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Stability of non-autonomous difference equations with applications to transport and wave propagation on networks
No full textInternational audienceIn this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable representation of their solutions in terms of their initial conditions and some time-dependent matrix coefficients. This enables us to characterize the asymptotic behavior of solutions in terms of such coefficients. In the case of difference equations with arbitrary switching, we obtain a delay-independent generalization of the well-known criterion for autonomous systems due to Hale and Silkowski. As a consequence, we show that exponential stability of transport systems and wave propagation on networks is robust with respect to variations of the lengths of the edges of the network preserving their rational dependence structure. This leads to our main result: the wave equation on a network with arbitrarily switching damping at external vertices is exponentially stable if and only if the network is a tree and the damping is bounded away from zero at all external vertices but at most one
Transient electrochemistry: beyond simply temporal resolution.
No full textInternational audienceSome physicochemical intrigues for which transient electrochemistry was necessary to solve the problem are summarized in this feature article. First, we highlight the main constraints to be aware of to access to low time scales, and particularly focus on the effects of stray capacitances. Then, the electron transfer rate constant measured for redox molecules in a self-assembled monolayer configuration is compared to the conductance measured through the same systems, but at the single molecule level. This evidences strong conformational changes when molecules are trapped in the nanogap created between both electrodes. We also report about dendrimers, for which a short electrochemical perturbation induces creation of a diffusion layer within the molecule, allowing the electron hopping rate to be measured and analyzed in terms of molecular motions of the redox centers. Finally, we show that transient electrochemistry provides also useful information when coupled to other methodologies. For example, when an ultrasonic field drives very fast movements of a bubble situated above the electrode surface, the motion can be detected indirectly through a modification of the diffusion flux. Another field concerns pulse radiolysis, and we describe how the reactivity (at the electrode or within the solution) of radicals created by a radiolytic pulse can be quantified, widening the possibilities of electrochemistry to operate in biological media
Parameter estimation of Ornstein-Uhlenbeck process generating a stochastic graph
No full textInternational audienceGiven Y a graph process defined by an incomplete information observation of a multivariate Ornstein-Uhlenbeck process X, we investigate whether we can estimate the parameters of X. We define two statistics of Y. We prove convergence properties and show how these can be used for parameter inference. Finally, numerical tests illustrate our results and indicate possible extensions and applications
Cross-Sectional Investigations on Epitaxial Silicon Solar Cells by Kelvin and Conducting Probe Atomic Force Microscopy: Effect of Illumination
No full textInternational audienceBoth surface photovoltage and photocurrent enable to assess the effect of visible light illumination on the electrical behavior of a solar cell. We report on photovoltage and photocurrent measurements with nanometer scale resolution performed on the cross section of an epitaxial crystalline silicon solar cell, using respectively Kelvin probe force microscopy and conducting probe atomic force microscopy. Even though two different setups are used, the scans were performed on locations within 100-μm distance in order to compare data from the same area and provide a consistent interpretation. In both measurements, modifications under illumination are observed in accordance with the theory of PIN junctions. Moreover, an unintentional doping during the deposition of the epitaxial silicon intrinsic layer in the solar cell is suggested from the comparison between photovoltage and photocurrent measurements
Special Issue on Computational Logic ( in honor to Roy Dyckhoff) of Journal of Logic and Computation
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A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine
No full textInternational audienceCombining insights from the study of type refinement systems and of monoidal closed chiralities, we show how to reconstruct Lawvere's hyperdoctrine of presheaves using a full and faithful embedding into a monoidal closed bifibration living now over the compact closed category of small categories and distributors. Besides revealing dualities which are not immediately apparent in the traditional presentation of the presheaf hyperdoctrine, this reconstruction leads us to an axiomatic treatment of directed equality predicates (modelled by hom presheaves), realizing a vision initially set out by Lawvere (1970). It also leads to a simple calculus of string diagrams (representing presheaves) that is highly reminiscent of C. S. Peirce's existential graphs for predicate logic, refining an earlier interpretation of existential graphs in terms of Boolean hyperdoctrines by Brady and Trimble. Finally, we illustrate how this work extends to a bifibrational setting a number of fundamental ideas of linear logic
Molding direction constraints in structural optimization via a level-set method
No full textInternational audienceIn the framework of structural optimization via a level-set method, we develop an approach to handle the directional molding constraint for cast parts. A novel molding condition is formulated and a penalization method is used to enforce the constraint. A first advantage of our new approach is that it does not require to start from a feasible initialization, but it guarantees the convergence to a castable shape. A second advantage is that our approach can incorporate thickness constraints too. We do not adress the optimization of the casting system, which is considered a priori defined. We show several 3d examples of compliance minimization in linearized elasticity under molding and minimal or maximal thickness constraints. We also compare our results with formulations already existing in the literature
Factoring Safe Semiprimes with a Single Quantum Query
No full textShor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform efficiently. SFA thus consists of a quantum order finding algorithm (QOFA), bookended by classical routines which, given the order, return the factors. But, with probability up to 1/2, these classical routines fail, and QOFA must be rerun. We modify these routines using elementary results in number theory, improving the likelihood that they return the factors.We present a new quantum factoring algorithm based on QOFA which is better than SFA at factoring safe semiprimes, an important class of numbers used in RSA encryption (and reputed to be the hardest to factor). With just one call to QOFA, our algorithm almost always factors safe semiprimes. As well as a speed-up, improving efficiency gives our algorithm other, practical advantages: unlike SFA, it does not need a randomly picked input, making it simpler to construct in the lab; and in the (unlikely) case of failure, the same circuit can be rerun, without modification.We consider generalising this result to other cases, although we do not find a simple extension, and conclude that SFA is still the best algorithm for general numbers (non safe semiprimes, in other words). Even so, we present some simple number theoretic tricks for improving SFA in this case
Moutard transform for the generalized analytic functions
No full textInternational audienceWe construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given
Filamentation and Pulse Self-compression in the Anomalous Dispersion Region of Glasses
No full textInternational audienceThe propagation of near-infrared ultra-short laser pulses in the regime of anomalous dispersion of transparent solids is associated with a host of self-induced effects including a significant spectral broadening extending from the ultraviolet into the infrared region, pulse self-compression down to few-cycle pulse durations, free and driven third harmonic generation, conical emission and the formation of stable filaments over several cm showing the emergence of conical light bullets. We review measurements performed in different experimental conditions and results of numerical simulations of unidirectional propagation models showing that the interpretation of all these phenomena proceed from the formation of non-spreading conical light bullets during filamentation