The aim of the course is to present in details some advanced theoretical tools in quantum mechanics with an emphasis on degenerate many-body systems and scattering theory.

« La chétive pécore, s’enfla si bien qu’elle creva ». « Je plie, et ne romps pas ». While taking inspiration from the living, La Fontaine noticed examples of organisms – frog and reed – that deform strongly, sometimes beyond unrecoverable limits.

Turbulent flows are present all around us and are crucial in fields such as aeronautics, industry, meteorology, astrophysics, climate. 

The development of animals, starting from a single cell to produce a fully formed organism, is a fascinating process. Its study is currently advancing at a rapid pace thanks to combined experimental and theoretical progress, yet many fundamental questions remain to be answered.

This course will address the fundamental theoretical concepts underlying the self-organization of multicellular systems, from gene regulation to the mechanics of active biological materials. The course will be based on various concepts from theoretical physics: dynamical systems, soft and active matter, the mechanics of continuous media, numerical modeling, etc.

The numerical resolution of fluid dynamics equations is becoming increasingly important in many aspects of scientific research. In this course, we will develop and analyze the methods used to solve the partial differential equations relevant to fluid dynamics (elliptic, parabolic and hyperbolic).

In this course we will cover the basics of ecology, evolution, and epidemiology, with the lens and tools of physics. 

The lectures offer a statistical-physics perspective on active matter, which encompasses systems whose fundamental constituents dissipate energy to exert forces on the environment. This out-of-equilibrium microscopic drive endows active systems with properties unmatched in passive ones. From molecular motors to bacteria and animals, active agents are found at all scales in nature. Over the past twenty years, physicists and chemists have also engineered synthetic active systems in the lab, by motorizing particles whose sizes range from nanometers to centimeters, hence paving the way towards the engineering of active materials.

The lectures will rely on the modern tools of statistical mechanics, from stochastic calculus to field theoretical methods, using both theoretical models and experimental systems to illustrate the rich physics of active matter.

Soft Matter refers to diverse materials such as polymers, colloids, granular materials or liquid crystals, that display complex features, as showing fluid or solid like properties depending on the external solicitation, anisotropic mechanical properties or the appearance of yield stresses

The Advanced Biophysics Course is a lecture course that covers modern concepts in experimental and theoretical physics of living systems, in the broadest sense.

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Image N. Desprat (LPENS)

Objectives : the lecture will present a broad overview of fluid mechanics at all scales, from bacterias to stars.