Abstract Today's design of optical systems relies largely on efficient ray tracing and optimization algorithms. Such a ‘step‐and‐repeat’ approach to typically requires considerable experience, intuition, trial‐and‐error guesswork. Brussels Photonics (B‐PHOT) researchers have developed method that allows highly systematic generation evaluation directly calculated freeform solutions enables rigor...

An 'oscillating' version of Brownian motion is defined and studied. 'Ordinary' Brownian motion and 'reflecting' Brownian motion are shown to arise as special cases. Transition densities, first-passage time distributions, and occupation time distributions for the process are obtained explicitly. Convergence of a simple oscillating random walk to an oscillating Brownian motion process is establis...

In this paper, we study the metric property of LexBFS-ordering on AT-free graphs. Based on a 2-sweep LexBFS algorithm, we show that every AT-free graph admits a vertex ordering, called the strong 2-cocomparability ordering, that for any three vertices u v w in the ordering, if d(u; w) 2 then d(u; v) = 1 or d(v; w) 2. As an application of this ordering, we provide a simple linear time recognitio...

We show that Zilber’s conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the firstorder types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-or...

2 We study mechanisms of anomalous transport in quenched random media. Broad disorder point distributions and strong disorder correlations cause anomalous transport and can lead to the same anomalous scaling laws for the mean and variance of the particle displacements. The respective mechanisms, however, are fundamentally different. This difference is reflected in the spatial particle densities...