Analysis of a tripartite entanglement distribution switch

Queueing Systems - We study a quantum switch that distributes tripartite entangled states to sets of users. The entanglement switching process requires two steps: First, each user attempts to...     

Algorithm for Optimal Triangulations in Scattered Data Representation and Implementation

Scattered data collected at sample points may be used to determine simple functions to best fit the data. An ideal choice for these simple functions is bivariate splines. Triangulation of the sample points creates partitions over which the bivariate splines may be defined. But the optimality of the approximation is dependent on the choice of triangulation. An algorithm, referred to as an Edge Swapping Algorithm, has been developed to transform an arbitrary triangulation of the sample points into an optimal triangulation for representation of the scattered data. A Matlab package has been completed that implements this algorithm for any triangulation on a given set of sample points.     

Jack van Lint (1932-2004): A survey of his scientific work

When Jack van Lint was appointed as full professor at the Eindhoven University of Technology at the age of 26 he combined a PhD in number theory with a very open scientific mind. It took a sabbatical visit to Bell Laboratories in 1966 to make him understand that a new and fascinating field of applied mathematics was emerging: discrete mathematics. It fascinated and inspired him for the rest of his life. When he passed away on September 28, 2004, he left behind a legacy of 18 books and 177 articles, covering many aspects of coding theory, combinatorics, and finite geometry.van Lint was also a strong international advocate of the role that discrete mathematics ought to play in modern applied mathematics curricula. Quite a few departments sought his advice. Years later, four different universities showed their appreciation by awarding him an honorary degree.This overview is an homage to van Lint's academic achievements and can serve as an introduction to his work for younger generations.     

Rank-one completions of partial matrices and completely rank-nonincreasing linear functionals

We obtain necessary and sufficient conditions for the existence and the uniqueness of rank-one completions of a partial matrix, and we verify a conjecture of Hadwin and Larson concerning the nature of completely rank-nonincreasing linear functionals defined on pattern subspaces.

     

Laboratory simulation of atmospheric turbulence-induced optical wavefront distortion

Real-time liquid crystal television-based technique for simulating optical wavefront distortion due to atmospheric turbulence is presented and demonstrated. A liquid crystal television (LCTV) operating in the “phase mostly” mode was used as an array of spatially correlated phase delays. A movie of the arrays in motion was then generated and displayed on the LCTV. The turbulence simulation system was verified by passing a collimated and doubled diode pumped Nd:YVO₄ laser beam (532 nm) through the transparent LCTV screen. The beam was then passed through a lens and the power spectra of the turbulence information carrying beam was detected as a measure of the far-field distribution. The same collimated laser beam, without the LCTV, was also transmitted down an open-air range and the power spectra detected as a measure of a real far-field distribution. Accepted turbulence parameters were measured for both arrangements and then compared.     

Fluid-fluid phase separation in colloid-polymer mixtures studied with small angle light scattering and light microscopy

Mixtures of colloidal silica spheres and polydimethylsiloxane in cyclohexane with a colloid-polymer size ratio of about one were found to phase separate into two fluid phases, one which is colloid-rich and one which is colloid-poor. In this work the phase separation kinetics of this fluid-fluid phase separation is studied for different compositions of the colloid-polymer mixtures, and at several degrees of supersaturation, with small angle light scattering and with light microscopy. The small angle light scattering curve exhibits a peak that grows in intensity and that shifts to smaller wave vector with time. The characteristic length scale that is obtained from the scattering peak is of the order of a few μm, in agreement with observations by light microscopy. The domain size increases with time as , which might be an indication of coarsening by diffusion and coalescence, like in the case of binary liquid mixtures and polymer blends. For sufficiently low degrees of supersaturation the angular scattering intensity curves satisfy dynamical scaling behavior.