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

Human Brainstem Auditory-Evoked Potentials in Deep Experimental Diving to Pressures up to 62,5 bar

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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

STRONG VIBRONIC COUPLING IN THE VISIBLE SYSTEMS OF YOH AND YOD

Author Institution: Department of Chemistry, University of New Brunswick; Department of Chemistry, University of British Columbia; Lambda-Physik, Inc., 3201 West Commercial Blvd.Extensive new spectra have been taken for the visible systems of YOH and YOD, in an attempt to establish the vibrational assignments in the very confused $\bar{B}^{1}\Pi$ and $\widetilde{C}^{1}\Sigma^{+}$ states. It turns out that there is very strong vibronic coupling through the bending vibration between the $\widetilde{C}^{1}\Sigma^{+}$ state and the $A^{\prime}$ (lower) Born-Oppenheimer component of the $\tilde{B}^{1}\Pi$ state. The effect is that the bending frequency of the $\bar{C}^{1}\Sigma^{+}$ state is increased by 50\% relative to the ground state, while that of the $A^{\prime}$ component of the $\widetilde{B}^{1}\Pi$ state is reduced so far that the molecule becomes non-linear, with a potential barrier of about $120 cm^{-1}$ at the linear configuration; the $A^{\prime \prime}$ (upper) component of the $\widetilde{B}^{1}\Pi$ state is not affected. The principal evidence for the barrier is that the 010 $\Sigma^{+}$ vibronic level lies $1.4 cm^{-1}$ below the 000 level (linear molecule notation) in the $\widetilde{B}^{1}\Pi$ state of YOD. The density of the level structure in the $\widetilde{C}^{1}\Sigma^{+}$ state arises partly because higher levels of the $\widetilde{B}^{1}\Pi$ state lying among the levels of the $\widetilde{C}^{1}\Sigma^{+}$ state gain intensity through the vibronic coupling