Gauss's law, infinite homogenous charge distributions and Helmholtz theorem

Homogenous Charge Compression Ignition (HCCI) Engines

Refraction of power-law spatial solitons – the Helmholtz-Snell law

The behaviour of a scalar optical beam at the boundary between two dissimilar nonlinear media is of fundamental interest in nonlinear photonics. Here, we report the first systematic generalization of our Kerr analyses to a wider class of power-law materials. Universal refraction laws will be given, and theorysimulation agreement demonstrated.

Infinite hierarchies and prior distributions

This paper introduces a way of constructing non-informative priors for Bayesian analysis, by taking a limit of priors arising from hierarchical constructions as the number of levels in the hierarchy converges to infinity. Results are proved showing that for location families, and other related cases, limits are often not dependent on the exact form of the increment distribution used.

Helmholtz solitons in power - law optical materials

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures broad beam evolution at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses and liquid crystals. Novel exact analytical soliton solutions are presented for a generic nonlinearity, within which kn...

Probability Distributions and Gleason’s Theorem

We discuss concrete examples for frame functions and their associated density operators, as well as for non-Gleason type probability measures.