Chirped pulse amplification in single mode Tm:fiber using a chirped Bragg grating

We report femtosecond pulse generation and chirped pulse amplification in Tm:fiber. A mode-locked oscillator operating in the soliton regime produced 800 fs pulses with 5 nm spectral bandwidth, at 40 pJ pulse energy. This oscillator seeded a pre-amplifier that utilizes a Raman soliton self-frequency shift to produce wavelength tunable pulses with 3 nJ energy, reduced pulse duration of 150 fs, and increased bandwidth of 30 nm. For further amplification, the pulses were stretched up to 160 ps using a chirped Bragg grating (CBG). Stretched pulses were amplified to 85 nJ after compression in single-mode Tm:fiber and recompressed with the CBG as short as 400 fs. Compressed pulses were coupled into a highly nonlinear tellurite fiber to investigate the potential of this ultrashort pulse 2-μm fiber source as a pump for mid-IR supercontinuum generation.     

Planar rectifiable curves are determined by their projections

In 1954 Steinhaus raised the question of whether a rectifiable curve is characterized by its projections. A projection onto a lineG at the pointp counts the number of points in the set which lie on the line which is perpendicular toG and passes throughp. We prove this is so, and give a method to reconstruct a closed connected rectifiable set from its projections.     

Riemannian Foliations and Eigenvalue Comparison

Eigenvalue comparison theorems for the Laplacian on a Riemannian manifold generally give bounds for the first Dirichlet eigenvalue on balls in the manifold in terms of an eigenvalue arising from a geometrically or analytically simpler situation. Cheng's eigenvalue comparison theory assumes bounds on the curvature of the manifold and then compares this eigenvalue to the eigenvalue of a ball in a constant curvature space form. In this paper we examine the basic Laplacian – the appropriate Laplacian on functions that are constant on the leaves of the foliation. The main theorems generalize Cheng's eigenvalue comparison theorem and other eigenvalue comparison theorems to the category of Riemannian foliations by estimating the first Dirichlet eigenvalue for the basic Laplacian on a metric tubular neighborhood of a leaf closure. Several other facts about the the first eigenvalue of such foliated tubes as well as some needed facts about the tubes themselves are established. This comparison theory, like Cheng's theorem, remains valid for large tubes that are not homotopic to the middle leaf closure and that may have irregular boundaries. We apply these results to obtain upper bounds for the eigenvalues of the basic Laplacian on a closed manifold in terms of curvature bounds and the transverse diameter of the foliation.     

Preparation and performance of a perovskite-type tubular membrane for the partial oxidation of methane

Thin-walled (∼200 μm) tubular membranes intended for the catalytic partial oxidation of natural gas have been manufactured from La_0.6Sr_0.4Co_0.2Fe_0.8O_3−δ (LSCF) powders using viscous plastic processing technology. The perovskite-type powders were synthesised using various conventional and novel techniques. The tubes have been characterised using a custom-built gas analysis rig with on-line mass spectrometry. Porosity levels of the membranes were found to be very low (<0.5%) as calculated using a mass spectrometry leakage test. This was confirmed by microstructural analysis of polished cross-sections using SEM. The spontaneous oxygen flux across the tubular membranes was determined as a function of temperature. Oxygen permeation rates were found to range from 0.1 to 0.3 μmol cm⁻²s⁻¹ at 1273 K. Paper presented at the 9th EuroConference on Ionics, Ixia, Rhodes, Greece, Sept. 15 – 21, 2002.     

Zur Bestimmung des Kalis und Natrons in Pflanzenaschen und ?hnlichen Substanzen

Ohne Zusammenfassung     

Hele Shaw Flows with Time-Dependent Free Boundaries Involving Injection Through Slits

Consider the classical Hele Shaw situation with two parallel planes separated by a narrow gap. Suppose a Newtonian fluid to be injected into this gap through straight-line slits as well as, possibly, at isolated points. We are interested in predicting the plan-view of the resultant expanding blob, or blobs, of fluid. We show that the method of solution developed earlier for dealing with such problems when the injection is only at isolated points can be adapted to yield solutions in this more general situation.     

A synchrotron radiation study of the electronic and geometric structure of CO on Pt{110}

Using both synchrotron and HeII radiation the electronic and geometric structure of Pt{110}-(2×1)p1g1 CO was examined. The shape resonance for the 4σ orbital of CO is found to be peaked at 38 eV, while that for the 5σ orbital is peaked at 28 eV. No shape resonance is observed from the 1π orbital. The $\text{5σ}\text{1π}$ ordering is reversed from that of gas phase CO. Further evidence, from the polar intensity variation of the non-bonding 4σ orbital, is presented for the tilted CO structure proposed previously.