A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

Trichothiazole A,a dichlorinated polyketide containing an embedded thiazole isolated from Trichodesmium blooms

Mass spectrometry-guided isolation of the lipophilic extract of Trichodesmium bloom material led to the isolation and structure characterization of a new thiazole-containing di-chlorinated polyketide (1). The structure of 1 was deduced using 1D and 2D NMR analysis, high-resolution mass spectrometry analysis and complementary spectroscopic procedures. Trichothiazole A possesses interesting structural features, such as a terminal alkyne, two vinyl chlorides and a 2,4-disubstituted thiazole. Trichothiazole A showed moderate cytotoxicity to Neuro-2 A cells (EC₅₀: 13.3 ± 1.1 μM).     

Gaseous flow measurements in an internal combustion engine assembly using molecular tagging velocimetry

A molecular tagging velocimetry (MTV) system was applied for mapping in-cylinder flows in an internal combustion engine. The images were captured inside an optical engine assembly that reproduces operation of a 2.2 L four stroke gasoline engine. A recently developed algorithm to process MTV images is based on a fast-normalized spatial correlation approach implemented using MATLAB software. The code allows accurate detection of the MTV grid nodes displacements. It processes simultaneously velocity vector and circulation fields for individual cycles, and ensemble averages of those over a few hundred sequential cycles to obtain mean and standard deviation values. Then probability density functions are reconstructed to quantify cycle-to-cycle variability of the in-cylinder flow.     

Intramolecular [2+2] Photocycloaddition of 3‐ and 4‐(But‐3‐enyl)oxyquinolones: Influence of the Alkene Substitution Pattern,Photophysical Studies,and Enantioselective Catalysis by a Chiral Sensitizer

The intramolecular [2+2] photocycloaddition of four 4‐(but‐3‐enyl)oxyquinolones (substitution pattern at the terminal alkene carbon atom: CH₂, Z‐CHEt, E‐CHEt, CMe₂) and two 3‐(but‐3‐enyl)oxyquinolones (substitution pattern: CH₂, CMe₂) was studied. Upon direct irradiation at λ=300 nm, the respective cyclobutane products were formed in high yields (83–95 %) and for symmetrically substituted substrates with complete diastereoselectivity. Substrates with a Z‐ or E‐substituted terminal double bond showed a stereoconvergent reaction course leading to mixtures of regio‐ and diastereomers with almost identical composition. The mechanistic course of the photocycloaddition was elucidated by transient absorption spectroscopy. A triplet intermediate was detected for the title compounds, which–in contrast to simple alkoxyquinolones such as 3‐butyloxyquinolone and 4‐methoxyquinolone–decayed rapidly (τ≈1 ns) through cyclization to a triplet 1,4‐diradical. The diradical can evolve through two reaction channels, one leading to the photoproduct and the other leading back to the starting material. When the photocycloaddition was performed in the presence of a chiral sensitizer (10 mol %) upon irradiation at λ=366 nm in trifluorotoluene as the solvent, moderate to high enantioselectivities were achieved. The two 3‐(but‐3‐enyl)oxyquinolones gave enantiomeric excesses (ees) of 60 and 64 % at ?25 °C, presumably because a significant racemic background reaction occurred. The 4‐substituted quinolones showed higher enantioselectivities (92–96 % ee at ?25 °C) and, for the terminally Z‐ and E‐substituted substrates, an improved regio‐ and diastereoselectivity.     

An ALE finite element method for a coupled Stefan problem and Navier–Stokes equations with free capillary surface

In this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition. We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction. A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd.