A parallel multi-configuration self-consistent field algorithm

A scalable multi-configuration self-consistent field (MCSCF) algorithm is described. The method for optimizing the orbital and configurational parameters is based upon the two-step Newton–Raphson approach with an augmented orbital Hessian matrix. A single copy of the two-electron integrals in the molecular orbital basis is distributed over the memory of all processors. Storage of the augmented Hessian is avoided by re-computing its elements as needed. A replicated data approach is used to parallelize the configuration interaction step. Scalability to 1024 processors is demonstrated.     

The effect of polymer additives on transition in pipe flow

Summary Small amounts of long chain water soluble polymers have a marked effect on turbulent flow resulting in an appreciable reduction of turbulent friction. The maximum reduction in pipe flow resistance is obtained at such low concentrations that the density and viscosity are not altered appreciably. The minimum friction curve varies as Re ^–2/3 and appears to be the same for all effective additives tested. The transition process is affected by these additives. Quantitative results are presented showing a reduction in the intensity of the turbulent flashes and the fraction of the time the flow is turbulent at a given Reynolds number.     

A unified theory of turbulent flow

Summary A critical analysis is made of the assumptions underlying Reynolds' equations for turbulent flow. It is shown that there are regions in a flow field where these assumptions break down, and it is therefore necessary to separate the flow into a turbulent core and a laminar sublayer. The importance of the boundary conditions to be imposed on the mean velocities and Reynolds stresses at the junction is emphasized as this is the way in which the effect of surface roughness enters the theory. A set of equations for calculating turbulent flows is proposed. The distinctive feature is that the turbulent stresses are represented as the difference between viscous terms with a large eddy viscosity and terms satisfying auxiliary differential equations proposed by Broszko. These terms may be associated with the free and wall turbulence respectively. The theory enables the idea of a large eddy viscosity to be applied even where the velocity gradient is large. The results obtained for specific configurations, which will be reported in detail in future papers, are previewed.     

Dissociation of Ethoxy Methyl Carbenium Hexachloroantimonate in Methylene Chloride Solution. I. Measurement of the Specific Conductivity and Dielectric Constant

The problems of measuring the specific conductivity of very low conductivity organic solutions are explored. A simple ac system using readily available components is described, and its limitations are examined. The low-frequency dielectric constant can also be determined with reasonable accuracy.     

An accurate and graphable solution for the integral of the Arrhenius function

An approximation to the integral of the Arrhenius function is found by incorporating a nearly-constant integrating factor. The solutions, which can be determined graphically, are of an accuracy comparable to that of the rational approximations.