A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems

FEM discretizations of arbitrary order r are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.     

Investigation of lengthscales, scalar dissipation, and flame orientation in a piloted diffusion flame by LES

This work investigates the structure of a diffusion flame in terms of lengthscales, scalar dissipation, and flame orientation by using large eddy simulation. This has been performed for a turbulent, non-premixed, piloted methane/air jet flame (Flame D) at a Reynolds-number of 22,400. A steady flamelet model, which was represented by artificial neural networks, yields species mass fractions, density, and viscosity as a function of the mixture fraction. This will be shown to suffice to simulate such flames. To allow to examine scalar dissipation, a grid of 1.97 × 10⁶ nodes was applied that resolves more than 75% of the turbulent kinetic energy. The accuracy of the results is assessed by varying the grid-resolution and by comparison to experimental data by Barlow, Frank, Karpetis, Schneider (Sandia, Darmstadt), and others. The numerical procedure solves the filtered, incompressible transport equations for mass, momentum, and mixture fraction. For subgrid closure, an eddy viscosity/diffusivity approach is applied, relying on the dynamic Germano model. Artificial turbulent inflow velocities were generated to feature proper one- and two-point statistics. The results obtained for both the one- and two-point statistics were found in good agreement to the experimental data. The PDF of the flame orientation shows the tilting of the flame fronts towards the centerline. Finally, the steady flamelet approach was found to be sufficient for this type of flame unless slowly reacting species are of interest.     

Maturation of the lantibiotic subtilin: matrix-assisted laser desorption/ionization time-of-flight mass spectrometry to monitor precursors and their proteolytic processing in crude bacterial cultures.

Bacillus subtilis synthesizes the lanthionine containing 32-amino-acid peptide antibiotic (lanti-biotic) subtilin from a ribosomally generated 56-amino-acid precursor pre-propeptide by extensive posttranslational modifications. Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) was used to monitor the production of matured subtilin within crude samples taken from B. subtilis culture media without prior fractionation. The processing reaction of subtilin was blocked with the serine protease inhibitor phenylmethylsulfonyl fluoride and different subtilin precursor peptides in the molecular mass range up to 6220 were observed. Two of these species were isolated by reversed-phase high-performance liquid chromatography (HPLC) and structurally analyzed by post-source decay MALDI-TOFMS. We provide evidence that the precursor species comprise the posttranslational modified C-terminal part of subtilin to which leader peptide moieties with different chain lengths are attached. These antimicrobial-inactive species could be processed to antibiotic-active subtilin by incubation with culture media of different subtilin-nonproducing B. subtilis strains as indicated by a combination of antimicrobial growth assays and MALDI-TOFMS analyses. These achievements are strong evidence for the sensitivity of MALDI-TOFMS methodology that allows straightforward investigations of analytes even in complex mixtures without time-consuming sample preparations.     

Toward an understanding of white-light generation in cubic media - polarization properties across the entire spectral range

We present an extensive investigation of the polarization properties of a femtosecond-laser-induced white-light (WL) continuum generated in a cubic crystal (CaF(2)). The WL spectrum and threshold energies have been examined for input polarizations with various degrees of ellipticity. For linear input polarization, the WL spectrum shows strong depolarization around the input wavelength, while the preservation of the input polarization is pronounced toward the blue spectral region. The observed depolarization effect has been elucidated in the framework of current models for WL generation.