M1 - Modeling Biological and Environmental Systems - Mention MECANIQUE - IDIL

The aim of this course is to introduce students to the finite element method as applied to one-, two- and three-dimensional problems in engineering and applied science. This presentation is made within the framework of linear elasticity and small perturbations in statics. Starting with prerequisites in mathematics and solid mechanics, the principle of discretization is first addressed through the approaches of Ritz and Gallerkine for one-dimensional media. Next, the problem of numerical integration is approached using the Gauss method. Meshing and validation of computational models is then addressed in the study of surface modeling with 2D elements. Finally, these notions will be used to set up the complete formalism of the finite element method within the framework of bar and beam elements, then triangle-type elements. A practical application of these important theoretical notions is carried out on an industrial calculation code (ANSYS) during practical work and a project.

See full page

See full page

The first part of this course deals with complements to probability theory: conditional expectation, Gaussian vectors. The second part presents one of the main families of discrete-time stochastic processes, Markov chains. These are sequences of dependent random variables, whose dependency relationship is relatively simple, since each variable depends only on the preceding one. They are also a very powerful modeling tool. We will study the main properties of these processes, as well as their behavior in long time and the estimation of their parameters.

See full page

See full page

See full page

See full page

See full page

See full page

See full page

See full page

See full page

The first part of this course deals with complements to probability theory: conditional expectation, Gaussian vectors. The second part presents one of the main families of discrete-time stochastic processes, Markov chains. These are sequences of dependent random variables, whose dependency relationship is relatively simple, since each variable depends only on the preceding one. They are also a very powerful modeling tool. We will study the main properties of these processes, as well as their behavior in long time and the estimation of their parameters.

See full page

See full page

See full page

See full page

See full page

See full page

See full page

See full page

See full page

See full page

See full page

This 42-hour course is divided into two parts (1/3, 2/3) to give the basics of heat transfer and fluid mechanics (3D). Fluids will be considered as continuous media. A particle is an element of volume infinitesimally small for mathematical description, but large enough relative to molecules to be described by continuous functions. This course extends the L3 course on modeling elastic media, as well as the 1D fluid mechanics course.

See full page

See full page

See full page

See full page

See full page

The course aims to give a general introduction to cellular and molecular biology, and to put into context the use of modern physics, with its quantitative methods and approaches, to describe biological systems and their complexity from the molecular to the cellular and tissue scales.

Quantifying phenomena, their physical interpretation and physico-mathematical modeling are also fundamental aspects of the course. The course opens up to philosophy and to the whole range of themes of this Master's program, centered on the study of the physical principles of the organization and dynamics of living, complex matter.

See full page

See full page

See full page

See full page