The year is divided into two semesters (semesters 3 and 4 of the Master). The first semester (S3) lasts from the beginning of September to the end of January. The second semester (S4) starts at the beginning of February. Each semester is validated by a minimum of 30 ECTS. See the Schedule
Third semester
Here are the Courses specific to the M2 Orientation "Numerical Modeling". These specific courses can be completed by courses from the M2 Orientation "Physics, Concepts and Applications" or "Chemistry Concepts and Applications".
Please note that some Courses are organized over several periods of the S3 Semester.
Title (en)
Advanced Computational Statistical Physics
Ralf Everaers
Ralf Everaers
Statistical Physics deals with behavior that emerges from the interactions of many particles. Since exact analytical solutions of the governing equations only exist for a small number of models, computer simulations have become an indispensable tool in the field and neighboring disciplines like Condensed Matter Physics, Theoretical and Physical Chemistry, Chemical and Biological Physics.
The cours introduces the methods employed for exploring the static and dynamic properties of particle based systems on an advanced level. Computational exercises, where these methods are applied to simple, but powerful models, form an integral part of the module.
- Molecular Dynamics Simulations for the exploration of emergent dynamic properties
- TD: Integrating Newton’s equations of motion for continuous potentials: The secret behind the Verlet algorithm
- Liouville formulation of symplectic and multiple-timestep integrators
- Langevin dynamics
- Thermodynamic averages, fluctuations and transformations between ensembles
- Linear response and Green-Kubo relations for transport coefficients
- TD: MD simulations of Lennard-Jones liquids
- Non-equilibrium Molecular Dynamics
- Monte Carlo Simulations for the exploration of emergent static properties
- Exact enumeration of small systems: Reweighting and the exact evaluation of partition functions
- Monte Carlo simulations
- Simple Sampling: Statistical errors and the limits of reweighting
- Importance Sampling: The Metropolis algorithm; Statistical errors, dynamical correlations and the power of well-designed trial moves: Glauber vs. Kawasaki vs Cluster moves for spin systems; Simulating polymers; Quenched disorder: spin glasses; Other ensembles.
- TD: Monte Carlo simulations of the Ising model
- Free energies
- Widom insertion and thermodynamic integration
- TD: free energy of a methane molecule in water from TI (L. Monticelli)
- Advanced techniques:
- TD: The density of states of the Ising model from Multihistogram analysis/WHAM
- TD: Protein binding energies from Umbrella Sampling and Steered Molecular Dynamics (L. Monticelli)
- Widom insertion and thermodynamic integration
- Exploring Rare events
- (sampling) transition states and paths
- Kinetic Monte Carlo
- Frenkel and Smit, Understanding Molecular Simulation
- Allen and Tildesley, Computer Simulation of Liquids
- Landau and Binder, A Guide to Monte Carlo Simulations in Statistical Physics
- Krauth, Algorithms and Computations
Physique statistique L3 and M1
Physique numérique L3
Mini-projet et examen écrit
Title (en)
Quantum approach of catalytic reactivity
Pascal Raybaud (IFPEN)
P. Raybaud
+ un intervenant extérieur (IFPEN)
Les avancées des méthodes quantiques (théorie de la fonctionnelle de la densité notamment) permettent aujourd’hui d’explorer la réactivité de systèmes catalytiques complexes (hétérogènes ou homogènes) utilisés industriellement ou susceptibles de l’être. Le cours illustre comment les approches quantiques modernes permettent :de comprendre la réactivité par le calcul de propriétés catalytiques ; d’aider à l’interprétation de résultats expérimentaux ; de prédire des propriétés clefs pour optimiser de nouveaux catalyseurs. Le cours abordera de nombreuses études de cas illustrant des systèmes d’intérêts industriels : surfaces de métaux, d’oxydes, sulfures, zéolithes, agrégats métalliques supportés, systèmes organométalliques… et réactions associées d’hydrogénation, hydrogénolyse, désulfuration, isomérisation, craquage, oligomérisation, …
1/Rappels fondamentaux : théorie de la fonctionnelle de la densité (hypothèses majeures), approches orbitalaires, structures de bandes dans un solide et en surface, logiciels académiques/commerciaux
2/Choix de modèles pertinents pour la description des sites actifs: moléculaires (organométalliques), périodiques (surfaces catalytiques)
3/Calculs de propriétés clefs en catalyse: structure, spectroscopie, thermodynamique et cinétique
4/Modélisation micro-cinétique et multi-échelle
5/« Catalysis by design » : vers la prédiction de descripteurs quantiques et relation structure-activité
R.G. Parr, W. Yang, « Density-Functional Theory of Atoms and Molecules », Oxford University Press, New York, 1989.
