Numerical modeling considerations for an applied nonlinear Schrödinger equation.

A model for nonlinear optical propagation is cast into a split-step numerical framework via a variable stencil-size Crank-Nicolson finite-difference method for the linear step and a choice of two different nonlinear integration schemes for the nonlinear step. The model includes Kerr, Raman scattering, and ionization effects (as well as linear and nonlinear shock, diffraction, and dispersion). We demonstrate the practical importance of numerical effects when interpreting computational studies of high-intensity optical pulse propagation in physical materials. Examples demonstrate the significant error that can arise in discrete, limited precision implementations as one attempts to improve practical operator accuracy through increased operator support size and sampling frequency. We also demonstrate the effect of the method used to obtain the finite-difference operator coefficients defining the equations ultimately used in the discrete model. Smooth, plausible, but incorrect solutions may result from these numerical effects. This implies the necessity of a complete, precise description of all numerical methods when reporting results of computational physics investigations in order to ensure proper interpretation and reproducibility.

CAVE and fishtank virtual-reality displays: a qualitative and quantitative comparison.

We present the results from a qualitative and quantitative user study comparing fishtank virtual-reality (VR) and CAVE displays. The results of the qualitative study show that users preferred the fishtank VR display to the CAVE system for our scientific visualization application because of perceived higher resolution, brightness and crispness of imagery, and comfort of use. The results of the quantitative study show that users performed an abstract visual search task significantly more quickly and more accurately on the fishtank VR display system than in the CAVE. The same study also showed that visual context had no significant effect on task performance for either of the platforms. We suggest that fishtank VR displays are more effective than CAVEs for applications in which the task occurs outside the user's reference frame, the user views and manipulates the virtual world from the outside in, and the size of the virtual object that the user interacts with is smaller than the user's body and fits into the fishtank VR display. The results of both studies support this proposition.