Publications

2013

• An Optimal Control Approach for EV Charging with Distribution Grid Ageing
  
  • Azad Amar Prakash
  • Beaude Olivier
  • Lasaulce Samson
  • Pfeiffer Laurent
  , 2013. In smart grids, the expected increase of electrical vehicle (EV) penetration will impose sizeable charging load, which can critically overburden the distribution network (DN) if the delivered power is non-pragmatically aggregated and induce significant impacts on various important existing grid assets. Among them, the residential distribution transformer is considered as one of the most important components in the grid. The ageing of the transformer is closely related to the temporal evolution of the hot-spot temperature (HST), which is induced by the operating load level history. We propose an optimal control approach to obtain a new EV charging algorithm: the novel aspect of this algorithm is that it takes inertial behavior of HST into account, which is the key parameter to capture the ageing. Though our formulation closely resembles to the linear quadratic control problem that includes costs induced from the state of the transformer and its present charging load, the natural constraints which are imposed to the instantaneous charging level (saturation constraints) induces intricate complicacy for the analytical solution. Thus, we follow the Pontryagin maximum principle approach to obtain the optimal charging policy and resort to numerical methods to compute the optimal charging trajectory. Numerical results allow us to evaluate and compare the performance of the proposed algorithm with various existing benchmark charging policies. (10.1109/blackseacom.2013.6623411)
  DOI : 10.1109/blackseacom.2013.6623411
• Ion transport in porous media: derivation of the macroscopic equations using up-scaling and properties of the effective coefficients
  
  • Allaire Grégoire
  • Brizzi Robert
  • Dufrêche Jean-François
  • Mikelic Andro
  • Piatnitski Andrey
  Computational Geosciences, Springer Verlag, 2013, 17 (3), pp.479-496. (10.1007/s10596-013-9342-6)
  DOI : 10.1007/s10596-013-9342-6
• Diverses croix fractales bidimensionnelles
  
  • Colonna Jean-François
  , 2013. Various bidimensional fractal crosses (Diverses croix fractales bidimensionnelles)
• New global stability estimates for the Calderón problem in two dimensions
  
  • Santacesaria Matteo
  Journal of the Institute of Mathematics of Jussieu, Cambridge University Press, 2013, 12 (3), pp.553-569. We prove a new global stability estimate for the Gel'fand-Calderón inverse problem on a two-dimensional bounded domain or, more precisely, the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$, where $v$ is a smooth real-valued potential of conductivity type defined on a bounded planar domain $D$. The principal feature of this estimate is that it shows that the more a potential is smooth, the more its reconstruction is stable, and the stability varies exponentially with respect to the smoothness (in a sense to be made precise). As a corollary we obtain a similar estimate for the Calderón problem for the electrical impedance tomography. (10.1017/S147474801200076X)
  DOI : 10.1017/S147474801200076X
• MODELLING COMPRESSIBLE MULTIPHASE FLOWS
  
  • Coquel Frédéric
  • Gallouët Thierry
  • Helluy Philippe
  • Hérard Jean-Marc
  • Hurisse Olivier
  • Seguin Nicolas
  ESAIM: Proceedings, EDP Sciences, 2013, 40, pp.34-50. We give in this paper a short review of some recent achievements within the framework of multiphase flow modeling. We focus first on a class of compressible two-phase flow models, detailing closure laws and their main properties. Next we briefly summarize some attempts to model two-phase flows in a porous region, and also a class of compressible three-phase flow models. Some of the main difficulties arising in the numerical simulation of solutions of these complex and highly non-linear systems of PDEs are then discussed, and we eventually show some numerical results when tackling two-phase flows with mass transfer. (10.1051/proc/201340003)
  DOI : 10.1051/proc/201340003
• Variation artistique sur un croix fractale tridimensionnelle -itération 2
  
  • Colonna Jean-François
  , 2013. Artistic variation on a tridimensional fractal cross -iteration 2- (Variation artistique sur un croix fractale tridimensionnelle -itération 2-)
• Variation artistique sur un croix fractale tridimensionnelle -itération 2
  
  • Colonna Jean-François
  , 2013. Artistic variation on a tridimensional fractal cross -iteration 2- (Variation artistique sur un croix fractale tridimensionnelle -itération 2-)
• Anaglyphe d'un croix fractale tridimensionnelle -itération 3
  
  • Colonna Jean-François
  , 2013. Anaglyph of a tridimensional fractal cross -iteration 3- (Anaglyphe d'un croix fractale tridimensionnelle -itération 3-)
• Anaglyphe d'un croix fractale tridimensionnelle -itération 2
  
  • Colonna Jean-François
  , 2013. Anaglyph of a tridimensional fractal cross -iteration 2- (Anaglyphe d'un croix fractale tridimensionnelle -itération 2-)
• Anaglyphe d'un croix fractale tridimensionnelle -itération 1
  
  • Colonna Jean-François
  , 2013. Anaglyph of a tridimensional fractal cross -iteration 1- (Anaglyphe d'un croix fractale tridimensionnelle -itération 1-)
• Croix fractale tridimensionnelle -itération 1
  
  • Colonna Jean-François
  , 2013. Tridimensional fractal cross -iteration 1- (Croix fractale tridimensionnelle -itération 1-)
• Anaglyphe d'un croix fractale tridimensionnelle -itération 4
  
  • Colonna Jean-François
  , 2013. Anaglyph of a tridimensional fractal cross -iteration 4- (Anaglyphe d'un croix fractale tridimensionnelle -itération 4-)
• Variation artistique sur un croix fractale tridimensionnelle -itération 4
  
