On the smallest scale for the incompressible Navier-Stokes equations

It is proven that for solutions to the two- and three-dimensional incompressible Navier-Stokes equations the minimum scale is inversely proportional to the square root of the Reynolds number based on the kinematic viscosity and the maximum of the velocity gradients. The bounds on the velocity gradients can be obtained for two-dimensional flows, but have to be assumed to be three-dimensional. Numerical results in two dimensions are given which illustrate and substantiate the features of the proof. Implications of the minimum scale result to the decay rate of the energy spectrum are discussed

Overture - Object-oriented tools for overset grid applications

The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It has support for grid generation, difference operators, boundary conditions, data-base access and graphics. Short sample code segments are presented to show the power of this approach

Numerical shock propagation using geometrical shock dynamics

A simple numerical scheme for the calculation of the motion of shock waves in gases based on Whitham's theory of geometrical shock dynamics is developed. This scheme is used to study the propagation of shock waves along walls and in channels and the self-focusing of initially curved shockfronts. The numerical results are compared with exact and numerical solutions of the geometrical-shock-dynamics equations and with recent experimental investigations

Computer and internet interventions to optimize listening and learning for people with hearing loss: accessibility, use, and adherence

Purpose: The aim of this research forum article was to examine accessibility, use, and adherence to computerized and online interventions for people with hearing loss. Method: Four intervention studies of people with hearing loss were examined: 2 auditory training studies, 1 working memory training study, and 1 study of multimedia educational support. Results: A small proportion (approximately 15%) of participants had never used a computer, which may be a barrier to the accessibility of computer and Internet based interventions. Computer competence was not a factor in intervention use or adherence. Computer skills and Internet access influenced participant preference for the delivery method of the multimedia educational support program. Conclusions: It is important to be aware of current barriers to computer and Internet-delivered interventions for people with hearing loss. However, there is a clear need to develop and future-proof hearing-related applications for online delivery

A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids

A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach

Optical patterning of trapped charge in nitrogen-doped diamond

The nitrogen-vacancy (NV) centre in diamond is emerging as a promising platform for solid-state quantum information processing and nanoscale metrology. Of interest in these applications is the manipulation of the NV charge, which can be attained by optical excitation. Here we use two-color optical microscopy to investigate the dynamics of NV photo-ionization, charge diffusion, and trapping in type-1b diamond. We combine fixed-point laser excitation and scanning fluorescence imaging to locally alter the concentration of negatively charged NVs, and to subsequently probe the corresponding redistribution of charge. We uncover the formation of spatial patterns of trapped charge, which we qualitatively reproduce via a model of the interplay between photo-excited carriers and atomic defects. Further, by using the NV as a probe, we map the relative fraction of positively charged nitrogen upon localized optical excitation. These observations may prove important to transporting quantum information between NVs or to developing three-dimensional, charge-based memories