A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions, the derivation of the Liouville equation must be adapted to exclude non-physical particle positions, and include the effect of instantaneous interactions. We present the weak formulation of the Liouville equation for interacting particles with general particle dynamics and interactions, and discuss the results using an example

Adaptive, spatially-varying aberration correction for real-time holographic projectors.

A method of generating an aberration- and distortion-free wide-angle holographically projected image in real time is presented. The target projector is first calibrated using an automated adaptive-optical mechanism. The calibration parameters are then fed into the hologram generation program, which applies a novel piece-wise aberration correction algorithm. The method is found to offer hologram generation times up to three orders of magnitude faster than the standard method. A projection of an aberration- and distortion-free image with a field of view of 90x45 degrees is demonstrated. The implementation on a mid-range GPU achieves high resolution at a frame rate up to 12fps. The presented methods are automated and can be performed on any holographic projector.Engineering and Physical Sciences Research CouncilThis is the final version of the article. It first appeared from the Optical Society of America via https://doi.org/10.1364/OE.24.01574