Nathalie Bertrand

Morgan Abily, Olivier Delestre, Laura Amossé et al.

High resolution (infra-metric) topographic data, including photogram-metric born 3D classified data, are becoming commonly available at large range of spatial extend, such as municipality or industrial site scale. This category of dataset is promising for high resolution (HR) Digital Surface Model (DSM) generation, allowing inclusion of fine above-ground structures which might influence overland flow hydrodynamic in urban environment. Nonetheless several categories of technical and numerical challenges arise from this type of data use with standard 2D Shallow Water Equations (SWE) based numerical codes. FullSWOF (Full Shallow Water equations for Overland Flow) is a code based on 2D SWE under conservative form. This code relies on a well-balanced finite volume method over a regular grid using numerical method based on hydrostatic reconstruction scheme. When compared to existing industrial codes used for urban flooding simulations, numerical approach implemented in FullSWOF allows to handle properly flow regime changes, preservation of water depth positivity at wet/dry cells transitions and steady state preservation. FullSWOF has already been tested on analytical solution library (SWASHES) and has been used to simulate runoff and dam-breaks. FullSWOFs above mentioned properties are of good interest for urban overland flow. Objectives of this study are (i) to assess the feasibility and added values of using HR 3D classified topographic data to model river overland flow and (ii) to take advantage of FullSWOF code properties for overland flow simulation in urban environment.

Nathalie Bertrand, Miheer Dewaskar, Blaise Genest et al.

We introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a biological system, namely a population of yeasts, where the controller may only change the environment common to all cells. We study a synchronisation problem for such populations: no matter how individual agents react to the actions of the controller , the controller aims at driving all agents synchronously to a target state. The agents are naturally represented by a non-deterministic finite state automaton (NFA), the same for every agent, and the whole system is encoded as a 2-player game. The first player (Controller) chooses actions, and the second player (Agents) resolves non-determinism for each agent. The game with m agents is called the m-population game. This gives rise to a parameterized control problem (where control refers to 2 player games), namely the population control problem: can Controller control the m-population game for all $m $\in$ N$ whatever Agents does? In this paper, we prove that the population control problem is decidable, and it is a EXPTIME-complete problem. As far as we know, this is one of the first results on parameterized control. Our algorithm, not based on cutoff techniques, produces winning strategies which are symbolic, that is, they do not need to count precisely how the population is spread between states. We also show that if there is no winning strategy, then there is a population size M such that Controller wins the m-population game if and only if $m $\le$ M$. Surprisingly, M can be doubly exponential in the number of states of the NFA, with tight upper and lower bounds.