Numerical calculation of Reynolds stresses in a square duct with secondary flow

A new model for the Reynolds stress equations is presented. This model is used to obtain a theoretical solution for the problem of fully developed turbulent flow in a square duct. Nine governing equations for the axial velocity, lateral vorticity, lateral stream function and six components of the Reynolds stresses are simultaneously solved, by a finite-difference technique. To ensure numerical stability of the solution a special linearised implicit representation of the source terms is proposed, and simultaneous solution of the equations at each.mesh point is obtained. Near the wall a special procedure is used, by which the Reynolds stress equations are assumed to be in local equilibrium, and the velocity profile is assumed to be logarithmic. However, due to the secondary motion the logarithmic velocity profile is inclined to the axial direction. The results bear reasonable agreement with experimental data. Computer time requirements are moderate.     

The formation of novel 1,3-dioxolanes: atypical Baylis-Hillman reaction of a sesquiterpene lactone parthenin

The Baylis-Hillman reaction of a sesquiterpene lactone parthenin with various aldehydes gave unexpected products containing a 1,3-dioxolane moiety. Both small aliphatic and aromatic aldehydes produced 1,3-dioxolanes, whereas higher aliphatic aldehydes produced normal Baylis-Hillman products.     

Phase transitions and the high temperature expansion for the reggeon calculus

We study a recently proposed lattice version of the reggeon field theory. First a simple one-dimensional system possessing many of the features of the reggeon calculus (Ising model in an imaginary magnetic field) is solved. Surprisingly, the system is found to undergo a phase transition at a non-zero critical temperature, which, although of first order obeys the universality and scaling laws previously postulated for the reggeon calculus. Returning to the full lattice theory, the machinery for performing a high temperature expansion is set up, and initial calculations carried out to order T^?3. In this order, best estimates for the critical indices η and v in the asymptotic elastic amplitude A(s,t) ～ is (ln s)^ηf(t(lns)^v) yield $\text{η = 0 (}\text{1}\text{2}\text{～ 1), v = 0(1}\text{1}\text{2}\text{～ 2)}$. Check on the method, including comparisons with known Ising model results, are also discussed.     

Why the neutron isn't all neutral

Experimental measurements of the electric form factor of the neutron indicate a spatially inhomogeneous distribution of charge. The quark model, with a spatially dependent spin-spin interaction, can accurately describe this inhomogeneity. We relate the neutron's charge radius to the nucleon-delta mass difference and discuss other experimental consequences of the inhomogeneity.     

Flux loops: More new heavy particles in the Weinberg-Salam model

Extending Nambu's suggestion that there are stringlike classical solutions in the Weinberg-Salam model, we argue that these include closed tori of weak neutral (Z⁰) flux.     

Synthesis of Some N-Substituted Benzene Alkamines

Synthesis of N-β-phenylethyl-2:4-dialkoxy-5-alkylbenzylamines having different alkyl and alkoxy groups have been described.     

Synthesis,characterization and single crystal x-ray analysis of a complex of iron(II) bis(2,4-dimethylphenyl)dithiophosphate with 4-ethylpyridine

Complex of iron(II) bis(2,4-dimethylphenyl)dithiophosphate with 4-ethylpyridine [{(2,4- (CH₃)₂C₆H₃O)2PS2}2Fe{NC₅H₄(C₂H₅)-4}₂] is synthesized and characterized by elemental analysis, magnetic moment, IR spectroscopy and single crystal X-ray analysis. Complex crystallizes in the monoclinic sp. gr. P2₁/n, Z = 2. Crystal structure consists of mononuclear units with Fe(II) ion chelated by four S atoms of the two diphenyldithiophosphate ligands in bidentate manner. N atoms from two 4-ethylpyridine ligands are axially coordinated to the Fe(II) atom leading to an octahedral geometry.     

Odoriferous Cyclic Ethers via Co‐Halogenation Reaction: Facile Preparation of Nerol Oxide,Florol®, Florol® Methyl Ether,and Pityol® Methyl Ether

A series of odoriferous cyclic ethers, including nerol oxide ( 1 ), Florol^® ( 2 ), Florol methyl ether ( 3 ), and Pityol^® methyl ether ( 4b ), were prepared by a versatile synthetic protocol based on co‐halogenation with 1,3‐dibromo‐5,5‐dimethylhydantoin (= 1,3‐dibromo‐5,5‐dimethylimidazolidine‐2,4‐dione; DDH) as the key step. The methodology provides a facile access to important perfumery molecules from abundantly available monoterpene alcohols.