  • Colonna Jean-François
  , 2013. Artistic variation on a tridimensional fractal cross -iteration 4- (Variation artistique sur un croix fractale tridimensionnelle -itération 4-)
• Variation artistique sur un croix fractale tridimensionnelle -itération 5
  
  • Colonna Jean-François
  , 2013. Artistic variation on a tridimensional fractal cross -iteration 5- (Variation artistique sur un croix fractale tridimensionnelle -itération 5-)
• Anaglyphe d'un croix fractale tridimensionnelle -itération 5
  
  • Colonna Jean-François
  , 2013. Anaglyph of a tridimensional fractal cross -iteration 5- (Anaglyphe d'un croix fractale tridimensionnelle -itération 5-)
• Croix fractale tridimensionnelle -itération 4
  
  • Colonna Jean-François
  , 2013. Tridimensional fractal cross -iteration 4- (Croix fractale tridimensionnelle -itération 4-)
• Croix fractale tridimensionnelle -itération 3
  
  • Colonna Jean-François
  , 2013. Tridimensional fractal cross -iteration 3- (Croix fractale tridimensionnelle -itération 3-)
• Croix fractale tridimensionnelle -itération 4
  
  • Colonna Jean-François
  , 2013. Tridimensional fractal cross -iteration 4- (Croix fractale tridimensionnelle -itération 4-)
• Croix fractale tridimensionnelle -itération 5
  
  • Colonna Jean-François
  , 2013. Tridimensional fractal cross -iteration 5- (Croix fractale tridimensionnelle -itération 5-)
• Croix fractale tridimensionnelle -itération 5
  
  • Colonna Jean-François
  , 2013. Tridimensional fractal cross -iteration 5- (Croix fractale tridimensionnelle -itération 5-)
• Croix fractale tridimensionnelle -itération 2
  
  • Colonna Jean-François
  , 2013. Tridimensional fractal cross -iteration 2- (Croix fractale tridimensionnelle -itération 2-)
• Energy management method for an electric vehicle
  
  • Granato Giovanni
  • Bonnans J. Frederic
  • Aouchiche K.
  • Grégory Rousseau
  • Zidani Hasnaa
  , 2013. The invention relates to a method for managing energy consumption for an automobile having an electric battery and a heat engine, said method making it possible to select the use phases of said engine along a given route so as to minimize the fuel consumption of said vehicle. The main characteristic of the method according to the invention is that it includes the following steps: a step of cutting the road network, which is taken into consideration for a given route, into a plurality of segments, each segment being defined by an input node and by an output node; a step of calculating, from a speed associated with said segment, the probability of a speed transition between a speed at an input node and a speed at an output node of a segment, while taking a plurality of speeds at the input node and a plurality speeds at the output node into consideration, said step being carried out gradually over all of the segments of the route; a step of applying a stochastic optimization algorithm taking all the possible transition scenarios between each input node and each output node, and the probability associated therewith, into account, and taking a fuel consumption model between two successive nodes into account, said step being carried out over all of the segments of the route; and a step of selecting use phases of the heat engine along the route.
• Hypoelliptic diffusion and human vision: a semi-discrete new twist on the Petitot theory
  
  • Boscain Ugo
  • Chertovskih Roman
  • Gauthier Jean-Paul
  • Remizov Alexey
  , 2013. This paper is devoted to present an algorithm implementing the theory of neurogeometry of vision, described by Jean Petitot in his book. We propose a new ingredient, namely working on the group of translations and discrete rotations SE(2,N). We focus on the theoretical and numerical aspects of integration of an hypoelliptic diffusion equation on this group. Our main tool is the generalized Fourier transform. We provide a complete numerical algorithm, fully parallellizable. The main objective is the validation of the neurobiological model.
• A discontinuous Galerkin scheme for front propagation with obstacles
  
  • Bokanowski Olivier
  • Cheng Yingda
  • Shu Chi-Wang
  Numerische Mathematik, Springer Verlag, 2013, 126 (1), pp.1-31. We are interested in front propagation problems in the presence of obstacles. We extend a previous work (Bokanowski, Cheng and Shu, SIAM J. Scient. Comput., 2011), to propose a simple and direct discontinuous Galerkin (DG) method adapted to such front propagation problems. We follow the formulation of (Bokanowski, Forcadel and Zidani, SIAM J. Control Optim. 2010), leading to a level set formulation driven by $\min(u_t + H(x,\nabla u), u-g(x))=0$, where $g(x)$ is an obstacle function. The DG scheme is motivated by the variational formulation when the Hamiltonian $H$ is a linear function of $\nabla u$, corresponding to linear convection problems in presence of obstacles. The scheme is then generalized to nonlinear equations, written in an explicit form. Stability analysis are performed for the linear case with Euler forward, a Heun scheme and a Runge-Kutta third order time discretization using the technique proposed in (Zhang and Shu, SIAM J. Control and Optim., 2010). Several numerical examples are provided to demonstrate the robustness of the method. Finally, a narrow band approach is considered in order to reduce the computational cost. (10.1007/s00211-013-0555-3)
  DOI : 10.1007/s00211-013-0555-3
• Dobrushin ergodicity coefficient for Markov operators on cones, and beyond
  
  • Gaubert Stéphane
  • Qu Zheng
  , 2013. The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's pro- jective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We generalize these properties to abstract consensus operators over normal cones, which include the unital completely positive maps (Kraus operators) arising in quantum information theory. In par- ticular, we show that the contraction rate of such operators, with respect to the Hopf oscillation seminorm, is given by an analogue of Dobrushin's ergodicity coefficient. We derive from this result a characterization of the contraction rate of a non-linear flow, with respect to Hopf's oscillation seminorm and to Hilbert's projective metric.