M1 - Modeling Biological and Environmental Systems - Mechanical Engineering Major - IDIL

The aim of this course is to introduce students to the finite element method applied to one-, two-, and three-dimensional problems in engineering and applied science. This introduction is given in the context 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 Ritz and Gallerkine approaches for one-dimensional media. Next, the issue of numerical integration is approached using the Gauss method. Meshing and validation of calculation models are then addressed during the study of surface modeling with 2D elements. Finally, these concepts will be used to implement the complete formalism of the finite element method in the context of bar and beam elements, then triangle-type elements. A practical application of these important theoretical concepts is carried out on an industrial calculation code (ANSYS) during practical work and a project.

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The first part of this course covers additional probability theory topics: conditional expectation, Gaussian vectors. The second part introduces 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 previous one. They are also a very powerful modeling tool. We will study the main properties of these processes, as well as their long-term behavior and the estimation of their parameters.

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The first part of this course covers additional probability theory topics: conditional expectation, Gaussian vectors. The second part introduces 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 previous one. They are also a very powerful modeling tool. We will study the main properties of these processes, as well as their long-term behavior and the estimation of their parameters.

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

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The course aims to provide a general introduction to cellular and molecular biology and to contextualize the use of modern physics, through its quantitative methods and approaches, to describe biological systems and their complexity from the molecular to the cellular and tissue levels.

Another fundamental topic covered is the quantification of phenomena, their physical interpretation, and their physical-mathematical modeling. The course introduces students to philosophy and the range of topics covered in this master's program, which focuses on the study of the physical principles of the organization and dynamics of living and complex matter.

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