Acronym :

EDPs2 : "Partial derivative equations : deterministic and probabilistic studies"

Team description :

The EDPs2 team is based on the federative topic of non linear partial derivative equations. This team is made up of several professors and researchers, all of them completing one another, specialists in analysis and/or scientific calculation of partial derivative equations, theory of stochastic processes and/or numerical probabilities.

This recent grouping (mixing deterministic and sotchastic aspects : theory and scientific calculation) is both original and ambitious, and matches the real need of a better understanding of complex systems all around us (environment, biology-medicine, industry, ...). It allows for example to tackle with different points of view : free boundary problems (dynamic and stable states, image processing, support evolution), scale and multiple physics problems (complex fluids, image processing), problems about homogenisation effects and defect measures (roughness, breaks), optimization and identification problems (optimal transport, data assimilation, parameter identification).

Some of our results :

Theoretical results :

Scientific calculation :


Sine-Gordon kink simulation in a Y-junction
D. Dutykh
Spectral minimizers for the Dirichlet-Laplacian under perimeter constraints
B. Bogosel & E. Oudet
Segmentation with the anisotropic Mumford-Shah functional
M. Foare
Evolution lam2 at aniso

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Numerical simulation of powder-snow avalanche interaction with an obstacle.
D. Dutykh & C. Acary-Robert
Tsunami simulation with VOLNA code: Okushiri island event (1993).
D. Dutykh & R. Poncet
Optimal partitionning.
E. Oudet, D. Bucur & Blaise Bourdin
Evolution Evolution Evolution
Evolution of the volumic fraction of the snow, function of time.
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Click on the image to display the video. A recursive optimization algorithm to avoid local minima for 512 cells (that is 130000000 degrees of freedom...)
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Water injection in an empty and downstream closed pipe.
C. Bourdarias, M. Ersoy & S. Gerbi
Double water injection in an empty and downstream closed pipe.
C. Bourdarias, M. Ersoy & S. Gerbi
Simulations of flows in pipes.
C. Bourdarias & S. Gerbi
Amont Aval Coup de bélier
Flow on a dry bottom, water hammer, upstream drying out.
Initial state. Click on the image to display the video.
Filling in up- and downstream on dry bottom
Initial state. Click on the image to display the video.
Water hammer for a 150m long, 2m diameter pipe on a 0.3% slope.
Initial state. Click on the image to display the video.


Kelvin's problem. E. Oudet. Optimization of 8 densities in a cube with periodic conditions.
What space-filling arrangement of similar cells of equal volume has minimal surface area ? We rediscover the counter example of Weaire and Phelan's (1994) : a space-filling unit cell consisting of six 14-sided polyhedra and two 12-sided polyhedra.


Reliability.
P. Briand & E. Idée
Resolution through finished elements of the lubrication equation.
J. Frassy & C. Lécot.
Fiabilité Evolution
Weibull law W(2,Η,Γ). Evolution of the density of the Γ estimator;according to Γ/Η.
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We simulate the spreading of a water drop on a chemically heterogeneous substrate : the drop is put astride on a horizontal hydrophobic band which seperates 2 absorbant areas (up and below).