On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension

In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in "New blow-up rates for fast controls of Schr\"odinger and heat equations`", we are able to give precise upper bounds on the time-dependance of the cost of fast controls when the time of control T tends to 0. We also give a lower bound of the cost of fast controls for the same class of equations, which proves the optimality of the power of T involved in the cost of the control. These general results are then applied to treat notably the case of linear KdV equations and fractional heat or Schr\"odinger equations

A non-controllability result for the half-heat equation on the whole line based on the prolate spheroidal wave functions and its application to the Grushin equation

In this article, we revisit a result by A. Koenig concerning the non-controllability of the half-heat equation posed on R, with a control domain that is an open set whose exterior contains an interval. The main novelty of the present article is to disprove the corresponding observability inequality by using as an initial condition a family of prolate spheroidal wave function (PSWF) translated in the Fourier space, associated to a parameter c that goes to ∞. The proof is essentially based on the dual nature of the PSWF together with direct computations, showing that the solution "does not spread out" too much during time. As a consequence, we obtain a new non-controllability result on the Grushin equation posed on R × R

The influence of perceived talker differences on the talker variability effect under cochlear implant simulation

Speech recognition is harder when communicating with multiple talkers. This “talker variability effect” has not been extensively examined for cochlear implant (CI) users, who have difficulty discriminating same-gender talkers but not different-gender talkers. A shadowing task was conducted with normal hearing listeners (N=19) under CI simulation. The test consisted of a single-talker condition (ST), and two multi-talker conditions with different male and female voices (MT-M) or only different female voices (MT-F). Response times were longer and accuracy was lower in MT-M compared to MT-F. Thus, the talker variability effect was observed only when talkers were perceptible under CI simulation

Addendum to "Local Controllability of the Two-Link Magneto-Elastic Micro-Swimmer"

In the above mentioned note (, , published in IEEE Trans. Autom. Cont., 2017), the first and fourth authors proved a local controllability result around the straight configuration for a class of magneto-elastic micro-swimmers.That result is weaker than the usual small-time local controllability (STLC), and the authors left the STLC question open. The present addendum closes it by showing that these systems cannot be STLC

Analysis of Original Finishes of Jules Bouy\u27s 1930 Interior for the Cosmopolitan Club of Philadelphia

This research looks at the original finishes of the interior of the Cosmopolitan Club of Philadelphia, an important interior of the Modern age designed in 1930 by interior decorator Jules Bouy. Although the building design has been extensively researched in a 2012 Thesis in Historic Preservation by Sarah Peterson, the interior finishes are not well understood. This research augments Peterson’s study by determining color palettes, painting techniques, and paint types of four of the most important rooms of the Club: the Entry, the Lounge, the Library and the Stair Hall. Relying primarily on the microscopic study of paint cross sections, analysis is augmented by more specific methods of analysis, such as FTIR, SEM-EDS, GC-MS, and Raman spectroscopy. A palette of greys, blues and tans were found in one room, while three shades of green with pale yellow in another. The study identifies linseed oil as the paint’s binding media. Pigments are found to include ultramarine, Prussian blue, and chrome yellow. The resulting information is interpreted in the context of the building and of the period. Results led to recommendations for steps to restore Bouy’s polychrome interior

Internal controllability for parabolic systems involving analytic non-local terms

“This is a post-peer-review, pre-copyedit version of an article published in Chinese Annals of Mathematics, Series B. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11401-018-1064-6”This article is dedicated to Phillippe G. Ciarlet in the occasion of his 80th birthday, with gratitude and admiration for his mastery and continuous support. Merci PhilippeThis paper deals with the problem of internal controllability of a system of heat equations posed on a bounded domain with Dirichlet boundary conditions and perturbed with analytic non-local coupling terms. Each component of the system may be controlled in a different subdomain. Assuming that the unperturbed system is controllable—a property that has been recently characterized in terms of a Kalman-like rank condition—the authors give a necessary and sufficient condition for the controllability of the coupled system under the form of a unique continuation property for the corresponding elliptic eigenvalue system. The proof relies on a compactness-uniqueness argument, which is quite unusual in the context of parabolic systems, previously developed for scalar parabolic equations. The general result is illustrated by two simple example

Internal observability for coupled systems of linear partial differential equations

First published in Journal on Control and Optimization in 57.2 (2019): 832-853, published by the Society for Industrial and Applied Mathematics (SIAM)We deal with the internal observability for some coupled systems of partial differential equations with constant or time-dependent coupling terms by means of a reduced number of observed components. We prove new general observability inequalities under some Kalman-like or Silverman-Meadows-like condition. Our proofs combine the observability properties of the underlying scalar equation with algebraic manipulations. In the more specific case of systems of heat equations with constant coefficients and nondiagonalizable diffusion matrices, we also give a new necessary and sufficient condition for observability in the natural L2-setting. The proof relies on the use of the Lebeau-Robbiano strategy together with a precise study of the cost of controllability for linear ordinary differential equations, and allows us to treat the case where each component of the system is observed in a different subdomainPierre Lissy is partially supported by the project IFSMACS (ANR-15-CE40-0010) funded by the french Agence Nationale de la Recherche, 2015-2019. Enrique Zuazua is partially supported by the Advanced Grant DYCON (Dynamic Control) of the European Research Council Executive Agency, FA9550-15-1-0027 of AFOSR, FA9550-14-1-0214 of the EOARD-AFOSR, the MTM2014-52347 and MTM2017-92996 Grants of the MINECO (Spain) and ICON (ANR-16-ACHN-0014) of the French Agence Nationale de la Recherch

Bilinear local controllability to the trajectories of the Fokker-Planck equation with a localized control

This work is devoted to the control of the Fokker-Planck equation, posed on a bounded domain of R^d (d>0). More precisely, the control is the drift force, localized on a small open subset. We prove that this system is locally controllable to regular nonzero trajectories. Moreover, under some conditions on the reference control, we explain how to reduce the number of controls around the reference control. The results are obtained thanks to a linearization method based on a standard inverse mapping procedure and the fictitious control method. The main novelties of the present article are twofold. Firstly, we propose an alternative strategy to the standard fictitious control method: the algebraic solvability is performed and used directly on the adjoint problem. Secondly, we prove a new Carleman inequality for the heat equation with one order space-varying coefficients: the right-hand side is the gradient of the solution localized on a subset (rather than the solution itself), and the left-hand side can contain arbitrary high derivatives of the solution