Paris Physics Master
STATISTICAL PHYSICS OF COMPLEX SYSTEMS VIA NUMERICAL MODELING
Format: each session combines a short lecture and hands-on numerical simulations in a computer room.
This teaching unit introduces students to the statistical physics of complex systems through the progressive construction of numerical simulations. The aim is to discover how simple models and numerical simulations can help understanding the hidden structure and dynamics of complex physical systems. It builds directly on the first-semester courses Numerical Physics, Statistical Physics, and Macroscopic and Complex Systems. Each session adds a new layer of physical modeling or computational technique, with an emphasis on intuition, practical implementation, and connections to real scientific problems (polymers, liquids, diffusion, proteins…). The focus is on intuition, physical insight, and practical implementation.
Throughout the course, students will:
- Build and analyze simulations of systems from single particles to interacting many-body systems.
- Explore Brownian motion, Langevin dynamics, random walks, and master equations.
- Model molecular liquids, condensed phases, and polymers (bead–spring models).
- Investigate phase transitions and structural metrics such as pair distribution functions.
- Discover how simplified models can capture essential physics, from polymer elasticity to protein folding.
1. Introduction – What is a model in physics?
From coarse-grained polymers to DNA elasticity. First numerical steps: simple chain models, Monte-Carlo sampling.
2. Explicit vs. implicit solvent models
Simulating particles in a solvent; comparison with Langevin dynamics. Hands-on exploration of pre-written codes.
3. Diffusion and Brownian motion
Langevin equation, noise, correlations, time-step effects, ergodicity.
4. From one particle to many
Ensemble averages, distribution analysis, extracting diffusion coefficients, external potentials.
5. Random walks and trajectory-based descriptions
Master equations, transition matrices, molecular association/dissociation examples.
6–7. Interacting particles and Lennard-Jones fluids (two sessions)
Liquids, gases, melting, phase transitions; pair distribution functions and structural analysis.
8. Polymer physics (I): bead–spring chains
Rouse dynamics, subdiffusion, single-chain simulations.
9. Polymer physics (II): interactions and coil–globule transition
Adding LJ interactions, equilibrium globules, density profiles.
10. Protein folding (intro)
Simple models with specific interactions; connecting to Langevin dynamics and parameter choices.
The course is mainly taught by Fabio Pietrucci and Maria Barbi with inputs from Marie-Anne Herve du Penhoat and Nicolas Rodriguez.
Maria Barbi is interested in understanding the physical mechanisms underlying the functioning of biological systems, and especially to all processes involving DNA. She is particularly interested in the study of broad field of nuclear architecture and functional dynamics of chromosomes, both from theoretical (polymer physics, statistical mechnaics, but also mechanics and electrostatics) and numerical point of view. In most cases, a strong effort is invested in the comparison with both in vitro and in vivo experimental results. As a teacher at SU, she teaches different disciplines, some of them at the physics-biology interface, and she is involved in the dissemination and sharing of pedagogical practices and in discussing their impact on learning.
Fabio Pietrucci worked at SISSA (Trieste) and EPFL (Lausanne) before becoming a "maître de conférences" at Sorbonne University in 2014. His research activity is focused on the development and application of new theoretical and computational approaches to study the transformations of matter. He explores the nucleation of crystals, chemical reactions in solution, and the folding of proteins as well as their interaction with other proteins or drugs. The aim is to establish a unified theoretical framework able to reconstruct transformation mechanisms, free-energy landscapes and kinetic rates for a wide range of different systems.