A generic framework for time-stepping partial differential equations (PDEs): general linear methods,object-oriented implementation and application to fluid problems

Time-stepping algorithms and their implementations are a critical component within the solution of time-dependent partial differential equations (PDEs). In this article, we present a generic framework – both in terms of algorithms and implementations – that allows an almost seamless switch between various explicit, implicit and implicit–explicit (IMEX) time-stepping methods. We put particular emphasis on how to incorporate time-dependent boundary conditions, an issue that goes beyond classical ODE theory but which plays an important role in the time-stepping of the PDEs arising in computational fluid dynamics. Our algorithm is based upon J.C. Butcher's unifying concept of general linear methods that we have extended to accommodate the family of IMEX schemes that are often used in engineering practice. In the article, we discuss design considerations and present an object-oriented implementation. Finally, we illustrate the use of the framework by applications to a model problem as well as to more complex fluid problems.     

Sarcophytolides G–L,New Biscembranoids from the Soft Coral Sarcophyton elegans

Six new biscembranoids, namely, sarcophytolides G–L ( 1 – 6 , resp.), together with six known analogs, were isolated from a marine soft coral Sarcophyton elegans. The structures of the new compounds were established on the basis of 1D‐ and 2D‐NMR (COSY, HSQC, HMBC, and NOESY) spectroscopic analysis together with the aid of MS, CD, and IR data. The unusual isobiscembranoid sarcophytolide G ( 1 ) was found for the first time in the genus Sarcophyton.     

Effects of long-range potentials on polarization of chlorine atoms from photodissociation of ICl

The polarization of Cl(2P3/2) atoms resulting from photodissociation of ICl in the range 490 nm to 560 nm has been analysed in detail. The most accurate-to-date set of the five Ω = 0+ and Ω = 1 adiabatic potential energy surfaces that correlate to the ground state Cl(2P3/2) + I(2P3/2) atoms have been constructed from available spectroscopic, ab initio, and long-range perturbation-theory data. Simulations of the photolysis-energy dependence of Cl-atom polarization, show non-adiabatic transitions occurring at Rx ～ 6.5 Å, with probabilities from B(3Π0+) to X(1Π0+) (P = 0.96), A(3Π1) to a(3Π1) (P = 0.12), and A(3Π1) to z(1Π1) (P = 0.49). The simulations are shown to be sensitive to changes in the potential energy surfaces on the order of ΔV = 30 cm-1 Å, reinforcing that these type of polarization experiments serve as an exceedingly stringent test of theory.     

A Short,Efficient, Multigram Synthetic Route to 2,3-Dimethylfuran and Some of its 2-Substituted Derivatives

A laboratory, multigram (1000 g in an hour) preparation procedure for 2,3-dimethylfuran, based on the frequently repeated thermal cyclization of (Z) 3-methyl-2-penten-4-yn-1-ol, as well as its subsequent formylation, acetylation and oxidation is described.