- 23 novembre 2022
- Robin Roussel (LJLL)
*Boundary Poincaré maps of harmonic fields near the standard torus*In the context of nuclear fusion, knowing geometrical and dynamical properties of magnetic field lines can give us an idea of the quality of confinement of the plasma. In this talk, we study field lines of so called harmonic fields (or vacuum fields), which are used in the study of stellarators (a type of fusion reactor). More specifically, we are interested in the Poincaré map of such fields on the boundary of toroidal domains which are small perturbations of the axisymmetric standard torus in R^3. On this original domain, field lines can be computed explicitly, but do not have the desired properties.

First, we will define the harmonic field of a toroidal domain, and see where the uniqueness of such fields comes from. Then, we will give a definition of the Poincaré map of such fields on the boundary, and explain how one can compute the differential of this Poincaré map with respect to the deformations. After this, we will look at a few preliminary results of the computations, and discuss how those can give us information on the dynamical properties of the field lines. - 15 novembre 2022
- Marco Inversi (University of Basel)
*How do oil and water interact?*Take a glass of water and pour some oil inside. How can we describe this system at equilibrium?

For some physical principle, the equilibrium corresponds to a critical point of some energy (that

we can choose!). Indeed, this is a phase transition problem and some energy functionals can be

proposed to describe this system. For example, it is natural to introduce a Ginzburg–Landau energy

(of local or nonlocal type), namely an integral functional which is given by the sum of a potential

term and a kinetic/interaction term. The problem of minimizing this energy has been widely studied

and it is a classical topic in the Calculus of Variations. Looking at the Euler–Lagrange equation to

this functionals, we discover a deep connection with a famous conjecture of De Giorgi on level sets

of solutions to the Allen–Cahn equation. These facts motivate beautiful results in the theory of

Gamma-Convergence, starting by Modica–Mortola in the ’70. I will try to describe in simple words

and pictures some of the basic ideas behind this huge theory. - 9 novembre 2022
- Dorian Martino (IMJ-PRG, Université Paris Cité)
*Conformally invariant systems in dimension 2*An old problem of surfaces in a manifold, is the Plateau problem: given a closed curve, is it possible to fill it with some disk that minimizes the area?

If we look at the area functional directly, the same problem arise : the area is a geometric quantity, so we cannot consider an arbitrary minimizing sequence and we have to be smart (Douglas obtained one of the first field medal in 1936 for understanding the existence of minimizing surfaces). A solution is to consider a functional which is not geometric but is still invariant by some transformations (conformal transformations of the domain of the parametrization).

Once we obtain an object by a minimization procedure, the next question is: what is the regularity of this object?

Since the problem is geometric, the associated PDE has to be critical in a certain sense. In particular, Calderon-Zygmund theory doesn't apply.

But since the energy is conformally invariant, Noether's theorem explains that there are conservation laws.

Using this, we can find coordinates where the PDE has a nice expression.

In this talk, I will explain one can prove the regularity (and study the compactness) of critical points of conformally invariant functionals in dimension 2 through three examples: minimal surfaces, constant mean curvature surfaces and Willmore surfaces. - 2 novembre 2022
- Sophie Thery (LJLL)
*Study of an iterative method on ocean-atmosphere coupling algorithms including boundary layer parametrisations.*The interactions between atmosphere and ocean play a major role in many geophysical situations (climate modeling, cyclone, weather forecast). Therefore geophysical scale numerical simulation requires coupled atmospheric and oceanic models, which properly represent the behavior of the boundary layers encompassing the air-sea interface and their two-way interactions. Nowadays, the currently used coupling methods implement a one way coupling through the interface condition. We propose to couple these models through a Schwarz iterative algorithm to better represent the interaction between atmosphere and ocean.

In this talk, I will present Schwarz algorithm and how it can be used to better implement the two-way coupling between ocean and atmosphere dynamics. We study in particular the convergence of the iterative algorithm on a one dimensional two-way coupled diffusion equation with Ekman boundary layers. The particularity of this study is to take into account the turbulent phenomena near the ocean-atmosphere interface, considering a spatially variable viscosity coefficient. We first focus on a linear version of the diffusion equation. We will see how the Coriolis effect and the vertical parametrization of the turbulence influence the convergence of the algorithm. We will then consider the full non linear equation, that includes non linear interface conditions and non linear diffusion coefficient. I will eventually discuss future research directions for this work. - 26 octobre 2022
- Anatole Guérin (LJLL)
*Parallèle pédagogique : transposition de l'art de la prestidigitation à l'enseignement*Tout comme l’enseignement, la prestidigitation est une discipline dans laquelle l’interaction avec son auditoire joue un facteur décisif au cœur d’un acte de partage de connaissances ou bien d’expériences.

C’est sous ce prisme que de nombreux points clés de la pédagogie sont abordés en s’appuyant ainsi sur des théories présentes dans la littérature magique et l’expérience de magiciens professionnels.

