ALTKAL: An optimum linear filter for GEOS-3 altimeter data

ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively

A Class of Free Boundary Problems with Onset of a new Phase

A class of diffusion driven Free Boundary Problems is considered which is characterized by the initial onset of a phase and by an explicit kinematic condition for the evolution of the free boundary. By a domain fixing change of variables it naturally leads to coupled systems comprised of a singular parabolic initial boundary value problem and a Hamilton-Jacobi equation. Even though the one dimensional case has been thoroughly investigated, results as basic as well-posedness and regularity have so far not been obtained for its higher dimensional counterpart. In this paper a recently developed regularity theory for abstract singular parabolic Cauchy problems is utilized to obtain the first well-posedness results for the Free Boundary Problems under consideration. The derivation of elliptic regularity results for the underlying static singular problems will play an important role

Uniqueness of a Negative Mode About a Bounce Solution

We consider the uniqueness problem of a negative eigenvalue in the spectrum of small fluctuations about a bounce solution in a multidimensional case. Our approach is based on the concept of conjugate points from Morse theory and is a natural generalization of the nodal theorem approach usually used in one dimensional case. We show that bounce solution has exactly one conjugate point at $\tau=0$ with multiplicity one.Comment: 4 pages,LaTe

Techniques for measuring atmospheric aerosols at the High Resolution Fly's Eye experiment

We describe several techniques developed by the High Resolution Fly's Eye experiment for measuring aerosol vertical optical depth, aerosol horizontal attenuation length, and aerosol phase function. The techniques are based on measurements of side-scattered light generated by a steerable ultraviolet laser and collected by an optical detector designed to measure fluorescence light from cosmic-ray air showers. We also present a technique to cross-check the aerosol optical depth measurement using air showers observed in stereo. These methods can be used by future air fluorescence experiments.Comment: Accepted for publication in Astroparticle Physics Journal 16 pages, 9 figure

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

Highly efficient single photon emission from single quantum dots within a two-dimensional photonic bandgap

We report highly efficient single photon generation from InGaAs self-assembled quantum dots emitting within a two-dimensional photonic bandgap. A strongly suppressed multiphoton probability is obtained for single quantum dots in bulk GaAs and those emitting into the photonic bandgap. In the latter case, photoluminescence saturation spectroscopy is employed to measure a ~17 times enhancement of the average photon extraction efficiency, when compared to quantum dots in bulk GaAs. For quantum dots in the photonic crystal we measure directly an external quantum efficiency up to 26%, much higher than for quantum dots on the same sample without a tailored photonic environment. The results show that highly efficient quantum dot single photon sources can be realized, without the need for complex nanopositioning techniques