Decentralized harmonic active vibration control of a flexible plate using piezoelectric actuator-sensor pairs

We have investigated decentralized active control of periodic panel vibration using multiple pairs combining PZT actuators and PVDF sensors distributed on the panel. By contrast with centralized MIMO controllers used to actively control the vibrations or the sound radiation of extended structures, decentralized control using independent local control loops only requires identification of the diagonal terms in the plant matrix. However, it is difficult to a priori predict the global stability of such decentralized control. In this study, the general situation of noncollocated actuator-sensor pairs was considered. Frequency domain gradient and Newton-Raphson adaptation of decentralized control were analyzed, both in terms of performance and stability conditions. The stability conditions are especially derived in terms of the adaptation coefficient and a control effort weighting coefficient. Simulations and experimental results are presented in the case of a simply supported panel with four PZT-PVDF pairs distributed on it. Decentralized vibration control is shown to be highly dependent on the frequency, but can be as effective as a fully centralized control even when the plant matrix is not diagonal-dominant or is not strictly positive real (not dissipative).     

How does crystalline substrate plasticity modify thin film buckling?

We report experimental atomic force microscopy observations and analytical modeling of buckling structures of thin films deposited on single crystal substrates. The formation of straight-sided blisters just above the step structures resulting from the dislocations emergence has been observed and explained in the framework of the F?ppl-von Karman theory of thin plates. A critical step height above which the buckling may occur has been determined and the asymmetry of the resulting blisters has been explained. Finally, the new buckling criterion has been compared with the classical one in the plane case and allows us to explain the blisters localization on step structures.     

Mode-coupling control in resonant devices: Application to solid-state ring lasers

We report the theoretical and experimental investigation of the effects of mode coupling in a resonant macroscopic quantum device, in the case of a solid-state ring laser. This is achieved by introducing an additional coupling source whose interplay with the already-existing nonlinear effects ensures the coexistence of two counterpropagating cavity modes yielding a rotation-sensitive beat note. The determination of the condition for rotation sensing, both theoretically and experimentally, allows a quantitative study of the role of various mode-coupling mechanisms, in particular, the gain-induced mode coupling. We point out the connection between our work and the theoretical work on mode coupling in superfluid devices. This work opens up the possibility of new types of active rotation sensors.     

Theory and simulation of wave phase conjugation

This paper briefly presents the general analytical solution for the resonant modes in 1D active magneto acoustic phase conjugators in contact with passive media of arbitrary impedance. The first non-resonant but amplified modes are also derived. All results are successfully compared with direct numerical simulations.     

Localization for Random Unitary Operators

We consider unitary analogs of one-dimensional Anderson models on defined by the product U _ω=D _ω S where S is a deterministic unitary and D _ω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of U _ω is pure point almost surely for all values of the parameter of S. We provide similar results for unitary operators defined on together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunsky coefficients of constant modulus and correlated random phases Mathematics Subject Classification. 82B44, 42C05, 81Q05     

Localization Properties of the Chalker–Coddington Model

The Chalker–Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove first that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly, that this implies spectral localization. Thirdly, we prove a Thouless formula and compute the mean Lyapunov exponent, which is independent of M.     

The regularity and exponential decay of solution for a linear wave equation associated with two-point boundary conditions

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated the boundary conditions of two-point type. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional. Finally, we present some numerical results.     

Novel Supports for Ethylene Polymerisation Based on Polystyrene Polymers

The industrial use of metallocene/methylaluminoxane catalytic systems and late transition metal catalysts requires the use of supports to directly get polyethylene (PE) with spherical morphology. The presence of residues of the inorganic support gives rise to PE contamination problems, therefore less contaminating organic supports may present an interesting alternative. In this work, linear hydroxypolystyrene (PS-OH) and polystyrene-block-isoprene copolymer (PS-b-PI) were tested as supports for ethylene polymerisation. The ability of these polymers when dissolved in a selective solvent to form micelles or aggregates, was investigated by light scattering techniques. Next, their capacity to act as MAO or TMA-activated supports towards MeDIP(2,6-iPrPh₂FeCl₂) catalyst was analysed by carrying ethylene polymerisation tests and PE morphology studies. The PS-b-PI copolymer, used as organic support in heptane, enabled the obtention of PE with well defined spherical morphology.     

A flexible MILP model for multiple-shift workforce planning under annualized hours

Flexibility in workforce planning is one of the best ways to respond to fluctuations of the demand. This paper proposes a flexible mixed integer linear programming (MILP) model to solve a multiple-shift workforce planning problem under annualized working hours. The model takes into account laws and collective agreements that impose constraints on overtime and holidays. We consider possible gradual hiring of full time and partial time workers. Several objectives are pursued such as balancing the workload of the employees or minimizing the workforce size. Computational experiments on a real life problem demonstrate the effectiveness of the model.