A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

Horizontal cells reveal cone type-specific adaptation in primate retina

The human cone visual system maintains contrast sensitivity over a wide range of ambient illumination, a property known as light adaptation. The first stage in light adaptation is believed to take place at the first neural step in vision, within the long, middle, and short wavelength sensitive cone photoreceptors. To determine the properties of adaptation in primate outer retina, we measured cone signals in second-order interneurons, the horizontal cells, of the macaque monkey. Horizontal cells provide a unique site for studying early adaptational mechanisms; they are but one synapse away from the photoreceptors, and each horizontal cell receives excitatory inputs from many cones. Light adaptation occurred over the entire range of light levels evaluated, a luminance range of 15–1,850 trolands. Adaptation was demonstrated to be independent in each cone type and to be spatially restricted. Thus, in primates, a major source of sensitivity regulation occurs before summation of cone signals in the horizontal cell.

The role of London forces in defining noncentrosymmetric order of high dipole moment–high hyperpolarizability chromophores in electrically poled polymeric thin films

Graphs of second harmonic generation coefficients and electro-optic coefficients (measured by ellipsometry, attenuated total reflection, and two-slit interference modulation) as a function of chromophore number density (chromophore loading) are experimentally observed to exhibit maxima for polymers containing chromophores characterized by large dipole moments and polarizabilities. Modified London theory is used to demonstrated that this behavior can be attributed to the competition of chromophore-applied electric field and chromophore–chromophore electrostatic interactions. The comparison of theoretical and experimental data explains why the promise of exceptional macroscopic second-order optical nonlinearity predicted for organic materials has not been realized and suggests routes for circumventing current limitations to large optical nonlinearity. The results also suggest extensions of measurement and theoretical methods to achieve an improved understanding of intermolecular interactions in condensed phase materials including materials prepared by sequential synthesis and block copolymer methods.