A chemical and theoretical way to look at bonding on surfaces. R. Hoffmann. Review of Modern Physics. 60 (1988) 601.
UE en lien avec la réactivité chimique ou la catalyse, ou la physico-chimie des matériaux (note : seules les notions minimales utiles seront introduites) ;
UE en lien avec les principaux fondamentaux en chimie théorique (note : les principes de la DFT utiles seront introduits 3h)
Examen final écrit de 1h30.
Title (en)
Theoretical photophysics and -chemistry
Thomas Niehaus
The light-matter interaction is important for a variety of technological applications ranging from optoelectronics to photovoltaics and relevant for biochemistry. This course addresses the question what happens after light is absorbed by matter, how the acquired energy is transported, leads to desired and undesired photoreactions and is finally released to the environment. The course is situated at the border of physics and chemistry and deals with molecules as well as with solids and new materials.
For more details you can find a presentation of the course on YouTube.
Theoretical considerations at the level of many-body quantum mechanics are accompanied by numerical studies in the practical sessions, which also cover some first principles calculations.
Chapter 1: Introduction to photochemistry
Keywords: Spectral irradiance, quantum yields, photochemical kinetics
Chapter 2: Molecular states
Keywords: Born-Oppenheimer approximation, Classification of excited states
Chapter 3: First principles methods for excited states
Keywords: TDDFT
Chapter 4: Electronic excitation and decay
Keywords: Vibrationally resolved spectra, Huang-Rhys factors, Kasha rule
Chapter 5: Wavepacket dynamics
Keywords: Franck-Condon excitation
Chapter 6: Non-adiabatic dynamics
Keywords: Conical intersections, Landau-Zener model, Surface Hopping and Ehrenfest dynamics
Chapter 7: Charge and energy transfer
Keywords: Förster/Dexter exciton transfer, H/J aggregates
Chapter 8: Photophysical properties of solids
Keywords: Intra- and interband absorption, Wannier-Mott excitons, Frenkel excitons, CT excitons
Quantum mechanics L3 or equivalent.
CP (30%, written) + ET (70%, computational project) if mark of CP > ET, ET (100%, computational project) otherwise.
Title (en)
Computational fluid dynamics
Guillaume Laibe
G. Laibre
E. Levèque
A. Venaille
Numerical simulations have become a key device of physicists’ toolbox, making it possible to study systems that have no analytic solutions, or for which the experiment is difficult, or even impossible. The CFD module is designed to deliver essentials of the art of computational hydrodynamics: choice and relevance of the discretisation method, design for stability and accuracy, implementation of different physical processes. The ubiquity of the principles will be demonstrated through problems ranging from flows at the laboratory scale up to the atmospheric and astrophysical flows.
- Introduce general concepts of computational fluid dynamics and numerical methods : stability and accuracy,
- Present different methods with their respective strengths and weaknesses,
- Applications to real physical systems
- Hands on with the help of sample codes and jupyter notebooks
- Multi-physics fluid dynamics : Lattice Boltzmann method.
- Geophysical fluid dynamics : Finite differences.
- Astrophysical fluid dynamics : Smooth Particle Hydrodynamics, Godunov methods.
- Toro : Riemann Solvers and Numerical Methods for Fluid Dynamics
- Violeau : Fluid Mechanics and the SPH method
- Krüger et al. : The Lattice Boltzmann Method: Principles and practice
- Numerical methods for fluid dynamics - with applications to geophysics, Dale Durran
Outils numériques et programmation (L3)
A report highlighting the relevance of a numerical method for a flow problem.