Publications

2016

• Korn-Poincare inequalities for functions with a small jump set
  
  • Chambolle Antonin
  • Conti Sergio
  • Francfort Gilles A
  Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2016, 65 (4), pp.1373 - 1399. (10.1512/iumj.2016.65.5852)
  DOI : 10.1512/iumj.2016.65.5852
• Stacking sequence and shape optimization of laminated composite plates via a level-set method
  
  • Allaire Grégoire
  • Delgado Gabriel
  Journal of the Mechanics and Physics of Solids, Elsevier, 2016, 97, pp.168-196. We consider the optimal design of composite laminates by allowing a variable stacking sequence and in-plane shape of each ply. In order to optimize both variables we rely on a decomposition technique which aggregates the constraints into one unique constraint margin function. Thanks to this approach, a rigorous equivalent bi-level optimization problem is established. This problem is made up of an inner level represented by the combinatorial optimization of the stacking sequence and an outer level represented by the topology and geometry optimization of each ply. We propose for the stacking sequence optimization an outer approximation method which iteratively solves a set of mixed integer linear problems associated to the evaluation of the constraint margin function. For the topology optimization of each ply, we lean on the level set method for the description of the interfaces and the Hadamard method for boundary variations by means of the computation of the shape gradient. Numerical experiments are performed on an aeronautic test case where the weight is minimized subject to different mechanical constraints, namely compliance, reserve factor and buckling load.
• Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensions
  
  • Novikov Roman
  The Journal of Geometric Analysis, Springer, 2016, 26 (1), pp.346-359. We consider phaseless inverse scattering for the Schrödinger equation with compactly supported potential in dimension d ≥ 2. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we give also a global uniqueness result for this problem with appropriate data on a fixed energy neighborhood. (10.1007/s12220-014-9553-7)
  DOI : 10.1007/s12220-014-9553-7
• A two-pool model to describe the IVIM cerebral perfusion
  
  • Fournet Gabrielle
  • Li Jing-Rebecca
  • Cerjanic Alex M
  • Sutton Bradley P
  • Ciobanu Luisa
  • Le Bihan Denis
  Journal of Cerebral Blood Flow and Metabolism, Nature Publishing Group, 2016. IntraVoxel Incoherent Motion (IVIM) is a magnetic resonance imaging (MRI) technique capable of measuring perfusion-related parameters. In this manuscript, we show that the mono-exponential model commonly used to process IVIM data might be challenged, especially at short diffusion times. Eleven rat datasets were acquired at 7T using a diffusion-weighted pulsed gradient spin echo sequence with b-values ranging from 7 to 2500 s/mm2 at three diffusion times. The IVIM signals, obtained by removing the diffusion component from the raw MR signal, were fitted to the standard mono-exponential model, a bi-exponential model and the Kennan model. The Akaike information criterion used to find the best model to fit the data demonstrates that, at short diffusion times, the bi-exponential IVIM model is most appropriate. The results obtained by comparing the experimental data to a dictionary of numerical simulations of the IVIM signal in microvascular networks support the hypothesis that such a bi-exponential behavior can be explained by considering the contribution of two vascular pools: capillaries and somewhat larger vessels. (10.1177/0271678X16681310)
  DOI : 10.1177/0271678X16681310
• Second order analysis of state-constrained control-affine problems
  
  • Aronna Maria Soledad
  • Bonnans J. Frederic
  • Goh Bean San
  Mathematical Programming, Series A, Springer, 2016, 160 (1), pp.115-147. In this article we establish new second order necessary and suffi-cient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.