## Home

I'm associate professor (maître de conférences) at the Institut Élie Cartan of Nancy.
I am a member of the partial differential equations research group and the CORIDA research team (INRIA Nancy).
I am supported by the ANRs CISIFS and GAOS and by the CPER MISN AOC.

### Contact

 Postal address Bureau 211 Institut de Mathématiques Élie Cartan Université de Lorraine B.P. 239 F-54506 Vandoeuvre-lès-Nancy Cedex France Phone (33) (0)3 83 68 45 41 Email alexandre.munnier[at]univ-lorraine.fr

### News

Since 2010, I have been in charge of the weekly PDE seminar.

## Research

My research activities focus on the study of mathematical systems modeling the dynamical interaction of a fluid with a rigid or deformable structure. The motion of rigid solids immersed in a fluid or swimming fish are two examples of such systems.

More precisely, I mainly address the following issues...

### Modeling

About this process, which consists in deriving a system of equations from physical principles, I've compared, for fluid-structure interaction systems, the Newtonian approach (of Classical Mechanics) to the Lagrangian formalism (of Analytic Mechanics).

### Biolocomotion

The biolocomotion is the study of fish and aquatic mammals locomotion. I work on all of the features of this problem: modeling, well posedness of the mathematical equations of motion, control (with T.Chambrion), numerical simulations (with B. Pinçon).

### Collisions

I'm interested in studying the asymptotic behavior of immersed rigid solids when they get close and eventually collide with a wall.

### Detection

Fish are endowed with a lateral line, a sense organ allowing them to detect immersed obstacles. C. Conca and I work on inverse problems that consist in recovering the position and the velocity of immersed rigid solids, from some data of the fluid.

## Publications

 [13] T. Chambrion and A. Munnier. Generic controllability of 3d swimmers in a perfect fluid. SIAM Journal on Control and Optimization, 50(5):2814–2835, 2012. [12] T. Chambrion and A. Munnier. Locomotion and control of a self-propelled shape-changing body in a fluid. Journal of Nonlinear Science, 21:325–385, 2011. 10.1007/s00332-010-9084-8. [11] A. Munnier. Passive and self-propelled locomotion of an elastic swimmer in a perfect fluid. SIAM J. Appl. Dyn. Syst., 10(4):1363–1403, 2011. [10] T. Chambrion and A. Munnier. When fish moonwalk. In American Control Conference (ACC), 2010, pages 2965 –2970, 30 2010-july 2 2010. [9] C. Conca, M. Malik, and A. Munnier. Detection of a moving rigid solid in a perfect fluid. Inverse Problems, 26(9):095010, 2010. [8] A. Munnier and B. Pincon. Locomotion of articulated bodies in an ideal fluid: 2d model with buoyancy, circulation and collisions. Math. Models Methods Appl. Sci., 20(10):1899–1940, 2010. [7] A. Munnier. Locomotion of deformable bodies in an ideal fluid: Newtonian versus lagrangian formalism. J. Nonlinear Sci., 19(6):665–715, 2009. [6] J. Houot and A. Munnier. On the motion and collisions of rigid bodies in an ideal fluid. Asymptot. Anal., 56(3-4):125–158, 2008. [5] A. Munnier. On the self-displacement of deformable bodies in a potential fluid flow. Math. Models Methods Appl. Sci., 18(11):1945–1981, december 2008. [4] A. Munnier and E. Zuazua. Large time behavior for a simplified N-dimensional model of fluid-solid interaction. Comm. Partial Differential Equations, 30(1-3):377–417, 2005. [3] J. Cartier and A. Munnier. Geometric Eddington factor for radiative transfer problems. In Numerical methods for hyperbolic and kinetic problems, volume 7 of IRMA Lect. Math. Theor. Phys., pages 271–293. Eur. Math. Soc., Zürich, 2005. [2] A. Munnier. Stability and linear oscillations of liquid bridges with varied boundary conditions under zero gravity. Z. Angew. Math. Phys., 54(6):977–1000, 2003. [1] A. Munnier. Petites oscillations d’un liquide, dans un container de révolution avec fond élastique, en l’absence de pesanteur. Z. Angew. Math. Phys., 48(4):629–645, 1997.

## Numerics

Some of my achievements in numerics…

### A Matlab toolbox

B. Pinçon and I have developed the Matlab Toolbox (BhT), allowing one to easily realize simulations of rigid solids moving in a perfect fluid with potential flow.

BhT contains also tools to study the exchanges of energy between the immersed solids and the fluid and to compute the work, the power or the torques exerted at the joints of the swimming articulated solid bodies.

Further information is available on BhT home page (hosted by Inria Gforge) and on the BhT demo page.

### Control of a 2D swimmer

T. Chambrion and I have studied the controllability of a model of shape-changing body swimming in a perfect fluid with potential flow.

Numerical simulations are available on the dedicated web page.

### An elastic swimmer

In this article, I show that a hyperelastic shape changing body is able to swim in a perfect fluid at zero energy cost. A dedicated web page containing many videos is available here.

### The SOLEIL project

SOLEIL is french acronym for SOLveur d'Equations Integral pour la Locomotion.
The purpose of the project was to design a set of Matlab functions to study fish locomotion.
We were mainly interested in the following issues: Motion planning, Optimal swimming strategies and Optimal fish shapes.
The main requirements were: 3D simulations, a flexible interface (allowing users to easily define their own fish) and fast computations (some minutes on a common laptop).

The result is available here.

### IES (Integral Equations Solver)

IES (Integral Equation Solver) is a set of Matlab functions to solve Laplace equations with mixed Neumann and Dirichlet boundary conditions in both interior and exterior domains of $\mathbb R^2$.

IES has its own dedicated web page.

### Some videos...

All of the videos have been realized with BhT or SOLEIL.

Simulation of fish catching food (realized with SOLEIL).

## Teaching

Some handouts from my teaching (all in french):
Introductions aux EDP and Étude qualitative des équations différentielles ordinaires.