The master 'mathematical modeling and macroscopic physics' is a PSL
program organized jointly by the Ecole Normale Supérieure and the
University of Paris Dauphine, as a component of the M2 'Applied and Theoretical Mathematics' (MATH in french) of
Université Paris Dauphine.
This master program offers courses in macroscopic
physics, out of equilibrium phenomena, fluid dynamics, solid mechanics,
non-linear waves and patterns generated by instability. The
corresponding mathematical tools are mainly dynamical systems,
partial differential equations and stochastic processes.
For which research topics is this training useful ?
• Nonlinear physics
• Out of equilibrium statistical physics
• Solid mechanics
• Fluid dynamics, turbulence
• Application of fluid dynamics to meteorology, oceanography, climate or more generally GAFD
• Industrial applications of fluid dynamics, energy transformation
• Plasma physics
• Dynamical modeling (applied math or theoretical physics)
• Applications to complex systems, networks, finance, theoretical biology, …, or any problem which technically requires to solve PDE’s or coupled ODE’s
A formation in physics and mathematics
This master is intended for physicists or mathematicians interested in macroscopic physics. It offers a solid training in order to continue to a PhD doctorate, whether the chosen topic is theoretical, experimental or numerical.
The mathematical part of the program, accessible to physics students, is important for the following reasons:
- The tools used in macroscopic physics involve mathematical
techniques: ODE's, PDE's, probability theory, etc.
- Macroscopic physics is the domain of physics in which there are the
strongest interactions between physicists and mathematicians (in UK
and the US, most researchers in this field belong to applied maths
departments).
- A minimal training in mathematics (at least learning the language)
will allow physicists to discuss their research topic with
mathematicians. Similarly, a minimal training in physics will allow
mathematicians to discuss their research topic with
physicists.
The academic year is divided into two semesters:
First semester: depending on their previous studies, students
will have the choice between several courses of physics and maths.
Second semester: students will have the choice between courses of the M2 and optional courses of the ENS-ICFP Master program subject to time compatibility. Finally, students will have to validate an internship in a research laboratory (24 ECTS).
All the courses are optional (no mandatory course). A total of 60 ECTS is required over the year, and the program study must include at least two courses in maths, and two first semester courses in physics. Note that several mathematics courses have no prerequisites and are accessible to physicists students even if they have not taken mathematics courses in L3 and M1 (see program here).