Planar Maps and Airy Phenomena

Scaling of Percolation on Infinite Planar Maps, I

We consider several aspects of the scaling limit of percolation on random planar triangulations, both finite and infinite. The equivalents for random maps of Cardy’s formula for the limit under scaling of various crossing probabilities are given. The limit probabilities are expressed in terms of simple events regarding Airy-Lévy processes. Some explicit formulas for limit probabilities follow f...

Philippe Flajolet and the Airy Function

1. Historical backgrounds: the Airy function in Physics 2 2. The area-Airy distributions: Brownian motion, linear probing hashing, additive parameters in grammars 4 2.1. Area under a Brownian excursion 4 2.2. On the analysis of linear probing hashing 4 2.3. Analytic variations on the Airy distribution 5 2.4. Hachage, arbres, chemins & graphes 6 3. Random matrices, Airy kernel and the Tracy–Wido...

Random maps, coalescing saddles, singularity analysis, and Airy phenomena

Three-dimensional modeling of transport phenomena in a planar anode-supported solid oxide fuel cell

In this article three dimensional modeling of a planar solid oxide fuel cell (SOFC) was investigated. The main objective was to attain the optimized cell operation. SOFC operation simulation involves a large number of parameters,   complicated equations, (mostly partial differential equations), and a sophisticated simulation technique; hence, a finite element method (FEM) multiphysics approach ...

Airy pattern approximation of a phased microphone array response to a rotating point source.

Deconvolution of phased microphone array source maps is a commonly applied technique in order to improve the dynamic range and resolution of beamforming. Most deconvolution algorithms require a point spread function (PSF). In this work, it is shown that the conventional definition of the PSF, based on steering vectors, is changed when the source is rotating. The effect of rotation results in an...