PhD Students

BOREUX Jehan (Starting date : January 2008)
Mean Field Theory and Control in Hamiltonian Mechanic
Thesis advisor : T. Carletti
We treat long range interactions, more specifically we use the Hamiltonian Mean Field (HMF) as model. In parallel we work on Hamiltonian control, developing the theory in discrete time especially designed to accelerator particles.

COMPÈRE Audrey (Starting date : September 2007)
Stability of multiple asteroidal systems
Thesis advisor : A. Lemaître
Multiple asteroidal systems are really common in our solar system and not yet well studied. In this thesis, different things are realised on the subject as the study of a point mass in rotation around an ellipsoidal asteroid, the study of the triple asteroidal system (87) Sylvia or even the search for an explanation regarding the lack of multiple asteroids among the Plutinos.

CRÉLOT Anne-Sophie (Starting date: September 2011)
Numerical optimization : Derivative-free mixed integer nonlinear programming, in partnership with Cenaero
Thesis advisor: A. Sartenaer
Many engineering applications are described using both integer and continuous variables. This type of problems is called a mixed integer program. We are interested in developing a method to solve such problems in the nonlinear case, when the objective function and the constraints are the result of (time expensive) computer simulations. We are working with the research centre Cenaero, which gives us a real application in the field of turbomachine design.

DEHAYE Jérémy (Starting date: September 2009)
Modeling, analysis and control of boundary control systems with observation
Thesis advisor : J. Winkin
Distributed parameter systems based on partial differential equations can generally be written as abstract infinite-dimensional linear differential systems with boundary control and observation, and the associated operators are thus unbounded. Under suitable assumptions, we consider an extended abstract linear differential system with bounded control and observation operators. We study the well-posedness, the relation between the classical solutions of both systems and the main properties, such as stability, reachability, observability, stabilisability and detectability. We also try to solve an LQ-optimal control problem and we consider some applications such as e.g. convection-diffusion-reaction systems.

DEHAYE Jonathan (Starting date: September 2011)
Thesis advisor : J. Winkin
This project deals with the positive stabilization problem for positive infinite-dimensional systems. The specific methods that are developed for this problem are based on semigroup theory and on positivity preserving numerical schemes (e.g. finite differences or spectral methods), with applications to e.g. tubular reactor models and more general distributed parameter models.

HUBAUX Charles (Starting date : October 2009)
Orbitography and study of the stability of space debris by means of celestial mechanics tools
Thesis advisor : A. Lemaître
The issues encountered with space debris can be studied by means of celestial mechanics and mathematical dynamics theory. The number of small objects larger than one millimeter in orbit around the Earth is currently estimated at more than 300 million. Objects larger than 10 cm are followed with fairly classical numerical integrations, making their real location rather questionable. The smaller objects are studied only statistically. A better determination of orbits of space debris, combined with a systematic and comprehensive study of the dynamics and stability, would avoid some catastrophic collisions and identify relatively stable “parking” areas, either for life-ending satellites, or as potential reservoirs of uncatalogued debris.
Main goals are:

  • The use of symplectic integrators in order to reduce the numerical drifts occurring for long integration times, as in this context, where some debris are present for nearly 50 years.
  • The consideration of gravitational resonances (between the object in orbit and rotation of the Earth) in averaged numerical integrations which are valid on long time spans.
  • The intensive use of chaos indicators to create stability maps and detect interesting stable areas.
  • The modelling of non-gravitational forces. The analysis of these forces is certainly a major challenge in the calculation of orbits. The solar radiation pressure is the greatest one, with tricky effects induced by the passage of debris into Earth's shadow.

MORIAMÉ Marie (Starting date : September 2012)
Constraining opinion dynamics models with stylized facts
Thesis advisors : T.Carletti, R.Lambiotte
This research project aims to study general opinion dynamics models and determine which models are able to reproduce some stylized facts or real world. To perform this task a preliminary wide review (starting from available ones in the literature) of models of opinion dynamics will be done. Then we should try to understand which stylizedfacts are relevant depending on the research questions. The final goal will be to possibly calibrate those abstract models using real data. This could be realized using the synthetic populations expertise already developed at naXys, to create agents closer to reality.

NICOLAY Delphine (Starting date : September 2012)
Neural networks learning : Heuristic methods and applications
Thesis advisors : T. Carletti, R. Lambiotte
This research project aims to study the structure formation in neural networks trained to achieve some goals: are there basic blocs used to perform multiple tasks or basic blocks specific to each task? We are also interested in the changes that can occur in stressful situations where a rapid response is necessary. The main used tool will be the neural network subjected to a learning process (eg GA but others may be considered). We could develop tools that will be tested on real robots.

SALNIKOV Vsevolod (Starting date: September 2012)
Complex temporal networks analysis and human mobility
Thesis advisor : R. Lambiotte
In our everyday life there exists many big networks (social, internet e.t.c.). We focus on studying their properties, taking into account their variability in time. Some of the questions lead to the analysis of human mobility and so-called data driven models.

