I’m Élodie, a PhD student on Condenced Matter Theory group on soft matter theory under the direction of Thomas Salez and Yacine Amarouchene .

My researches is to simulate and understand how a Brownian particles is moving near a wall.

I hugely appreciate give some teaching physics and mathematics. I greatly like search how to explain something on the good way with the level of the public in front of me. Of course, I love vulgarization of science.

I studied fundamental physic, some chemistries specialties and mathematics for PDE and their numerical simulations.


What is a brownian motion?

In 1827, Robert Brown discovered a strange movement while studying Pollen. Immersed in water, he moves randomly without any deterministic movement. At that time, scientists didn’t believe Robert, but later on, it was finally seen to be real and was called the Brownian movement.

Much later, in 1901, Louis Bachelier worked on the mathematics of this movement and he was the first to put the first bricks to describe a random movement. This research was first applied to finance.

Three years later, Albert Einstein highlighted a general law for an erratic particle in free space. He defined the diffusion coefficient which is a constant balance between the fluctuation of the particle due to thermal agitation and its dissipation in space.

Finally, in 1909, Jean Perrin used Albert Einstein’s diffusion model to calculate the Avogadro number – the quantity of element in a system containing as many elementary entities as there are atoms in 0.012 kg of carbon 12 . To do this, he coupled these results with other theories already acquired at that time.

What about now?

Currently, we know how to describe the movement of a micrometric particle in bulk space. The big problem with this theory is that nothing is free or far from any other object in nature.

For example, take the red blood cells in the blood vessels. Can theses laws be applied in this confined case? We realized that no and that a lot of physical phenomena come into play to modulate the Brownian motion equations. The presence of the blood vessel wall induces a force on the particle, but not only that, it also induces a dependency depending on the position of the particle in the diffusion coefficient. The latter is therefore no longer a constant of the problem but another variable to be taken into account in the calculations.

We also know that we don’t have only one red blood cell in the blood vessels, because of that, interactions between particles also induce an effect. Then we need to investigate Brownian motion laws in these cases to understand more what happens at microscopic object in real life.

In my research, I simulate and seek to understand the forces at play in such a problem. I am first interested in the case of a flat wall, with one particle alone and then with N particles. In this problematic, I also try to understand the impact of an external flow but also what happens in the case where the particle is self-propelled or where the wall is soft.

All these fields of research are still little known and numerical simulation is a tool to help us understand the mechanisms at play coupled with experimental results.


Diagram of the problem with a single particle of radius R and mass m, immersed in a fluid of density ρ and viscosity η and close to a rigid wall.

Curriculum vitae


2020-2023 :

Ph.D. in lasers, matter, nanosciences – LOMA, University of Bordeaux.

2019-2020 :

First year of M.Sc Applied mathematics, statistics, path Partial differential equations and Modeling – University of Bordeaux.

2018-2019 :

M.Sc Fundamental physics and applications, Physics Aggregation course – University of Bordeaux.

2016-2018 :

M.Sc Fundamental physics and applications, Lasers, matter and nanosciences courses – University of Bordeaux..

2015-2016 :

B.Sc Physics – University of Bordeaux.

2013-2015 :

Two years of B.Sc Physics and Chemistry – University of Bordeaux.


2020-2021 :

Teaching missions – BSc degree – Optics, Mathematics for Chemistry, Thermodynamics, Vibration, University of Bordeaux.

2020 :

Reserches intership – Brownian particles near a rigid wall – LOMA, University of Bordeaux.

2018-2019 :

Teaching internship in “Classe préparatoire aux grandes écoles” – Teached in lab class, tutorials and “Khôlles” – Montaigne Hight school, Bordeaux.

2018 :

Reserches intership – Actives particles at interfaces – LOMA, University of Bordeaux.

2017-2019 :

Oral examination jury of second year or B.Sc of physics – University of Bordeaux.

2017 :

Reserches internship – Methanol deutered in a region of Orion nebula – Laboratoire d’Astrophysique de Bordeaux, University of Bordeaux.

2016 :

Reserches internship – Simutation of laser equations – Centre d’étude de laser intence et applications, University of Bordeaux.



  • Brownian motion,
  • Statistical physics,
  • Fluid and solid physics,
  • Basic in biophysics.


  • : Python, Cython, basics in C.
  • : You can visit my Github page.
  • Numerical simulations in PDE

2020 – 2021

L1 Life and Earth Science – Optic Lab class.

L2 Chemistry. Mathematics methode Tutorials.

L2 Physics – Thermodynamics Lab class.

L3 Mechanics and Engineering science – Vibration Tutorials and lab class.


Laboratoire Ondes et Matière d’Aquitaine (LOMA)
351 cours de la libération
33405 Talence Cedex

Phone : + 33 (0)5 40 00 62 09
E-mail: elodie.millan@etu.u-bordeaux.fr
Office : 202