Real-cases of electromagnetic immunity and reliability in embedded electronics architectures

This papers concerns works about electromagnetic immunity and reliability investigations on electronics devices, combined with different physical impacts as temperature

Strange Heat Flux in (An)Harmonic Networks

We study the heat transport in systems of coupled oscillators driven out of equilibrium by Gaussian heat baths. We illustrate with a few examples that such systems can exhibit ``strange'' transport phenomena. In particular, {\em circulation} of heat flux may appear in the steady state of a system of three oscillators only. This indicates that the direction of the heat fluxes can in general not be "guessed" from the temperatures of the heat baths. Although we primarily consider harmonic couplings between the oscillators, we explain why this strange behavior persists under weak anharmonic perturbations

A Wigner-Seitz model of charged lamellar colloidal dispersions

A concentrated suspension of lamellar colloidal particles (e. g. clay) is modelled by considering a single, uniformly charged, finite platelet confined with co- and counterions to a Wigner-Seitz (WS) cell. The system is treated within Poisson-Boltzmann theory, with appropriate boundary conditions on the surface of the WS cell, supposed to account for the confinement effect of neighbouring platelets. Expressions are obtained for the free energy, osmotic and disjoining pressures and the capacitance in terms of the local electrostatic potential and the co- and counterion density profiles. Explicit solutions of the linearized Poisson-Boltzmann (LPB) equation are obtained for circular and square platelets placed at the centre of a cylindrical or parallelepipedic cell. The resulting free energy is found to go through a minimum as a function of the aspect ratio of the cell, for any given volume (determined by the macroscopic concentration of platelets), platelet surface charge and salt concentration. The optimum aspect ratio is found to be nearly independent of the two latter physical parameters. The osmotic and disjoining pressures are found to coincide at the free energy minimum, while the total quadrupole moment of the electric double-layer formed by the platelet and the surrounding co- and counterions vanishes simultaneously. The osmotic equation-of-state is calculated for a variety of physical conditions. The limit of vanishing platelet concentration is considered in some detail, and the force acting between two coaxial platelets is calculated in that limit as a function of their separation.Comment: 21 pages, RevTeX, 12 figures available on request to [email protected], submitted to Physical Review

Intermittency and transition to chaos in the cubical lid-driven cavity flow

Transition from steady state to intermittent chaos in the cubical lid-driven flow is investigated numerically. Fully three-dimensional stability analyses have revealed that the flow experiences an Andronov-Poincar\'e-Hopf bifurcation at a critical Reynolds number $Re_c$ = 1914. As for the 2D-periodic lid-driven cavity flows, the unstable mode originates from a centrifugal instability of the primary vortex core. A Reynolds-Orr analysis reveals that the unstable perturbation relies on a combination of the lift-up and anti lift-up mechanisms to extract its energy from the base flow. Once linearly unstable, direct numerical simulations show that the flow is driven toward a primary limit cycle before eventually exhibiting intermittent chaotic dynamics. Though only one eigenpair of the linearized Navier-Stokes operator is unstable, the dynamics during the intermittencies are surprisingly well characterized by one of the stable eigenpairs.Comment: Accepted for publication in Fluid Dynamics Researc

Collective Moral Hazard, Maturity Mismatch and Systemic Bailouts

The paper elicits a mechanism by which private leverage choices exhibit strategic complementarities through the reaction of monetary policy. When everyone engages in maturity transformation, authorities have little choice but facilitating refinancing. In turn, refusing to adopt a risky balance sheet lowers the return on equity. The key ingredient is that monetary policy is non-targeted. The ex post benefits from a monetary bailout accrue in proportion to the number amount of leverage, while the distortion costs are to a large extent fixed. This insight has important consequences. First, banks choose to correlate their risk exposures. Second, private borrowers may deliberately choose to increase their interest-rate sensitivity following bad news about future needs for liquidity. Third, optimal monetary policy is time inconsistent. Fourth, macro-prudential supervision is called for. We characterize the optimal regulation, which takes the form of a minimum liquidity requirement coupled with monitoring of the quality of liquid assets. We establish the robustness of our insights when the set of bailout instruments is endogenous and characterize the structure of optimal bailouts.Monetary Policy, Funding Liquidity Risk, Strategic Complementarities, Macro-Prudential Supervision

Collective Moral Hazard, Maturity Mismatch and Systemic Bailouts

The paper elicits a mechanism by which private leverage choices exhibit strategic complementarities through the reaction of monetary policy. When everyone engages in maturity transformation, authorities haver little choice but facilitating refinancing. In turn, refusing to adopt a risky balance sheet lowers the return on equity. The key ingredient is that monetary policy is non-targeted. The ex post benefits from a monetary bailout accrue in proportion to the number amount of leverage, while the distortion costs are to a large extent fixed. This insight has important consequences. First, banks choose to correlate their risk exposures. Second, private borrowers may deliberately choose to increase their interest-rate sensitivity following bad news about future needs for liquidity. Third, optimal monetary policy is time inconsistent. Fourth, macro-prudential supervision is called for. We characterize the optimal regulation, which takes the form of a minimum liquidity requirement coupled with monitoring of the quality of liquid assets. We establish the robustness of our insights when the set of bailout instruments is endogenous and characterize the structure of optimal bailouts.

Singular trajectories of control-affine systems

When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the underlying optimal control problem. In this article, we provide characterizations for singular trajectories of control-affine systems. We prove that, under generic assumptions, such trajectories share nice properties, related to computational aspects; more precisely, we show that, for a generic system -- with respect to the Whitney topology --, all nontrivial singular trajectories are of minimal order and of corank one. These results, established both for driftless and for control-affine systems, extend previous results. As a consequence, for generic systems having more than two vector fields, and for a fixed cost, there do not exist minimizing singular trajectories. We also prove that, given a control system satisfying the LARC, singular trajectories are strictly abnormal, generically with respect to the cost. We then show how these results can be used to derive regularity results for the value function and in the theory of Hamilton-Jacobi equations, which in turn have applications for stabilization and motion planning, both from the theoretical and implementation issues