RESEARCH PROJECTS
By resorting to Creutz’s demon algorithm, a Monte Carlo Markov Chain (MCMC) is generated on the iso-energetic phase space surfaces of a binary mixture of interacting particles via Lennard-Jones potentials ; the latter being a glass forming supercooled liquid. Along this MCMC some geometric quantities of topological meaning are computed in search for a signature of the glassy transition. A numerical tool is developed with the aim of being used to perform further investigations. (numerical modeling report)
M.sc. (2nd year) research project under the supervision of Pr. Marco Pettini (CPT).
The reachability map of Berlin is first simulated from a shorter-path-based analysis of the Berlin Center Road Network (BCRN) datas. A network-based traffic model is then developed : from microscopic cellular automaton to emergent diffusion process. An model of information spreading is thus developed and collective dynamics on a road network can be seen as a transition to ordered behavior in dried active matter on a complex network.
M.sc. (2nd year) research project with Isaac Labé (M.Sc.).
By studying active matter models, a better understanding of stationary properties associated to this class of systems will be achieved. Escape and correlations issues will be notably examined in the cases of Active Brownian Particles models and Active Ornstein-Uhlenbeck Particles. One will try to understand a dynamical phase transition between weak and strong activity regimes since a few results have been recently highlighted in these two limits. Finaly the weak noise approach will be generalized to an arbitrary noise.
5 months M.sc. (2nd year) research internship under the supervision of Dr. Vivien Lecomte (LIPhy).
BIBLIOGRAPHICAL PROJECTS
An introduction to the description of far-from-equilibrium-states evolution and irreversible road to equilibrium attractors (H theorem) is achieved. The connections between microscopic descriptors, mesoscopic Boltzmann equation and local tranport equations of macroscopic observables are provided by means of Coarse-graining, BBGKY and Chapman-Enskog procedures.
M.sc. (2nd year) literature review proofread by Pr. Marco Pettini (CPT).
An introduction to the Ginzburg-Landau theory for statics and dynamics of phase transitions is providedby means of the statistical field framework : Coarse-graining procedure and mean field approximation are thus applied to statics of heterogeneous systems phase transitions.
M.sc. (2nd year) literature review proofread by Pr. Marco Pettini (CPT).
A global (metapopualation) epidemic spreading is described through the coupling of subpopulations endemic epidemic reactions with the world-air-transportation network fluxes. The arrival time statistics of a global disease spreading throughout each subpopulation is studied from toys networks to 2d complex networks within the mean-field approximation.
M.sc. (2nd) year bibliographical project with Elisabeth Lemaitre (M.Sc.) under the supervision of Pr. Alain Barrat (CPT).