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

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

Incidence and main factors associated with early unplanned hospital readmission among French medical inpatients aged 75 and over admitted through emergency units

Background: among elderly patients, readmission in the month following hospital discharge is a frequent occurrence which involves a risk of functional decline, particularly among frail subjects. While previous studies have identified risk factors of early readmission, geriatric syndromes, as markers of frailty have not been assessed as potential predictors. Objective: to evaluate the risk of early unplanned readmission, and to identify predictors in inpatients aged 75 and over, admitted to medical wards through emergency departments. Design: prospective multi-centre study. Setting: nine French hospitals. Subjects: one thousand three hundred and six medical inpatients, aged 75 and older admitted through emergency departments (SAFES cohort). Methods: using logistic regressions, factors associated with early unplanned re-hospitalisation (defined as first unplanned readmission in the thirty days after discharge) were identified using data from the first week of hospital index stay obtained by comprehensive geriatric assessment. Results: data from a thousand out of 1,306 inpatients were analysed. Early unplanned readmission occurred in 14.2% of inpatients and was not related with sociodemographic characteristics, comorbidity burden or cognitive impairment. Pressure sores (OR=2.05, 95% CI = 1.0-3.9), poor overall condition (OR = 2.01, 95% CI = 1.3-3.0), recent loss of ability for self-feeding (OR = 1.9, 95% CI = 1.2-2.9), prior hospitalisation during the last 3 months (OR = 1.6, 95% CI = 1.1-2.5) were found to be risk factors, while sight disorders appeared as negatively associated (OR = 0.5, 95% CI = 0.3--0.8). Conclusions: markers of frailty (poor overall condition, pressure sores, prior hospitalisation) or severe disability (for self-feeding) were the most important predictors of early readmission among elderly medical inpatients. Early identification could facilitate preventive strategies in risk grou

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

Large enhancement of the thermopower in Nax_xCoO2_2 at high Na doping

Research on the oxide perovskites has uncovered electronic properties that are strikingly enhanced compared with those in conventional metals. Examples are the high critical temperatures of the cuprate superconductors and the colossal magnetoresistance in the manganites. The conducting layered cobaltate $\rm Na_xCoO_2$ displays several interesting electronic phases as $x$ is varied including water-induced superconductivity and an insulating state that is destroyed by field. Initial measurements showed that, in the as-grown composition, $\rm Na_xCoO_2$ displays moderately large thermopower $S$ and conductivity $\sigma$. However, the prospects for thermoelectric cooling applications faded when the figure of merit $Z$ was found to be small at this composition (0.6$<x<$0.7). Here we report that, in the poorly-explored high-doping region $x>$0.75, $S$ undergoes an even steeper enhancement. At the critical doping $x_p\sim$ 0.85, $Z$ (at 80 K) reaches values $\sim$40 times larger than in the as-grown crystals. We discuss prospects for low-temperature thermoelectric applications.Comment: 6 pages, 7 figure

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

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