C. C. Chancey
American Journal of Undergraduate Research, University of Northern Iowa, Cedar Falls, Iowa 50614-0150 USA
Authors and Affiliations:
Department of Mathematics, Grand Valley State University, 1 Campus Drive. Allendale, Michigan 49401 USA
Division of Science & Mathematics Education, Michigan State University, 116 North Kedzie Hall, East Lansing, Michigan 48824 USA
The outer billiard dynamical system models the motion of a particle around a compact domain, such as a planet orbiting a star. When considering outer billiards in hyperbolic space, an interesting problem is to determine precisely the conditions in which an orbiting particle breaks orbit and escapes to infinity. Past work has classified triangular and Penrose kite billiard tables according to whether or not their orbiting particles escape. This article presents a classification of regular polygonal tables.
Joseph Hashem, Tiankuan Liu, Zhihua Liang, and Jingbo Ye
Department of Physics, Southern Methodist University, Dallas, Texas 75275 USA
We present an experimental method based on Ohm’s Law to calibrate the Keithley 6485 picoammeter with the calibration error less than 0.4 pico-ampere (pA), which is specified as the highest sensitivity of this instrument. The maximum calibration difference between the measurement current and the calibration current in the picoammeter’s 2 nano-ampere (nA) range is 0.25 pA. This difference is far less than the highest accuracy, 0.4 pA, specified by the instrument. Measurement errors are estimated and discussed.
Authors and Affiliations:
Chemical and Biological Engineering Department, Princeton University, Princeton, New Jersey 08544 USA
Michael J. Kelley
Applied Science, Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 USA
The focus of this project was to design and construct a model controlled-flow apparatus to study electropolishing of one cm2 niobium coupons at surface flow rates typical of cavity processing. A simulation of the apparatus was constructed using CFDesign, a flow and thermal simulation software, to ensure that the selected dimensions may be expected to provide steady-state, laminar flow across the surface of the niobium coupon. Based on these dimensions, a sample system and apparatus was produced to determine the correct reservoir elevation heights for the desired flow rates for fluid viscosities represented in the mixed acid electrolyte. From the CFDesign simulations, it was found that the flow channel supplied laminar flow rates when the center of the niobium coupon was located 40 mm downstream from the inlet stream. The corresponding system, based on the CFDesign simulations, showed that the reservoir elevation heights for flow rates of 0 cm/s to 5 cm/s ranged from 0 to 1.27 cm. The correlation between pressure heads and flow rates has been analyzed and an equation for flow rate was determined using experimental results. The detailed dimensions regarding the flow channel and information regarding the respective pressure heads serve as resources to finding the optimal flow rate for electropolishing the niobium cavities. Although previous research has found a correlation between the quality of electropolishing and internal surface flow rates, research facilities, including Jefferson Lab, did not have the equipment to pursue further analysis. Each nine-cell niobium cavity costs over $50,000, so it is cost prohibitive to use real cavities to conduct early stage research. The prototype built through this research work provides a cost effective alternative. It can be used to validate some of the theoretical results obtained through simulation. In addition, the device allows for easy variable measurements that are either difficult or impractical with an enclosed niobium cavity, as sensors can be embedded into the device in the construction stage. Moreover, the data collected through our experiment furthers superconducting radiofrequency (SRF) technology by allowing Jefferson Lab to design a more effective electropolishing process.