On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow

In this article, we study the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older regular surfaces of revolution embedded in R^3 and satisfying periodic boundary conditions. We also give conditions for global existence of solutions and prove that solutions are real analytic in time and space. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability and bifurcation behavior, with the radius acting as a bifurcation parameter for the problem.Comment: 37 pages, 6 figures, To Appear in SIAM J. Math. Ana

THE ELECTRONIC SPECTRUM OF TANTALUM METHYLIDYNE, TaCH

$^{*}$ Present address: School of Chemistry, University of Sydney, Building P11, Sydney, N. S. W. 2006. Australia.Author Institution: Department of Chemistry, University of British ColumbiaTantalum methylidyne, TaCH, has been produced in a supersonic free jet expansion in helium by the reaction between laser ablated tantalum and methan e. TaCD has been made similarly using $CD_{4}$. Pulsed dye laser excitation spectra from the $\Omega=0 (\tilde{X}\Sigma^{+}$) state of TaCH have been assigned to two electronic transitions whose upper states have $\Omega=0^{+}$ which proably is $^{3}\Pi$, and $\Omega=1$. The (0,0) bands of these states lie at 15638.6 cm $^{-1}$ and 16398.3 cm $^{-1}$, respectively. Wavelength resolved fluorescence emission from the $\Omega=O^{+}$ excited state has revealed a low lying $\Omega=1$ electronic state $3620 cm^{-1}$ above the ground state; this appears to be a $^{3}\Delta$ state. Two of the $\tilde{X}$ state vibrational fundamentals have been determined for TaCH(TaCD): $\nu_{2}=641(492)$ cm $^{-1}$ and $\nu_{3} = 955(910)$ cm $^{-1}$. The values determined for the $a^{3}\Delta_{t}$ state were $\nu_{2}= 606(449)$ cm $^{-1}$ and $\nu_{3} = 925(864)$ cm $^{-1}$. High resolution spectra are being recorded for selected bands; these will allow the molecular structure and the spectroscopic parameters to be detedmined accurately. The magnetic and quadrupolar hyperfine structure of $^{181}$Ta is fully resolved in the high resolution study

A variational problem for constant mean curvature surfaces with free boundary

SIGLETIB: RN 4020 (768) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Focus on London

Includes bibliographical referencesAvailable from British Library Document Supply Centre- DSC:3964. 2177(2003) / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo