Propagation of a pre-existing turbulent fluid fracture

The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture.     

Carboxylic Acids as Directing Groups for C−H Bond Functionalization

The selective transformation of C?H bonds is one of the most desirable approaches to creating complexity from simple building blocks. Several directing groups are efficient in controlling the regioselectivity of catalytic C?H bond functionalizations. Among them, carboxylic acids are particularly advantageous, since they are widely available in great structural diversity and at low cost. The carboxylate directing groups can be tracelessly cleaved or may serve as the anchor point for further functionalization through decarboxylative couplings. This Minireview summarizes the substantial progress made in the last few years in the development of reactions in which carboxylate groups direct C?H bond functionalizations with formation of C?C, C?O, C?N, or C?halogen bonds at specific positions. It is divided into sections on C?C, C?O, C?N, and C?halogen bond formation, each of which is subdivided by reactions and product classes. Particular emphasis is placed on methods that enable multiple derivatizations by combining carboxylate‐directed C?H functionalization with decarboxylative couplings.     

Isopropenyl acetate: A cheap and general acylating agent of alcohols under metal-free conditions

Functionalized primary, secondary and tertiary alcohols are efficiently acetylated by isopropenyl acetate and catalytic p-TsOH.     

On the simplicity of some kac-moody groups

Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple.     

Introduction of C-Sulfonate Groups into Disaccharide Derivatives

To prepare C-sulfonate derivatives of disaccharides two different strategies were followed. Thus 6- and 6′-C-sulfocellobiosides 4 and 10–12 were prepared starting from a suitably protected cellobioside. The 6′-C-sulfoaminocellobioside 18 was prepared by construction of the molecule through a glycosylation reaction. In both cases, the synthetic pathway involves regioselective tosylation, introduction of a sulfur atom by nucleophilic displacement with potassium thioacetate and oxidation with hydrogen peroxide.     

Locally s-distance transitive graphs and pairwise transitive designs

The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs with a star quotient is equivalent to the study of a particular family of designs with strong symmetry properties that we call nicely affine and pairwise transitive. We show that a group acting regularly on the points of such a design must be abelian and give general construction for this case.     

Synthesis and photovoltaic properties of conjugated side chains polymers with different electron‐withdrawing and donating end groups

A series of novel low band gap polymers containing conjugated side chains with 4,7‐dithien‐5‐yl‐2,1,3‐benzodiathiazole and different electron‐withdrawing end groups of aldehyde ( PT‐DTBTCHO ), 2‐ethylhexyl cyanoacetate ( PT‐DTBTCN ), 1,3‐diethyl‐2‐thiobarbituric acid ( PT‐DTBTDT ), and electron‐donating end group of 2‐methylthiophene ( PT‐DTBTMT ) have been designed and synthesized. All polymers exhibit good solubility in common organic solvents, film‐forming ability, and thermal stability. These conjugated polymers show the broad ultraviolet‐visible absorption and the narrow optical band gaps in the range of 1.65–1.90 eV. Through changing the end group of conjugated side chains, the photophysical properties and energy levels of the polymers were tuned effectively. Bulk heterojunction solar cells based on the blend of these polymers and (6,6)‐phenyl‐C₆₁‐butyric acid methyl ester (PC₆₁BM) reached the best power conversion efficiency (PCE) of 2.72%. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

利用单参数Lie群组的一种可解性求自治系统首次积分的方法

讨论了自治系统接受的单参数Lie群组具有一种可解性的情况下求系统的一个首次积分的具体方法.对于n阶自治系统,给出相应参数的一组确定取值,求得系统首次积分；对于三阶自治系统,当系统接受的单参数Lie群组可解时,验证求得首次积分的条件一定成立.     

Methylol‐functional benzoxazines as precursors for high‐performance thermoset polymers: Unique simultaneous addition and condensation polymerization behavior

A new class of high‐performance resins of combined molecular structure of both traditional phenolics and benzoxazines has been developed. The monomers termed as methylol‐functional benzoxazines were synthesized through Mannich condensation reaction of methylol‐functional phenols and aromatic amines, including methylenedianiline (4,4′‐diaminodiphenylmethane) and oxydianiline (4,4′‐diaminodiphenyl ether), in the presence of paraformaldehyde. For comparison, other series of benzoxazine monomers were prepared from phenol, corresponding aromatic amines, and paraformaldehyde. The as‐synthesized monomers are characterized by their high purity as judged from ¹H NMR and Fourier transform infrared spectra. Differential scanning calorimetric thermograms of the novel monomers show two exothermic peaks associated with condensation reaction of methylol groups and ring‐opening polymerization of benzoxazines. The position of methylol group relative to benzoxazine structure plays a significant role in accelerating polymerization. Viscoelastic and thermogravimetric analyses of the crosslinked polymers reveal high T_g (274–343 °C) and excellent thermal stability when compared with the traditional polybenzoxazines. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012