Mathematical and Computer Science Contributions to Software for Computer Aided Multi-scale Model Derivation and its Application

Michel Lenczner
Job Description: 

Applications are invited for a three year PhD scholarship in the framework of a collaboration between the FEMTO-ST Institute (see in Besançon, LORIA in Nancy (, and Laboratory of Astrophysics (LAM) in Marseille ( in FRANCE.

Closing date for applications: July 1st, 2013.

This PhD thesis is in the context of development of mathematical tools and software MEMSALab for aided design of multi-physics and multi-scale systems based on asymptotic methods. The first applications are for arrays of micro-systems and nano-systems, but broader range of applications are expected. The multi-scale model construction starts from a system of partial differential equations and combines principles of multi-scale approximation with symbolic computation methods from computer sciences. MEMSALab is an implementation of such mathematical model derivations by rewriting techniques with TOM, a well-known existing rewrite based tool developed at LORIA. In the medium term, it will allow to automatically generate a wide class of multi-scale models. By nature, they are also systems of partial differential equations, but much less expensive to solve by a computer. Once built, they should be automatically transferred to a finite element software package. In our package, we complement it by a toolkit for parameter optimization and calibration.

The PhD thesis will derive a multi-scale model for the LAM’s array of micro-mirrors. Mathematical and computer science techniques will be established for more general modeling in MEMSALab. The model of micro-mirror array will be used for simulation, design optimization, parameter calibration and to prepare an optimized version of the device.

Arrays of micro-mirrors are designed for generating slit masks at the entrance of multi-object spectrographs (MOS) in Astronomy. This astronomical technique is used extensively to investigate the formation and evolution of galaxies. MOS with multi-slits is the best approach to eliminate the problem of spectral confusion, to optimize the quality and the SNR of the spectra, to reach fainter limiting fluxes and to maximize the scientific return both in cosmology and in legacy science. Conventional masks or complex fiber-optics-based mechanisms are limited for future space and ground-based telescopes. The programmable multi-slit mask requires remote control of the multi-slit configuration in real time. A promising solution is the use of micro-electro-optical-mechanical system (MOEMS) devices such as micro-mirror arrays, generating reflective slits. This device is also foreseen for applications in Physics or Biology. LAM, in collaboration with EPFL (Switzerland), are engaged in a European development of micro-mirror arrays for generating reflective slit masks. Prototypes with 2048 individually addressable micro-mirrors made of single-crystalline silicon were successfully designed, fabricated and tested.
The scholarship is valued at about 1,400€ net per month for three years. Application to a room on the campus is possible for low rate. Applicants should have a good undergraduate degree and a master in Pure or Applied Mathematics, or in Physics. Additional background in theoretical computer science is welcome.

Please email a CV and a letter outlining your areas of research interest, along with names and contact details of two referees who can comment on your academic suitability to Dr. Michel Lenczner, Dr. Horatiu Cirstea and Dr. Frédéric Zamkotsian. The contacts for this project are:

Dr. Michel Lenczner, FEMTO-ST 26, Chemin de l’épitaphe 25030 Besançon. Phone: +33 (0) 3 81 40 28 27, e-mail: michel.lenczner[at];

Dr. Horatiu Cirstea, LORIA, Batiment C, Campus scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex. Phone: +33 (0)3 54 95 84 06, e-mail : Horatiu.Cirstea[at]loria.frf;

Dr. Frédéric Zamkotsian, LAM-CNRS, 38 rue Frédéric Joliot-Curie, 13388 Marseille Cedex 13. Phone: +33 (0) 4 95 04 4151, e-mail: frederic.zamkotsian[at]

Job Categories: 
Graduate student fellowships
Partial differential equations, Multi-scale modeling, Asymptotic methods, Rewriting techniques, Application to Microsystems
Deadline for Application: 
Jul 1 2013