Transparent colloid containing upconverting nanocrystals: An alternative medium for three-dimensional volumetric display

We report an alternative medium of transparent upconverting colloid containing lanthanide ion doped NaYF4 nanocrystals for three-dimensional (3D) volumetric display. The colloids exhibit tunable upconversion luminescence with a wide spectrum of colors by adjusting the doping concentrations of the nanocrystals and the compositions of the colloids. Our preliminary experimental result indicates that an upconverting colloid-based 3D volumetric display using a convergent, near infrared laser beam to induce a localized luminescent spot near the focus is technically feasible. Therefore arbitrary 3D objects can be created inside the upconverting colloid by use of computer controlled 3D scanning systems. (C) 2008 Optical Society of America

Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.