Well-posedness of Hydrodynamics on the Moving Elastic Surface

The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the dynamic equations of the two-dimensional fluid, and the incompressible equation, all of which operate within a curved geometry. In this paper, we prove the local existence and uniqueness of the solution to the reduced elastic surface model by reformulating the model into a new system in the isothermal coordinates. One major difficulty is that of constructing an appropriate iterative scheme such that the limit system is consistent with the original system.Comment: The introduction is rewritte

Atomic scale structure of the 5-fold surface of an AlPdMn quasicrystal: A quantitative X-Ray photoelectron diffraction analysis

The atomic scale structure of the 5-fold symmetric surface of an AlPdMn quasicrystal is investigated quantitatively by comparing x-ray photoelectron diffraction (XPD) simulations to experiment. The observed 5-fold symmetry of the diffraction patterns indicates that the surface is quasicrystalline with no hint of a reconstruction from the bulk structure. In analyzing the experimental data, many possible bulk terminations have been tested. Those few that fit best to the data have in common that they contain an Al-rich surface layer followed by a dense mixed Al/Pd/Mn layer. These best terminations, while not identical to each other, are suggested to form terraces coexisting on a real surface. Structural relaxations of the quasicrystal surface are also analyzed: mixing several best-fit terminations gives average best-fit interlayer spacing changes of Dd12 = -0.057 Angstrom, Dd24 = +0.159 Angstrom. These results are in good agreement with a prior structure determination by LEED on a sample that was prepared in a different manner