Entropy-Preserving Coupling Conditions for One-dimensional Euler Systems at Junctions

This paper is concerned with a set of novel coupling conditions for the $3\times 3$ one-dimensional Euler system with source terms at a junction of pipes with possibly different cross-sectional areas. Beside conservation of mass, we require the equality of the total enthalpy at the junction and that the specific entropy for pipes with outgoing flow equals the convex combination of all entropies that belong to pipes with incoming flow. Previously used coupling conditions include equality of pressure or dynamic pressure. They are restricted to the special case of a junction having only one pipe with outgoing flow direction. Recently, Reigstad [SIAM J. Appl. Math., 75:679--702, 2015] showed that such pressure-based coupling conditions can produce non-physical solutions for isothermal flows through the production of mechanical energy. Our new coupling conditions ensure energy as well as entropy conservation and also apply to junctions connecting an arbitrary number of pipes with flexible flow directions. We prove the existence and uniqueness of solutions to the generalised Riemann problem at a junction in the neighbourhood of constant stationary states which belong to the subsonic region. This provides the basis for the well-posedness of the homogeneous and inhomogeneous Cauchy problems for initial data with sufficiently small total variation.Comment: 17 pages, 2 figure

Approximate stochastic dynamic programming for hydroelectric production planning

This paper presents a novel approach for approximate stochastic dynamic programming (ASDP) over a continuous state space when the optimization phase has a near-convex structure. The approach entails a simplicial partitioning of the state space. Bounds on the true value function are used to refine the partition. We also provide analytic formulae for the computation of the expectation of the value function in the “uni-basin” case where natural inflows are strongly correlated. The approach is experimented on several configurations of hydro-energy systems. It is also tested against actual industrial data

Entropy-Preserving Coupling of Hierarchical Gas Models

This paper is concerned with coupling conditions at junctions for transport models which differ in their fidelity to describe transient flow in gas pipelines. It also includes the integration of compressors between two pipes with possibly different models. A hierarchy of three one-dimensional gas transport models is built through the 3x3 polytropic Euler equations, the 2x2 isentropic Euler equations and a simplified version of it for small velocities. To ensure entropy preservation, we make use of the novel entropy-preserving coupling conditions recently proposed by Lang and Mindt [Netw. Heterog. Media, 13:177-190, 2018] and require the continuity of the total enthalpy at the junction and that the specific entropy for pipes with outgoing flow equals the convex combination of all entropies that belong to pipes with incoming flow. We prove the existence and uniqueness of solutions to generalised Riemann problems at a junction in the neighbourhood of constant coupling functions and stationary states which belong to the subsonic region. This provides the basis for the well-posedness of certain Cauchy problems for initial data with sufficiently small total variation.Comment: 28 pages, 3 figures. arXiv admin note: text overlap with arXiv:1704.0403

Controlled approximation of the value function in stochastic dynamic programming for multi-reservoir systems

We present a new approach for adaptive approximation of the value function in stochastic dynamic programming. Under convexity assumptions, our method is based on a simplicial partition of the state space. Bounds on the value function provide guidance as to where refinement should be done, if at all. Thus, the method allows for a trade-off between solution time and accuracy. The proposed scheme is experimented in the particular context of hydroelectric production across multiple reservoirs

One way to design the control law of a mini-UAV.

International audienceThis paper deals with a method used to design the control law of the μDrone MAV. This vehicle uses six propellers to fly and the dynamic model approximation for the motion is a MIMO linear time-invariant system. As we want to design a linear regulator, it is necessary to build a robust feedback control law. The LQ state feedback regulator design is applied to a standard model, tacking into account some perturbations. This is why the model is augmented with a perturbation vector and an observable subsystem is extracted in order to build a state estimator whose gain is the solution of a LQ problem. The subsystem is then decomposed into a controllable set and an uncontrollable one. The use of an asymptotic rejection strategy of the influence of uncontrollable modes gives the possibility to find a state feedback applied only to the controllable ones. Here again feedback matrix is chosen as the solution of a LQ problem. To compute the weighting matrices of quadratic criterions we use a “partial observability gramian”. The great advantage of this method is due to the use of only three scalars to synthesize the control law

An Agent-Based Framework for Urban Mobility Simulation

International audienceMobility study is composed of many research areas which one interests us: urban mobility. In the literature, urban mobilities are represented by analytical techniques like stochastic laws or they are defined by simulation tools like Multi-Agents Systems (MAS). The goal of our work is to define citizen behaviour in order to observe population dynamics by a simulation. This strategy is facilitated by a meta-model and a toolkit which are used with a particular method. The latter begins by a conceptual representation of each mobile and finishes by a mobility simulator. This paper aims at describing the mobility simulation toolkit. Thanks to this framework, mobility simulator development is sim- plified. It allows us to create distributed applications which are based on MAS

Transport properties of a molecule embedded in an Aharonov-Bohm interferometer

We theoretically investigate the transport properties of a molecule embedded in one arm of a mesoscopic Aharonov-Bohm interferometer. Due to the presence of phonons the molecule level position ($\epsilon_d$) and the electron-electron interaction ($U$) undergo a \emph{polaronic shift} which affects dramatically the electronic transport through the molecular junction. When the electron-phonon interaction is weak the linear conductance presents Fano-line shapes as long as the direct channel between the electrodes is opened. The observed Fano resonances in the linear conductance are originated from the interference between the spin Kondo state and the direct path. For strong enough electron-phonon interaction, the electron-electron interaction is renormalized towards negative values, {\it i.e.} becomes effectively attractive. This scenario favors fluctuations between the empty and doubly occupied charge states and therefore promotes a charge Kondo effect. However, the direct path between the contacts breaks the electron-hole symmetry which can efficiently suppress this charge Kondo effect. Nevertheless, we show that a proper tuning of the gate voltage is able to revive the Kondo resonance. Our results are obtained by using the Numerical Renormalization approximation to compute the electronic spectral function and the linear conductance.Comment: 17 pages, 12 figure

Lock-in spin structures and ferrimagnetism in polar Ni2−xCoxScSbO6 oxides

International audienceThe new phase Co2ScSbO6 and Ni2-xCoxScSbO6 solid solutions adopt the polar Ni3TeO6-type structure and order magnetically below 60 K. A series of long-period lock-in [0 0 1/3n] spin structures with n = 5, 6, 8 and 10 is discovered, coexisting with a ferrimagnetic [0 0 0] phase at high Co-contents. The presence of electrical polarisation and spontaneous magnetisations offers possibilities for multiferroic properties