Gael Raoul home page

Gael RAOUL.

Gael Raoul
DAMTP,
Centre for Mathematical Sciences,
Cambridge University,
Wilberforce Road,
Cambridge CB3 0WA, UK.
g.raoul[at]damtp.cam.ac.uk

I am now a postdoc in the group Partial Differential Equations of Peter Markowich. In February 2012, I will join the biology lab CEFE in Montpellier, as a CNRS researcher. I am interested in qualitative properties of kinetic PDEs appearing in mathematical biology. I have focused so far on two models:

A simple integro-differential model introduced by theoretical biologists to study evolution (how species are created, etc...):

Numerically, we observe that for most coefficients a( ) and b( , ), the population converges to a sum of Dirac masses (each is a species). The study of this asymptotic behavior is the main subject of my phd thesis. The first picture below shows how a single species can evolve into two different species, and the second picture shows how many species will appear in a system (defined by the selection strength parameter A).

$asymptotic profile for A\in [0,3]$

A non-local aggregation model, which appear in various biological models:

It describes the evolution of a density of interacting particles. W() is the interaction potential attached to each particle, and V() is an external potential. Numerically, the behavior of the solution depends on the properties of W(x) at x=0: it blows-up to sums of Dirac masses in finite time for singular attractive W, it blows up in an infinite time for regular W(), and remains bounded if W is singular repulsive at x=0. In each case, the precise asymptotic profile of the solution depends on the shape of W() and V().

As described above, the asymptotic behavior of those two models have similarities, although they are very different mathematically: the second one has a gradient flow structure, whereas the first one doesn't preserve any quantity and doesn't have any entropy (in general).

CV: Raoul_CV.pdf

PhD thesis: Raoul_PhDThesis.pdf

(Pre)Publications: download all publications

L. Desvillettes

P.E. Jabin

S. Mischler

On selection dynamics for continuous structured populations

[2] G. Raoul, Local stability of Evolutionary attractors for continuous structured populations, accepted in Monatshefte fur Mathematik,

[3] K. Fellner, G. Raoul, Stable stationary states of non-local interaction equations, Mathematical Models and Methods in Applied Sciences, Vol 20, No 12 (2011),

[4] K. Fellner, G. Raoul, Stability of stationary states of non-local equations with singular interaction potentials, Mathematical and Computer Modelling, Vol 53, No 7-8 (2011),

[5] P.E. Jabin, G. Raoul, On selection dynamics for competitive interactions, Journal of Mathematical Biology, Vol 63, No 3 (2011),

[6] G. Raoul, Long time evolution of populations under selection and vanishing mutations, Acta Applicandae Mathematica Vol 114 (2011),

[7] N. Champagnat, P.E. Jabin, G. Raoul, Convergence to equilibrium in competitive Lotka-Volterra equations, Comptes Rendus Mathématiques de l'Académie des Sciences de Paris Vol 348, No 23-24 (2010),

[8] G. Raoul, Non-local interaction equations: Stationary states and stability analysis, submitted,

[9] A. Calsina, S. Cuadrado, L. Desvillettes, G. Raoul, Asymptotics of steady states of a selection mutation equation for small mutation rate, submitted.

[10] S. Mirrahimi, G. Raoul, Population structured by a space variable and a phenotypical trait, preprint,

[11] D. Balague, J.A.J. Carrillo, T. Laurent, G. Raoul, Nonlocal interactions by repulsive-attractive potentials: radial in/stability, submitted.

Invitations/visits of other universities:

December 2007, Universitat Autonoma de Barcelona, 1 week,
August 2008 -january 2009, University of Vienna, 5 months,
October 2008, University of Nice, 1 week,
April 2009, University of Cambridge, 1 week,
May 2009, Universitat Autonoma de Barcelona, 2 weeks,
June 2010, Universitat Autonoma de Barcelona, 1 week,
November 2010, University of Heidelberg, 1 week.
February 2011, Centre d'ecologie Fonctionelle et Evolutive, Montpellier, 3 days,
May 2011, University of Toulouse, 1 week,
May 2011, University of Bordeaux, 1 week,
October 2011, University of Barcelona, 1 week,
Novembver 2011, UCLA/UC Riverside, 2 weeks,
December 2011, Ecole Normale Superieure of Lyon, 1 week,
January 2012, University of Barcelona, 1 week.

Recent presentations of my work:

April 15 2009, UCLA, Los Angeles,
Mai 1 2009, seminar Cambridge University, Cambridge,
July 13 2009, workshop "Multiscale Analysis of Self-Organization in Biology", Banff,
October 6 2009, workshop "Concentration en vitesse et en espace dans les modèles cinétiques et diffusifs", Institut Henri Poincaré, Paris,
November 27 2009, workshop "First Minho meeting on mathematical physics", Braga,
December 10 2009, seminar, University of Rennes,
January 12 2010, seminar, University of Paris-Dauphine,
January 14 2010, seminar, team ANUBIS, INRIA-Bordeaux,
January 21 2010, seminar, University of Tours,
February 2010, conference "PDE and Mathematical Biology", La Havanna,
May 13 20010, workshop "Nonlinear diffusions and entropy dissipation: from geometry to biology", Banff,
June 3 2010, SIAM conference "Emerging Topics in Dynamical Systems and Partial Differential Equations", Barcelona,
September 8 2010, "Fluid-Kinetic Modelling in Biology, Physics and Engineering, Newton Institute", Cambridge,
November 30 2010, seminar, University of Heidelberg,
December 11 2010, "Classical and Quantum Mechanical Models of Many-Particles Systems", Oberwolfach,
December 16 2010, seminar, Centre d'ecologie Fonctionelle et Evolutive of Montpellier,
January 6 2011, "Population Genetics Group meeting", University of Hull,
April 27-29 2011, "Mathematics of Microbes: Biological Details of the Evolving Cell", Imperial College, London,
May 17 2011, seminar, University of Toulouse,
June 29 2011, 8th European Conference on Mathematical and Theoretical Biology, Krakow,
July 4 2011, summer school, Weissensee,
August 4 2011, Equadiff conference, Loughborough,
November 14-17 2011, SIAM Conference on Analysis of Partial Differential Equations, San Diego,
December 6 2011, seminar, Ecole Normale Superieur of Lyon.

Teaching:

2007/2008: Licence 3: Introduction to Matlab,
2007/2008, 2009/2010: "préparation à l'agregation": Integration theory,
2007/2008, 2008/2009, 2009/2010:"préparation à l'agregation": numerical analysis,
2008/2009: "préparation à l'agregation": Examination correction.