TANNIER Charlotte (Starting date: September 2009)
Design and study of block diagonal preconditioners using spectral information for saddle-point systems
Thesis advisor: A. Sartenaer
This research project focusses on the development and the study of block diagonal preconditioners for very badly conditioned saddle-point systems (of KKT form) due to the combined effect of very small eigenvalues of the (1,1) block and of very small singular values of the off-diagonal block. Under the assumption that spectral information related to these very small eigenvalues/singular values can be extracted separately, different approximations of the "ideal" block diagonal preconditioner of Murphy, Golub and Wathen (2000) with exact Schur complement are considered, based on an approximation of the Schur complement that combines the available spectral information.

VERHEYLEWEGEN Emilie (Starting date : October 2009)
Updates and advances in the dynamics of the main satellites of Uranus
Thesis advisor : A. Lemaître, in collaboration with B. Noyelles
We re-analyse the N-body problem of Uranus with its five main satellites Miranda, Ariel, Umbriel, Titania and Oberon. We use new computing tools and improve some previous results by a new global visualization with chaos and orbital scales maps. The aim of this study is to understand the past evolution for a better knowledge/understanding of the current system, including the evolution of the inner satellites.

Post-Docs

DIMASSI Habib (Starting date: February 2013)

Robust and adaptive observer design for uncertain infinite-dimensional systems

Host : J. Winkin

Infinite-dimensional systems cover many physical and mathematical models which may be encountered in different engineering applications such as mechanical engineering, electrical engineering, chemical engineering: parabolic and hyperbolic distributed parameter systems, mechanical systems with flexible structure, infinite-dimensional vibrating systems, convection-diffusion-reaction process, etc. In practice, these systems are often subject to external disturbances, unknown source terms, unmodeled dynamics, unknown parameters and model uncertainties. These unknown parameters or inputs are required either to be rejected or estimated. This problem was widely investigated in the literature of finite-dimensional control theory but more much effort needs to be addressed to the infinite-dimensional case. The aim of this research project is to develop robust and adaptive strategies to solve such problems.

LIBERT Anne-Sophie (Starting date : October 2008)
Networks and dynamical systems
Host : A. Lemaître
My research focuses on the modelling and stability study of (non-linear) dynamical systems (e.g. planetary n-body problem), and the centrality measures and community detection in large graphs (e.g. PageRank). Both theoretical and computational aspects are considered.

NOYELLES Benoît (F.R.S.-FNRS post-doctoral fellow since Oct. 2010)
Rotation of the natural satellites: Influence of their internal structure
Host : A. Lemaitre
This research project aims at characterizing the influence of the internal structure of the main natural satellites of Jupiter and Saturn on their rotation. Thanks to space missions, these satellites are known not to be rigid but composed of a molten outer core below a rigid mantle (like Io) or an internal ocean below an icy crust (like Titan or Europa). These complex internal structures induce some couplings (electromagnetic, gravitational, etc.) between the different layers whose influence on the rotation is poorly known. There are currently two approaches of this problem. The first one, which has been mine up to now, is to consider these bodies as rigid, and to use a Hamiltonian formulation to describe their 3-degree-of-freedom rotational dynamics, the 3 degrees being the spin velocity, the obliquity of the angular momentum, and the polar motion of the body. This approach allows to detect every likely resonant effect between the proper frequencies of the system and the forcing ones (due to the orbital motion of the body about its parent planet). In particular, it has been used to explain the slightly super-synchronous measured rotation of Titan. The other one is to consider every internal process of a differenciated body, but in only one degree of freedom. This way, the possibility of detecting resonant effects is very limited, and some phenomena like polar wander (i.e. a strong reorientation of the surface with respect to its rotation axis, this has probably happened for Europa) cannot be modeled. My project consists in merging the two approaches in writing complete Hamiltonian models of multi-layered rotating satellites, in particular in characterizing the behavior of each degree of freedom with respect to the physical parameters used in the model. I intend to add couplings due to intermediate fluid layers (molten outer core or internal icean), but also dissipative processes like viscosity or tidal interactions with the parent body.

SANSOTERRA Marco (Starting date: Nov 2011)
Dynamics near invariant manifolds (DyNeInMa)
Host : A. Lemaître
My research activity is mainly focused on Dynamical Systems and Celestial Mechanics. I deal with both the theoretical and the computational aspects, with a special care on their interplay. The main goal of my research activity is the study of the stability properties of planetary systems. For this purpose, I investigated the dynamics in the neighbourhood of some invariant objects, like maximal dimension KAM tori, equilibrium points and lower dimensional elliptic tori. Actually I am working on the study of the secular evolution of extrasolar planetary systems, a project in collaboration with Anne-Sophie Libert (naXys, FUNDP). Moreover I am involved in a collaboration with Christoph Lhotka (ROMEO & naXys, FUNDP) to study the spin-orbit problem and in particular the problem of finding the Cassini states.

TABOURIER Lionel (Starting date : September 2012)
Random graph generation methods to model real-world networks
Host : R. Lambiotte
Real-world interaction networks result from a swarm of interwoven individual behaviors which are often misunderstood. As such, they exhibit complex structures poorly described by usual graph models. That is why generating random graphs with arbitrary constraints is a corner-stone to mimic real-world networks, and then propose dynamical processes that account for the observed structures. During this project, we will explore the expediency of using Markov-chain switching methods to achieve this task efficiently, and applying them to practical problems such as enhancing the robustness of ad hoc communication networks.

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