Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

High resolution infrared spectra of bulge globular clusters: Liller~1 and NGC 6553

Using the NIRSPEC spectrograph at Keck II, we have obtained echelle spectra covering the range 1.5-1.8um for 2 of the brightest giants in Liller 1 and NGC 6553, old metal rich globular clusters in the Galactic bulge. We use spectrum synthesis for the abundance analysis, and find [Fe/H]=-0.3 +/- 0.2 and [O/H]=+0.3 +/- 0.2 dex. The composition of the clusters is similar to that of field stars in the bulge and is consistent with a sceanrio in which the clusters formed early, with rapid enrichment. We have dificulty achieveing a good fit to the spectrum of NGC 6553 using either the low or the high values recently reported in the literature, unless unusually large, or no alpha-element enhancements are adopted, respectively.Comment: To appear in the Astronomical Journal, March 200

Diseño y fabricación de microinductor planar para microválvula activa para el tratamiento de glaucoma utilizando tecnología MEMS

This paper presents the modeling, design and characterization of planar microinductor, to be used in telemetry systems that supply energy to miniaturized implants. First, a model for the electrical characteristics of planar coils will be discussed. Parasitic electrical effects that may become important at AC-frequencies of several MHz are evaluated. The fabrication process and electrical characterization of planar microcoils will be described. Different configurations of planar microinductor were made with the use of micromachining technologies such as thin film deposition, standard photolithography processes and electroplating. With this technology small coils are relatively easy to fabricate reproducibly. The parameters and performance of fabricated inductor will be evaluated by electrical measurements. Measurements show a good agreement between calculated and measured values.Centro de Técnicas Analógico-Digitale