Objectifs :

- Expérimenter les failles de notre perception et en identifier les

concepts sous-jacents permettant de diriger au mieux l’attention de nos étudiants

et de comprendre leur point de vue.

- Identifier les enjeux que présentent une séance d’enseignement dans son ensemble (écriture, pratique, ajustements) et s’approprier des

outils pertinents pour répondre à ces attentes.

- 18 octobre 2022
- Ariane Cwiling (Université Paris Cité / CNRS)
*Machine Learning for survival data prediction: Application of the super learner on pseudo-observations*Because of its simple interpretation, the restricted mean survival time (RMST) is an interesting quantity of interest in survival analysis. Its prediction with regard to the attributes of a patient can be of great interest in health care. However few survival methods exist in practice for this purpose. To achieve this goal, a recent article applied a deep neural network on pseudo-observations, the latter being a transformation of the incomplete observed times into data that can be handled as uncensored (Zhao, 2021). In this work, we propose a new prediction model for the RMST based on pseudo-observations combined with the super learner, a prediction algorithm which fits a weighted combination of candidate learners. - 13 octobre 2022
- Liangying Chen (LJLL)
*Relationships Between the Maximum Principle and Dynamic Programming for Infinite Dimensional Stochastic Control Systems*The Pontryagin type maximum principle and Bellman's dynamic

programming principle serve as two of the most important tools in

solving optimal control problems. There is a huge literature on the

study of relationship between them. In this talk, I will

present the latest progress about the relationship between the Pontryagin type

maximum principle and the dynamic programming principle for control

systems governed by stochastic evolution equations in infinite

dimensional space, with the control variables entering into both the

drift and the diffusion terms. To do so, we first prove the dynamic

programming principle for those systems without employing the

martingale solutions. Then we establish the desired relationships in

both cases that value function associated is smooth or nonsmooth.

For the nonsmooth case, in particular, by employing the relaxed

transposition solution, we discover the connection between the

superdifferentials and subdifferentials of value function and the

first-order and second-order adjoint equations. As an application,

we provide a stochastic verification theorem for optimal control

problems of stochastic evolution equations. - 5 octobre 2022
- Pauline Chassonnery (LJLL)
*Mathematical 3D modelling of adipose tissue morphogenesis.*The spatial organization of any living tissue has a deep impact on this tissue’s functionality. We study the case of white adipose tissue (WAT), which can represent up to 50% of the body weight and is now recognized to be an important endocrine organ involved in all physiological functions. Mature WAT consists of lobular clusters of adipocyte cells surrounded by an organized collagen fiber network. However, tri-dimensional observations show that the cells clusters are not as well separated as what 2D imaging could lead us to believe, but are instead organized into connected macro-structures. Hence, a fully tridimensional investigation of how WAT acquire its functional structure is needed..

In this talk, we will explore the hypothesis that the emergence of WAT structuration could be explained by simple mechanical interactions between adipocyte cells and collagen fibers. To this aim, we will present a 3D model featuring cells represented as spheres appearing and growing in a dynamical 3D network of cross-linked spherocylinders (modelling the collagen fibers). By the development of efficient numerical methods – limiting the computational costs of 3D simulations – and state-of-the-art 3D data visualization tools, we will show that the model is able to produce structures that compare qualitatively well to experimental images. Through fine parametrical analysis, we will identify the key parameters of the model and study their influence on the simulation outcome. We will show that this simple model can give insights on how complex 3D cell and fiber structures could spontaneously emerge as a result of simple mechanical interactions between cells and fibers, highlighting the key role of mechanics in tissue structuration. - 29 juin 2022
- Ioanna-Maria Lygatsika (LJLL)
*The Hartree-Fock problem in electronic structure and Gaussian discretisations*The behaviour of electrons in atoms and molecules is governed by the N-body Schrödinger equation. We provide simple examples of systems under study, issued from the field of quantum chemistry. The Hartree-Fock model, that replaces the N-body problem by a mean field one-electron approximation, will be the main topic of this talk. We focus on its Galerkin approximation over a Gaussian-type orbital (GTO) basis set. The discretised Hartree-Fock equations will be presented in detail. As an attempt to illustrate why GTOs are widely used in today's quantum chemistry codes, we demonstrate the advantages and common issues of such a basis set, throughout numerical examples on atoms and small molecules, using the PySCF electronic structure code (https://pyscf.org/). - 22 juin 2022
- Alexis Leculier (LJLL)
*Propagation phenomena in a homogeneous field, how it happens ? how can we prevent it ?*In the end of the thirties, the muskrat starts to invade France starting from a few amount of individual in the north east of the France. The same happens for the tiger mosquitoes since 2008 (only during the summer) from the south east of the France. It is remarkable that in both cases, the invasions occur with a constant speed and just a few of individuals at the begining. We propose to study a general model that allow to capture this dynamics. In the final part of the talk, we will see some new results that allow to prevent a such invasion phenomena. This final part is a joint work with Nga Nguyen. Admin