Mathias Rousset

Research topics

• Timescale Problem in Molecular Simulation, Free Energy Computations.

  • Articles: (13), (11), (9), (7), (6), (5) and (4).
    
  • The main challenge: Simulating molecular systems with multiple time scales: fast timescales (e.g. rapid oscillations of atoms) are coupled to slow ones (e.g. conformation of molecules).
    
  • Numerical illustrations:
    (i)-In this simulation with periodic boundary conditions, a dimer (in red) is coupled to a solvant (in green). The slow degree of freedom (reaction coordinate) is the distance between the two atoms of the dimer, and has two different stable configurations (blue or red). The fast degrees of freedom comes from the motion of the atoms of the solvant (in green). In a second simulation, an adaptive biasing technique is used to accelerate the transition between configurations (between blue and red) of the dimer (references: (11), (7), and (6)).
    (ii)-In this simulation, we simulate a large polymeric chain of atoms attached at one hand and coupled to a thermostat. Bonds, and bond angles between atoms are rigid, and the time step is limited by the fast oscillation of the torsion angles. In a second simulation, the oscillation of torsion angles are correlated, using an implicit mass-matrix penalty which does not modify the probability distribution of the different configurations of the system. It results in larger time steps, and in an accelerated simulation (references: (9)).
    

• Particle methods for Schrödinger Groundstates, Quantum Monte-Carlo methods.

  • Articles: (10) and (2)
    
  • The main challenge: Solving eigenvalue problems associated to an elliptic differential operator in high dimension (the Schrödinger operator) using stochastic particle methods (Monte-Carlo). This includes the hard problem of Fermionic (skew-symmetric) solutions and excited states (the sign problem).
    

• Hybrid Particle methods for multiscale PDEs.

  • Articles: (12) and (8)
    
  • The main challenge: Simulating/analyzing a multiscale physical phenomenon described by a hierarchy of PDEs (e.g. a kinetic equation at the microscopic level, and a diffusion equation at the macroscopic level). The idea is to use a particle (Monte-Carlo) method at the micro level, coupled with a classical grid method at the macro one.
    

Support

Collaborators

Publications

• Pre-prints
  (13)-M.Rousset and G.Samaey: Individual-based models for bacterial chemotaxis and variance reduced simulation. (Preprint pdf )
  
• Monographs
  (12)-T.Lelièvre, M.Rousset and G.Stoltz (2010): Free energy computation: a mathematical perspective. Imperial College Press
  
• Published articles
  (11)-T. Lelièvre, M. Rousset and G. Stoltz: Langevin dynamics with constraints and computation of free energy differences. Maths of Comp. to appear: (Preprint pdf)
  (10)-M.Rousset (2010): On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes. M2AN, Vol. 44, Issue 5, p 977-995. (Preprint version: pdf)
  (9)-P. Plechac and M. Rousset (2009): Implicit Mass-Matrix Penalization of Hamiltonian dynamics with application to exact sampling of stiff systems. SIAM MMS, 8, No 2, arXiv:0805.1092.
  (8)-T. Goudon and M. Rousset (2009): Stochastic Acceleration in an Inhomogeneous Time Random Force Field. Appl Math Res Express. 2009: 1-46 (Preprint version: pdf )
  (7)-T. Lelièvre, M. Rousset and G. Stoltz (2008): Long time convergence of the Adaptive Biaising Force method. Nonlinearity, 21, 1155-1181 (Preprint version: pdf)
  (6)-T.Lelièvre, M.Rousset and G.Stoltz (2007): Computation of free energy differences with parallel adaptive dynamics . J. Chem. Phys, Vol.126, No.13. (Preprint version: pdf)
  (5)-T.Lelièvre, M.Rousset and G.Stoltz (2007): Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case. J. Comp. Phys. 222(2), 624-643. (Preprint version: pdf)
  (4)-M.Rousset and G.Stoltz (2006): Equilibrium sampling from nonequilibrium dynamics. J. Stat. Phys., 123 (6), 1251-1272. (Preprint version: pdf)
  (3)-A.Doucet and M.Rousset (2006): Discussion of "Exact and computationnally efficient likelihood estimation of discretely observed diffusions" (by Beskos and co.). J. Roy. Stat. Soc. B. 68, 333. (Preprint version: pdf)
  (2)-M.Rousset (2006): On the control of an interacting particle approximation of Schrödinger ground states. SIAM J. Math. Anal., 38 (3), 824-844.(Preprint version: pdf)
  (1)-M.Rousset (2004): Sur la rigidité de polyèdres hyperboliques en dimension 3: cas de volume fini, cas hyperidéal, cas fuchsien. Bull. SMF 132, 233-261. (Preprint version: pdf)
  

Teaching (in french)

• Cours de M2: Mathematical introduction to quantum mechanics (pdf). Online courses: (Stoltz and co., Teschl, Basdevant)
  

Events

• Formation EDPs, Probabilités, Convergence à l'équilibre, les 6 et 7 septembre 2010, Lille.
  
• HIM Junior Semester Programm, Bonn, April 7-11th 2008.
  
• ODYN III, march 13,14,15 2008, Lille.
  
• Saddam