A vector equilibrium problem for the two-matrix model in the quartic/quadratic case

We consider the two sequences of biorthogonal polynomials (p_{k,n})_k and (q_{k,n})_k related to the Hermitian two-matrix model with potentials V(x) = x^2/2 and W(y) = y^4/4 + ty^2. From an asymptotic analysis of the coefficients in the recurrence relation satisfied by these polynomials, we obtain the limiting distribution of the zeros of the polynomials p_{n,n} as n tends to infinity. The limiting zero distribution is characterized as the first measure of the minimizer in a vector equilibrium problem involving three measures which for the case t=0 reduces to the vector equilibrium problem that was given recently by two of us. A novel feature is that for t < 0 an external field is active on the third measure which introduces a new type of critical behavior for a certain negative value of t. We also prove a general result about the interlacing of zeros of biorthogonal polynomials.Comment: 60 pages, 9 figure

Electrically controllable saturable absorption in hybrid graphene-silicon waveguides

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Extremely uniform lasing wavelengths of InP microdisk lasers heterogeneously integrated on SOI

A standard deviation in lasing wavelength lower than 500pm is characterized on nominally identical and optically-pumped microdisk lasers, heterogeneously integrated on the same SOI circuit. This lasing wavelength uniformity is obtained using electron-beam lithography

Design and prototype of a train-to-wayside communication architecture

Telecommunication has become very important in modern society and seems to be almost omnipresent, making daily life easier, more pleasant and connecting people everywhere. It does not only connect people, but also machines, enhancing the efficiency of automated tasks and monitoring automated processes. In this context the IBBT (Interdisciplinary Institute for BroadBand Technology) project TRACK (TRain Applications over an advanced Communication networK), sets the definition and prototyping of an end-to-end train-to-wayside communication architecture as one of the main research goals. The architecture provides networking capabilities for train monitoring, personnel applications and passenger Internet services. In the context of the project a prototype framework was developed to give a complete functioning demonstrator. Every aspect: tunneling and mobility, performance enhancements, and priority and quality of service were taken into consideration. In contrast to other research in this area, which has given mostly high-level overviews, TRACK resulted in a detailed architecture with all different elements present