Velocity–vorticity–helicity formulation and a solver for the Navier–Stokes equations

For the three-dimensional incompressible Navier–Stokes equations, we present a formulation featuring velocity, vorticity and helical density as independent variables. We find the helical density can be observed as a Lagrange multiplier corresponding to the divergence-free constraint on the vorticity variable, similar to the pressure in the case of the incompressibility condition for velocity. As one possible practical application of this new formulation, we consider a time-splitting numerical scheme based on an alternating procedure between vorticity–helical density and velocity–Bernoulli pressure systems of equations. Results of numerical experiments include a comparison with some well-known schemes based on pressure–velocity formulation and illustrate the competitiveness on the new scheme as well as the soundness of the new formulation.     

Damage Evolution and Post-peak Gas Permeability of Raw Coal Under Loading and Unloading Conditions

Coalbed methane, a naturally occurring gas in coal, is regarded as a relatively clean-burning and eco-friendly resource. During mining, coalbed methane may be leaked to the environment, leading to potential coal mine catastrophes such as coal and gas outbursts, and gas explosions. In the interest of mine stability, and to enhance resource recovery and utilisation, it is fundamentally important to understand the permeability characteristics of coal, in particular its post-peak permeability behaviour. In this paper, an in-house developed tri-axial apparatus with the ability to investigate coupled thermal–hydrological–mechanical behaviour under servo-controlled seepage has been used to carry out a series of gas permeation experiments in coal samples. The coal samples were subjected to tri-axial tests, including the simulation of coal extraction by unloading the confining pressure applied on the test specimens. The deformation and permeability characteristics of raw coal during these tests were recorded. The volume changes of the coal samples during the tests were observed to occur in three stages: Stage 1: contraction, Stage 2: little or no volume change, and Stage 3: dilation. Corresponding to the volume changes, the gas seepage can also be divided into three stages: seepage decrease, steady seepage, and accelerated seepage. Based on the observed behaviour of coal samples during the tri-axial permeation tests, an analytical model to simulate damage evolution and its effect on the permeability of coal containing gas is proposed in this paper. It may be used to study the evolution of permeability with stress changes, and to provide insights into coal and gas outbursts in practice.     

Gels with exceptional thermal stability formed by bis(amino acid) oxalamide gelators and solvents of low polarity

Some bis (amino acid) oxalamide gelators form common thermo-reversible gels with various organic solvents but also gels of exceptional thermal stability with some solvents of medium and low polarity; the latter gels can be heated up to 50 degrees C higher temperatures than the bp of the solvent without apparent gel-to-sol transition.     

Pectenotoxin-2 synthetic studies. 1. Alkoxide precoordination to [Rh(NBD)(DIPHOS-4)]BF(4) allows directed hydrogenation of a 2,3-dihydrofuran-3-ol without competing furan production

[reaction: see text] The alkoxide-directed hydrogenation shown is reported as a key step in a concise synthesis of a fully functionalized precursor to the C29-C40 F/G sector of pectenotoxin-2.