Fabrice Philippe

Generating connected acyclic digraphs uniformly at random

We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non-necessarily connected.

Illustration of the Fermi–Dirac statistics

The distribution of electrons in small one-dimensional systems is obtained under the assumption of evenly spaced energy levels. The method consists of considering isolated systems and shifting electrons from their zero-temperature location. The distribution is then expressed in terms of the number of partitions of integers. When the system is in thermal contact with an electrical insulator, the electron distribution is obtained by averaging the previous result with the Boltzmann factor as a weight. Finally, when the system is in thermal and electrical contact with a large medium, the Fermi–Dirac distribution emerges through averaging over the number N of electrons. The statistics of light emitted or absorbed by the electron gas is obtained without quantization of the optical field. Our rigorous though elementary treatment helps clarify concepts employed in statistical mechanics.

A simple model for Carnot heat engines

We present a (random) mechanical model consisting of two lottery-like reservoirs at altitude

Fluorescence from a few electrons

E_h

Dual-wavelength laser for THz generation by photo-mixing

and

Monte Carlo modeling of the dual-mode regime in quantum-well and quantum-dot semiconductor lasers.

E_l<E_h

On Classical Ideal Gases

, respectively, in the earths gravitational field. Both reservoirs consist of

A New Perspective on Classical Ideal Gases

N

Two-level laser light statistics

possible ball locations. The upper reservoir contains initially

Monte Carlo markovian modeling of modal competition in dual-wavelength semiconductor lasers

n_h\le N