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.

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.

Brain-derived neurotrophic factor is an endogenous modulator of nociceptive responses in the spinal cord

The primary sensory neurons that respond to noxious stimulation and project to the spinal cord are known to fall into two distinct groups: one sensitive to nerve growth factor and the other sensitive to glial cell-line-derived neurotrophic factor. There is currently considerable interest in the ways in which these factors may regulate nociceptor properties. Recently, however, it has emerged that another trophic factor—brain-derived neurotrophic factor (BDNF)—may play an important neuromodulatory role in the dorsal horn of the spinal cord. BDNF meets many of the criteria necessary to establish it as a neurotransmitter/neuromodulator in small-diameter nociceptive neurons. It is synthesized by these neurons and packaged in dense core vesicles in nociceptor terminals in the superficial dorsal horn. It is markedly up-regulated in inflammatory conditions in a nerve growth factor-dependent fashion. Postsynaptic cells in this region express receptors for BDNF. Spinal neurons show increased excitability to nociceptive inputs after treatment with exogenous BDNF. There are both electrophysiological and behavioral data showing that antagonism of BDNF at least partially prevents some aspects of central sensitization. Together, these findings suggest that BDNF may be released from primary sensory nociceptors with activity, particularly in some persistent pain states, and may then increase the excitability of rostrally projecting second-order systems. BDNF released from nociceptive terminals may thus contribute to the sensory abnormalities associated with some pathophysiological states, notably inflammatory conditions.