Numerical rheometry of bulk materials using a power law fluid and the lattice Boltzmann method

In the present study, the flow of bulk materials is characterised as a non-Newtonian fluid and modelled using the lattice Boltzmann method. A power law and a Bingham model is implemented in the LBM, which is hydrodynamically coupled to the discrete element method (DEM) for structural interaction. The performance of both non-Newtonian models is assessed, both qualitatively and quantitatively, in benchmark problems. The validated, non-Newtonian LBM–DEM framework is then applied to the geometry of a cylindrical Couette rheometer to numerically determine the constitutive response of a sample of Leighton Buzzard sand. The numerical results, which employ the power law, are compared with experimental data, and a number of other synthetic soil samples are defined using the presented process of numerical rheometry. Finally, the numerical stress–strain rate response of the synthetic soil samples is interpreted within the context of a regularised Bingham model, and the similarities discussed.     

Values of games without side payments

A value forn-person games without side payments is given which coincides with theShapley value for games with side payments, and with theNash value for two-person games.     

A class of loss functions of catenary form

The catenary form of loss function is considered in the framework of Bayesian decision theory. The mathematical tractability of this form seems to be unrecognized; it contains quadratic loss as a limiting case. For various probability distributions expressions are given for posterior analysis, and limiting properties are investigated.     

Optimal threat strategies of bimatrix games

A bi-matrix threat game is defined as a triple (A,B,S) whereA andB arem×n payoff matrices, andS is a closed convex subset of the plane, with (a _ij,B _ij) εS for eachi,j. Given (threat) mixed strategiesx andy,Nash's model suggests that the eventual outcome will be that point (u, v) εS which maximizes the product (u ?xAy ^t) (v ?xBy ^t) subject tou ≥xAy ^t,v ≥xBy ^t. Optimality of the threat strategies is then defined in the obvious way. A constructive proof of existence of optimal threat strategies is given; in particular, it is shown that they are optimal strategies for the matrix gameA-kB, wherek is to be determined. In this paper,k is approximated by aNewton-Raphson technique. Two examples are solved in detail.     

Infrared spectra and molecular conformation of butyronitrile and methyl thioacetonitrile

The infrared absorption spectra of two related compounds, butyronitrile (CH₃CH₂-CH₂CN) and methylthioacetonitrile (CH₃SCH₂CN) have been examined in the liquid and solid phases. Vapour phase spectra of butyronitrile have also been recorded. Evidence is given for the existence of two rotational isomers trans and gauche, for both compounds. In both cases the energy difference between the two rotamers appears to be small with the gauche form identified as the low energy conformer for butyronitrile. For methylthioacetonitrile it was not possible to determine the more stable rotational isomer.     

Melt rheology of ion-containing polymers. I. Effect of ionic content in a model polyesterionomer

The effects of copolymerizing small amounts of an ionic moiety (0–7 mol %) into the backbone of a polycondensation polymer have been investigated by a combination of linear viscoelastic, steady-shear, and extensional testing. At a constant viscosity in dilute solution, both the zero-shear-rate viscosity and the maximum relaxation time in the melt increase monotonically with an increase in the ionic character. These effects are present after the data are normalized to remove the increase in the glass transition temperature T_g with increased ionic content. Large-strain, steady-shear flow experiments showed that the viscoelastic memory of the melt is affected by ionic content. An increase in ion content causes a decrease in the effect of strain on the memory function. This effect is not apparent in extensional flow experiments, which indicate that the ionic content does not affect the response if the tests are conducted at a constant temperature above T_g.     

Highly efficient blue-light generation from a compact, diode-pumped femtosecond laser by use of a periodically poled KTP waveguide crystal

We present a simplified, potentially portable, and highly efficient blue-light source from a periodically poled KTP waveguide crystal with a compact femtosecond Cr:LiSAF laser. This light source generates 5.6 mW of blue average output power at 424 nm with 27 mW of incident fundamental in a single-pass extracavity arrangement at room temperature. The overall system efficiency of electrical power to blue light is 0.5%, and the internal second-harmonic generation conversion efficiency is as high as 37%. The slope efficiency of 5.5% pJ(-1) at low pulse energies is, to our knowledge, the highest slope efficiency yet reported for frequency conversion into the blue spectral region.     

Wall mediated transport in confined spaces: exact theory for low density

We present a theory for the transport of molecules adsorbed in slit and cylindrical nanopores at low density, considering the axial momentum gain of molecules oscillating between diffuse wall reflections. Good agreement with molecular dynamics simulations is obtained over a wide range of pore sizes, including the regime of single-file diffusion where fluid-fluid interactions are shown to have a negligible effect on the collective transport coefficient. We show that dispersive fluid-wall interactions considerably attenuate transport compared to classical hard sphere theory.