, eps

Real-time beam-profile monitor for a medical cyclotron

Introduction Measuring the beam profile on a medical cyclo-tron in real time can aid in improved tuning of the cyclotron and give important information for a smooth operation. Typically the beam profile is measured by an autoradiography technique or even by a scintillator that can be viewed in real time [1, 2]. Another method is to use collimators in front of the target to assess the beam center-ing [3]. All these methods have potential draw-backs including; an inability to monitor the beam in real time for the radiograph, exhibiting a non-linear correlation in signal response to the power deposited for a scintillator, and not providing a 2-dimensional profile of the complete beam for collimators. Our goal was to design a realtime, linear, 2-dimensional beam-profile monitor that is able to withstand the high power of a PET cyclotron. Material and Methods The beam-profile monitor (PM) is designed for the TR13, a 13MeV negative hydrogen-ion cyclotron at TRIUMF. The design follows the concept of a ‘harp’ monitor, widely used at TRIUMF for tuning proton and radioactive ion beams, and is installed on the extraction port without separation from the tank vacuum. The TR13 monitor is designed to withstand a 13 MeV proton beam with a beam current of up to 25 µA, has an active area of 10 by 10 mm and does not affect the 10-7 torr tank vacuum. The device consists of a water-cooled Faraday cup made out of aluminium for low activation and two orthogonal rows of eight tungsten electrodes each mounted on a water-cooled support frame. Electrodes are spaced 1 mm apart from each other, see FIG. 1. The electrodes are electrically isolated from each other and each has a current pickup soldered to it. The material and the shape of the electrodes are optimized to withstand the deposited power of the proton beam. A voltage of -90 V is applied to the electrodes to repel secondary electrons and prevent crosstalk between neighbouring electrodes. The electrode current is amplified using a custom current amplifier, and read by an ADC. From there, the current data is displayed on a PC. This allows one to observe changes of the beam profile in real time. The electronics are designed to read out all sixteen channels in parallel, or, if only a limited number of ADC channels are available, to cycle through the different channels. In our current setup all sixteen channels are read out simultaneously. Results and Conclusion The beam-profile monitor provides a real-time representation of the proton beam, see FIG. 2. The data can also be recorded and analyzed at a later time. The linearity of the monitor has been measured up to 30 µA of proton beam current [4]. With the use of the monitor, it was possible to increase the output of the ion source into the target by 50% in comparison to the standard tune

Unconventional MBE Strategies from Computer Simulations for Optimized Growth Conditions

We investigate the influence of step edge diffusion (SED) and desorption on Molecular Beam Epitaxy (MBE) using kinetic Monte-Carlo simulations of the solid-on-solid (SOS) model. Based on these investigations we propose two strategies to optimize MBE growth. The strategies are applicable in different growth regimes: During layer-by-layer growth one can exploit the presence of desorption in order to achieve smooth surfaces. By additional short high flux pulses of particles one can increase the growth rate and assist layer-by-layer growth. If, however, mounds are formed (non-layer-by-layer growth) the SED can be used to control size and shape of the three-dimensional structures. By controlled reduction of the flux with time we achieve a fast coarsening together with smooth step edges.Comment: 19 pages, 7 figures, submitted to Phys. Rev.

Focused Ion Beam Fabrication

Contains summary of research program and reports on four research projects.Charles Stark Draper Laboratory (Contract DL-H-225270)Hughes Research LaboratoriesInternational Business Machines, Inc. (Contract 456614)Nippon Telegraph and Telephone, Inc.U.S. Navy - Office of Naval Research (Contract N00014-84-K-0073)U.S. Department of Defense (Contract MDA903-85-C-0215)Hitachi Central Research Laborator

The deuteron: structure and form factors

A brief review of the history of the discovery of the deuteron in provided. The current status of both experiment and theory for the elastic electron scattering is then presented.Comment: 80 pages, 33 figures, submited to Advances in Nuclear Physic