Renormalization group theory for turbulence: Assessment of the Yakhot-Orszag-Smith theory

The purpose of this paper is to estimate the renormalization group theory for turbulence developed by Yakhot and Orszag [J. Sci. Comput. 1 (1986) 3] and reformulated by Yakhot and Smith [J. Sci. Comput. 7 (1992) 35]. We go into details of their basic theory for the Navier-Stokes equations, the transport equations for the turbulent kinetic energy K, and its dissipation rate . As a result, it becomes evident that their theory bears no relationship to Wilson's renormalization group theory for critical phenomena. Their model is not directly obtained from the renormalization group theory. They evaluated the Kolmogorov constant by setting the expansion parameter ε = 0 and ε = 4 in the same equations. Furthermore, all the constants in their model are invalid because of the same problem.     

Palladium-catalyzed oxidation of vinyl ether to acetate with hydrogen peroxide

The selective hydrogen peroxide oxidation of vinyl ethers to give acetates was developed using triphenylphosphine palladium and triethyl amine catalysts under mild reaction conditions.     

Silver(I) and copper(I) complexes supported by fully fluorinated 1,3,5-triazapentadienyl ligands

Synthesis of the perfluorinated 1,3,5-triazapentadiene [N{(CF(3))C(C(6)F(5))N}(2)]H and the use of its conjugate base as a supporting ligand for the isolation of silver(i) and copper(i) complexes are reported. Some of the related chemistry involving [N{(C(3)F(7))C(C(6)F(5))N}(2)](-) (that has bulkier -C(3)F(7) groups on the 1,3,5-triazapentadienyl ligand backbone) is also presented. X-ray crystallographic data show a wide variety of structures ranging from intermolecular, hydrogen-bonded chain structure for [N{(CF(3))C(C(6)F(5))N}(2)]H with a twisted W-shaped N(3)C(2) core, monomeric [N{(CF(3))C(C(6)F(5))N}(2)]Ag(CN(t)Bu)(2) and [N{(C(3)F(7))C(C(6)F(5))N}(2)]Ag(CN(t)Bu)(2) where the κ(1)-bonded triazapentadienyl ligand bonding to the metal fragment via the central nitrogen atom, monomeric [N{(CF(3))C(C(6)F(5))N}(2)]Ag(PPh(3))(2) and [N{(C(3)F(7))C(C(6)F(5))N}(2)]Ag(PPh(3))(2) that feature κ(1)-bonded triazapentadienyl ligand bonding to the metal fragment via one of the terminal nitrogen atoms, to that of the monomeric [N{(CF(3))C(C(6)F(5))N}(2)]Cu(CN(t)Bu)(2) containing a κ(2)-bonded triazapentadienyl ligand and a U-shaped NCNCN ligand backbone. The isocyanide adducts show relatively high ν(CN) values in the IR spectra.     

Cooperative catalytic reactions using organocatalysts and transition metal catalysts: enantioselective propargylic alkylation of propargylic esters with aldehydes

The enantioselective propargylic alkylation of propargylic esters with aldehydes in the presence of a copper complex and an optically active secondary amine as cocatalysts has been found to give the corresponding propargylic alkylated products in good yields as a mixture of two diastereoisomers with a high enantioselectivity.     

Copper-catalyzed enantioselective propargylic amination of nonaromatic propargylic esters with amines

The enantioselective propargylic amination of propargylic pentafluorobenzoates bearing an alkyl group at the propargylic position with amines in the presence of catalytic amounts of a copper complex and an optically active diphosphine such as BINAP has been found to give the corresponding propargylic amines in good yields with high enantioselectivity.