Global-in-time solutions for the isothermal Matovich-Pearson equations

In this paper we study the Matovich-Pearson equations describing the process of glass fiber drawing. These equations may be viewed as a 1D-reduction of the incompressible Navier-Stokes equations including free boundary, valid for the drawing of a long and thin glass fiber. We concentrate on the isothermal case without surface tension. Then the Matovich-Pearson equations represent a nonlinearly coupled system of an elliptic equation for the axial velocity and a hyperbolic transport equation for the fluid cross-sectional area. We first prove existence of a local solution, and, after constructing appropriate barrier functions, we deduce that the fluid radius is always strictly positive and that the local solution remains in the same regularity class. To the best of our knowledge, this is the first global existence and uniqueness result for this important system of equations

Characterization of polysilicon films by Raman spectroscopy and transmission electron microscopy: A comparative study

Samples of chemically-vapor-deposited micrometer and sub-micrometer-thick films of polysilicon were analyzed by transmission electron microscopy (TEM) in cross-section and by Raman spectroscopy with illumination at their surface. TEM and Raman spectroscopy both find varying amounts of polycrystalline and amorphous silicon in the wafers. Raman spectra obtained using blue, green and red excitation wavelengths to vary the Raman sampling depth are compared with TEM cross-sections of these films. Films showing crystalline columnar structures in their TEM micrographs have Raman spectra with a band near 497 cm{sup {minus}1} in addition to the dominant polycrystalline silicon band (521 cm{sup {minus}1}). The TEM micrographs of these films have numerous faulted regions and fringes indicative of nanometer-scale silicon structures, which are believed to correspond to the 497cm{sup {minus}1} Raman band