An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Conducting polymer diffraction gratings on gold surfaces created by microcontact printing and electropolymerization at submicron length scales

Conducting polymer diffraction gratings on Au substrates have been created using microcontact printing of C18-alkanethiols, followed by electropolymerization of either poly(aniline) (PANI) or poly(3,4-ethylenedioxythiophene) (PEDOT). Soft-polymer replicas of simple diffraction grating masters (1200 lines/mm) were used to define the alkanethiol template for polymer growth. Growth of PANI and PEDOT diffraction gratings was followed in real time, through in situ tapping-mode atomic force microscopy, and by monitoring diffraction efficiency (DE) as a function of grating depth. DE increased as grating depth increased, up to a limiting efficiency (13-26%, with white light illumination), defined by the combined optical properties of the grating and the Au substrate, and ultimately limited by the loss of resolution due to coalescence of the polymer films. Grating efficiency is strongly dependent upon the grating depth and the refractive index contrast between the grating material and the surrounding solutions. Both PEDOT and PANI gratings show refractive index changes as a function of applied potential, consistent with changes in refractive index brought about by the doping/dedoping of the conducting polymer. The DE of PANI gratings are strongly dependent on the pH of the superstrate solution; the maximum sensitivity (DeltaDE/DeltapH) is achieved with PANI gratings held at +0.4 V versus Ag/AgCl, where the redox chemistry is dominated by the acid-base equilibrium between the protonated (emeraldine salt) and deprotonated (emeraldine base) forms of PANI. Simulations of DE were conducted for various combinations of conducting polymer refractive index and grating depth, to compute sensitivity parameters, which are maximized when the grating depth is ca. 50% of its maximum obtainable depth.     

Probing RNA hairpins with cobalt(III)hexammine and electrospray ionization mass spectrometry

In this work, electrospray ionization mass spectrometry (ESI MS) was employed to study the interactions of cobalt(III) hexammine, Co(NH3)6(3+), with five RNA hairpins representing the 790 loop of 16S ribosomal RNA and 1920 loop of 23S ribosomal RNA. The RNAs varied in mismatch identity (G.U versus A.C) and level of base modification (pseudouridine versus uridine). Co(NH3)6(3+) binding was observed with the four RNA hairpins that contained a G.U wobble pair in the stem region. ESI MS revealed 1:1 and 1:2 complex formation with all RNAs. Weaker binding was observed with the fifth RNA hairpin that contained an A.C wobble pair in the stem region. The effects of pH on Co(NH3)6(3+) binding were also examined.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.