A duality method for mean-field limits with singular interactions

We introduce a new approach to justify mean-field limits for first-and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to cover for the first time arbitrary square-integrable interaction forces at possibly vanishing temperature. In case of first-order systems, it allows to recover in particular the mean-field limit to the 2d Euler and Navier-Stokes equations. We postpone to a forthcoming work the development of quantitative estimates and the extension to more singular interactions

Combined battery SOC/SOH estimation using a nonlinear adaptive observer

International audience— This work presents a modeling and estimation techniques for State of Charge and State of Health estimation for Li-ion batteries. The analysis is done using an adaptive estimation approach for joint state and parameter estimation and by simplifying an existing nonlinear model previously obtained from experiments tests. A switching mechanism between two observers, one for the charging phase and one for the discharging phase, is done to avoid transients due to the discontinuity of model's parameters. Simulations on experimental data show that the approach is feasible and enhance the interest of the proposed estimation technique

Prediction-Based Control of Linear Systems by Compensating Input-Dependent Input Delay of Integral-Type

International audienceThis study addresses the problem of delay compensation via a predictor-based output feedback for a class of linear systems subject to input delay which itself depends on the input. The equation defining the delay is implicit and involves past values of the input through an integral relation, the kernel of which is a polynomial function of the input. This modeling represents systems where transport phenomena take place at the inlet of a system involving a nonlinearity, which frequently occurs in the processing industry. The conditions of asymptotic stabilization require the magnitude of the feedback gain to comply with the initial conditions. Arguments for the proof of this novel result include general Halanay inequalities for delay differential equations and take advantage of recent advances in backstepping techniques for uncertain or varying delay systems

Compressible primitive equation: formal derivation and stability of weak solutions

We present a formal derivation of a simplified version of Compressible Primitive Equations (CPEs) for atmosphere modeling. They are obtained from $3$-D compressible Navier-Stokes equations with an \emph{anisotropic viscous stress tensor} where viscosity depends on the density. We then study the stability of the weak solutions of this model by using an intermediate model, called model problem, which is more simple and practical, to achieve the main result

Weak solutions to problems involving inviscid fluids

We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method of convex integration we show the existence of infinitely many weak solutions for prescribed initial data and kinetic energy

Stability with respect to domain of the low Mach number limit of compressible viscous fluids

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter \ep \to 0 and the fluid is confined to an exterior spatial domain \Omega_\ep that may vary with \ep. As $\epsilon \rightarrow 0$, it is shown that the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier-Stokes equations on a limit domain. The velocities approach the limit strongly (a.a.) on any compact set, uniformly with respect to a certain class of domains. The proof is based on spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.Comment: 32 page

Existence of weak solution for compressible fluid models of Korteweg type

This work is devoted to prove existence of global weak solutions for a general isothermal model of capillary fluids derived by J.- E Dunn and J. Serrin (1985) [6], which can be used as a phase transition model. We improve the results of [5] by showing the existence of global weak solution in dimension two for initial data in the energy space, close to a stable equilibrium and with specific choices on the capillary coefficients. In particular we are interested in capillary coefficients approximating a constant capillarity coefficient. To finish we show the existence of global weak solution in dimension one for a specific type of capillary coefficients with large initial data in the energy space

Projected impact of heat on mortality and labour productivity under climate change in Switzerland

Extreme temperatures have reached unprecedented levels in many regions of the globe due to climate change, and a further increase is expected. Besides other consequences, high temperatures increase the mortality risk and severely affect the labour productivity of workers. We perform a high-resolution spatial analysis to assess the impacts of heat on mortality and labour productivity in Switzerland and project their development under different Representative Concentration Pathway (RCP) scenarios, considering that no socio-economic changes take place. The model is based on the risk framework of the Intergovernmental Panel on Climate Change (IPCC), which combines the three risk components: hazard, exposure, and vulnerability. We model the two impact categories in the same spatially explicit framework, and we integrate uncertainties into the analysis by a Monte Carlo simulation. We model first that about 658 deaths are associated with heat exposure currently each year in Switzerland. Second, the economic costs caused by losses in labour productivity amount to around CHF 665 million (approx. USD 700 million) per year. Should we remain on an RCP8.5 emissions pathway, these values may double (for mortality) or even triple (for labour productivity) by the end of the century. Under an RCP2.6 scenario impacts are expected to slightly increase and peak around mid-century, when climate is assumed to stop warming. Even though uncertainties in the model are large, the underlying trend in impacts is unequivocal. The results of the study are valuable information for political discussions and allow for a better understanding of the cost of inaction