Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Shortest node-disjoint paths on random graphs

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process global information and distribute paths optimally. Statistical properties such as scaling with system size and number of paths, average path-length and the transition to the frustrated regime are analyzed. The performance of the suggested algorithm is evaluated through a comparison against a greedy algorithm. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

Top-hat random fiber Bragg grating

We examined the possibility of using noise or pseudo-random variations of the refractive index in the design of fiber Bragg gratings (FBGs). We demonstrated theoretically and experimentally that top-hat FBGs may be designed and fabricated using this approach. The reflectivity of the fabricated top-hat FBG matches quite well with that of the designed one. © 2015 Optical Society of America.

Ultra-long fibre-based random lasers

The emerging science and applications of ultra-long random fibre lasers will be overviewed. The lasers with cavity length up to several hundred km exploit random distributed feedback provided by Rayleigh scattering amplified through Raman effect. © 2014 OSA.