From: "Becky L. Klein" <bezell@soe.ucsc.edu> Date: Fri, 1 Jun 2001 16:16:51 -0700 Subject: Upcoming AMS Seminar Message-Id: <p04330110b73dcfc3947f@[128.114.135.62]>
The University of California, Santa Cruz Jack Baskin School of Engineering Applied Sciences and Statistics Seminar Presents " An efficient method to obtain numerical solutions for periodic orbits of the n-body problem." By Michael Nauenberg Professor of Physics University of California, Santa Cruz Friday, June 8, 2001 12:30 pm-1:30 pm Baskin Engineering Room 330 ABSTRACT: Since Newton's pioneering work on lunar theory, the 3-body problem in dynamics has been a major challenge to mathematical physics. Following the work of Cris Moore in 1993 on a general classification of possible periodic orbits in a plane, recently several new orbits have been discovered for the special case of equal mass bodies which travel on a common orbital curve. In particular, for the case of three bodies, Moore found a periodic orbit in the shape of a figure eight which recently was re-discovered independently by Richard Montgomery and Alan Chenciner who have given an existence proof for the special case of zero angular momentum. In this talk I will review some of these new results, and discuss an efficient numerical method to obtain such orbits, and to discover new ones. As examples, I will discuss the extension of the figure eight orbit to finite angular momentum and show that for certain attractive power law forces the classic 1772 solution of Lagrange for three equal mass particles is the limit of a family of orbits which are periodic in a uniformly rotating frame. Some numerical results for n bodies of equal mass, and for three bodies of different masses will also be presented. Bio: Nauenberg received his Ph.D in physics at Cornell (with H. Bethe) and taught at Columbia and Stanford before coming to the University of California at Santa Cruz in 1966. He was one of the founding members of its Physics Dept. where he is now Professor Emeritus. His primary research interests are in particle physics, condensed matter physics, and nonlinear dynamics, and he has written numerous articles in these areas publications. His most recent work is on a new quantum mechanical treatment of neutrino and neutral meson oscillations and on the dynamics of wave packets in weak external fields. Host: Professor Neil Balmforth ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Anyone needing special arrangements to accommodate a disability is encouraged to call Becky Klein at the Baskin School of Engineering, (831) 459-2970.
From: "Becky L. Klein" <bezell@soe.ucsc.edu> Date: Fri, 1 Jun 2001 08:47:17 -0700 Subject: This Week's Condensed Matter Seminar Message-Id: <p04330102b73d696b88c8@[128.114.135.62]>
UCSC Physics Dept. Condensed Matter Seminar DATE: FRIDAY, JUNE 1, 2001 TIME: 2:00 p.m. LOCATION: KERR 289 http://physics.ucsc.edu/events/condensed.html Host: Bud Bridges ********************************************************************** Speaker: Daliang Cao Title: Local Structure Study of the Negative Thermal Expansion Material: ZrW<sub>2</sub>O<sub>8</sub> Abstract: A local structure study of ZrW<sub>2</sub>O<sub>8</sub> was carried out using the X-ray Absorption Fine Structure (XAFS) technique at the W L<sub>III</sub>- and Zr K-edge. ZrW<sub>2</sub>O<sub>8</sub> shows a very interesting isotropic negative thermal expansion (NTE) effect over a very large temperature range (5 to 1000~K). It has been proposed that the lattice contraction is due to the transverse O vibrations on Zr-O-W bonds, which induces a tilt of the WO<sub>4</sub> tetrahedra. XAFS measurements as a function of temperature on this sample shows that W-O pair distribution width, sigma, has almost no change from 5 K up to 315 K; sigma for the Zr-O bond also changes little with temperature, which agrees with the rigid unit mode (RUM) model used. In addition, sigma for the W-Zr pair also doesn't change very much with temperature; there is only a small broadening as the temperature increases from 5 K to 315 K. This appears inconsistent with the prediction that the transverse vibrations on the Zr-O-W bond induce the NTE effect in this sample. XAFS result shows that sigma for the W<sub>1</sub>-W<sub>2</sub> pair has a very large temperature dependences, as does sigma for the Zr-Zr pair. This indicates that the WO<sub>4</sub> tetrahedra and its three nearest ZrO<sub>6</sub> octahedra are rigidly connected, and the NTE in this material is due to the correlated vibrations between WO<sub>4</sub> tetrahedra and ZrO<sub>6</sub> octahedra.