Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering

Standard numerical methods for the Birkhoff-Rott equation for a vortex sheet are unstable due to the amplification of roundoff error by the Kelvin-Helmholtz instability. A nonlinear filtering method was used by Krasny to eliminate this spurious growth of round-off error and accurately compute the Birkhoff-Rott solution essentially up to the time it becomes singular. In this paper convergence is proved for the discretized Birkhoff-Rott equation with Krasny filtering and simulated roundoff error. The convergence is proved for a time almost up to the singularity time of the continuous solution. The proof is in an analytic function class and uses a discrete form of the abstract Cauchy-Kowalewski theorem. In order for the proof to work almost up to the singularity time, the linear and nonlinear parts of the equation, as well as the effects of Krasny filtering, are precisely estimated. The technique of proof applies directly to other ill-posed problems such as Rayleigh-Taylor unstable interfaces in incompressible, inviscid, and irrotational fluids, as well as to Saffman-Taylor unstable interfaces in Hele-Shaw cells.

     

Global existence,singular solutions,and ill‐posedness for the Muskat problem

The Muskat, or Muskat‐Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele‐Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele‐Shaw problem (the one‐phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable, forward Muskat problem, in which the higher‐viscosity fluid expands into the lower‐viscosity fluid, we show global‐in‐time existence for initial data that is a small perturbation of a flat interface. The initial data in this result may contain weak (e.g., curvature) singularities. For the unstable, backward problem, in which the higher‐viscosity fluid contracts, we construct singular solutions that start off with smooth initial data but develop a point of infinite curvature at finite time. © 2004 Wiley Periodicals, Inc.     

Synthesis and characterization of LaFeO3 powders prepared by a mixed mechanical/thermal processing route

Lanthanum ferrite, LaFeO₃ (LF), has raised considerable interest since it can be used in many applications such as solid-oxide fuel cell electrode, sensor material (H₂O and ethanol) and catalyst. Since the conventional ceramic route of synthesis has some disadvantages, mainly related to an exaggerated grain growth, LF has been prepared by different methods including combustion synthesis, sol–gel, hydrothermal processes, polymerizable complex method and mechanochemistry. As concerns this last method, a problem occurs due to the moisture sensitivity of La2O₃. To overcome the problem, we used lanthanum acetate sesquihydrate [La(CH₃COO)₃·1.5H₂O] and iron (II) oxalate dehydrate [FeC₂O₄·2H₂O] as precursors. The mechanism of the solid-state reactions in the mixtures has been studied by TG–DSC and XRPD. Synthesis of LaFeO₃ has been realized by annealing the mechanically activated mixtures for 3 h at temperatures between 500 and 800 °C. While LF prepared at 500 °C < T < 600 °C has an amorphous character, LF obtained at T ≥ 600 °C is free from carbonaceous impurities as it is shown by FT-IR and TG measurements. The specific area of the LaFeO₃ powders obtained starting from the mechanically activated mixture is decreasing by increasing the annealing temperature. On the contrary, the annealing on samples of physical mixture at temperatures up to 800 °C only yields a mixture of LaFeO₃, La₂O₃ and Fe₂O₃.

     

Combined cup loading, bis(2-hydroxyethyl) disulfide, and protein precipitation protocols to improve the alkaline proteome of Lactobacillus hilgardii

Despite the large number of papers dealing with bacterial proteomes, very few include information about proteins with alkaline pI's, because of the limits inherent in 2-DE technology. Nonetheless, analyses of in silico proteomes of many prokaryotes show a bimodal distribution of their proteins based on their pI's; the most crowded areas lying between pI 4-7 and 9-11. The aim of the present research was to set up a general, simple, and standardizable 2-DE protocol suitable for studying the alkaline proteome of Lactobacillus hilgardii, a Gram-positive bacillus isolated from wine. The method has also been tested on a Gram-negative bacterium able to degrade aromatic pollutants, Acinetobacter radioresistens S13. Optimization of the method was mainly focused on improving protein extraction and IEF (pI 6-11) separation protocols. Concerning IEF, different methods for sample loading (in-gel rehydration and cup loading), and different reducing agents (DTT and bis(2-hydroxyethyl) disulfide (HED)) were tested and compared. The proposed protocol was found to resolve efficiently alkaline proteins from both of our Lactobacillus and Acinetobacter strains, in spite of their different external layers, thus, enabling a more comprehensive study of their proteomes.     

The Time Scale of Electronic Resonance in Oxidized DNA as Modulated by Solvent Response: An MD/QM-MM Study

The time needed to establish electronic resonant conditions for charge transfer in oxidized DNA has been evaluated by molecular dynamics simulations followed by QM/MM computations which include counterions and a realistic solvation shell. The solvent response is predicted to take ca. 800–1000 ps to bring two guanine sites into resonance, a range of values in reasonable agreement with the estimate previously obtained by a kinetic model able to correctly reproduce the observed yield ratios of oxidative damage for several sequences of oxidized DNA.     

Docking small ligands in flexible binding sites

A novel procedure for docking ligands in a flexible binding site is presented. It relies on conjugate gradient minimization, during which nonbonded interactions are gradually switched on. Short Monte Carlo minimization runs are performed on the most promising candidates. Solvation is implicitly taken into account in the evaluation of structures with a continuum model. It is shown that the method is very accurate and can model induced fit in the ligand and the binding site. The docking procedure has been successfully applied to three systems. The first two are the binding of progesterone and 5β-androstane-3,17-dione to the antigen binding fragment of a steroid binding antibody. A comparison of the crystal structures of the free and the two complexed forms reveals that any attempt to model binding must take protein rearrangements into account. Furthermore, the two ligands bind in two different orientations, posing an additional challenge. The third test case is the docking of N^α-(2-naphthyl-sulfonyl-glycyl)-D -para-amidino-phenyl-alanyl-piperidine (NAPAP) to human α-thrombin. In contrast to steroids, NAPAP is a very flexible ligand, and no information of its conformation in the binding site is used. All docking calculations are started from X-ray conformations of proteins with the uncomplexed binding site. For all three systems the best minima in terms of free energy have a root mean square deviation from the X-ray structure smaller than 1.5 Å for the ligand atoms. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 21–37, 1998