Almost optimal adaptive LQ control: observed state case

In this paper we propose an almost optimal indirect adaptive controller for input/state dynamical systems. The control part of the adaptive scheme is based on a modified LQ control law: by adding a time varying gain to the certainty equivalent control law we avoid the conflict between identification and contro

Chemical analysis and aqueous solution properties of Charged Amphiphilic Block Copolymers PBA-b-PAA synthesized by MADIX

We have linked the structural and dynamic properties in aqueous solution of amphiphilic charged diblock copolymers poly(butyl acrylate)-b-poly(acrylic acid), PBA-b-PAA, synthesized by controlled radical polymerization, with the physico-chemical characteristics of the samples. Despite product imperfections, the samples self-assemble in melt and aqueous solutions as predicted by monodisperse microphase separation theory. However, the PBA core are abnormally large; the swelling of PBA cores is not due to AA (the Flory parameter chiPBA/PAA, determined at 0.25, means strong segregation), but to h-PBA homopolymers (content determined by Liquid Chromatography at the Point of Exclusion and Adsorption Transition LC-PEAT). Beside the dominant population of micelles detected by scattering experiments, capillary electrophoresis CE analysis permitted detection of two other populations, one of h-PAA, and the other of free PBA-b-PAA chains, that have very short PBA blocks and never self-assemble. Despite the presence of these free unimers, the self-assembly in solution was found out of equilibrium: the aggregation state is history dependant and no unimer exchange between micelles occurs over months (time-evolution SANS). The high PBA/water interfacial tension, measured at 20 mN/m, prohibits unimer exchange between micelles. PBA-b-PAA solution systems are neither at thermal equilibrium nor completely frozen systems: internal fractionation of individual aggregates can occur.Comment: 32 pages, 16 figures and 4 tables submitted to Journal of Interface and Colloidal Scienc

Partitioning of energy in highly polydisperse granular gases

A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a, giving rise to a corresponding continuous temperature profile, T(a), which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves towards a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.Comment: 10 pages; 5 figure

Critical point network for drainage between rough surfaces

In this paper, we present a network method for computing two-phase flows between two rough surfaces with significant contact areas. Low-capillary number drainage is investigated here since one-phase flows have been previously investigated in other contributions. An invasion percolation algorithm is presented for modeling slow displacement of a wetting fluid by a non wetting one between two rough surfaces. Short-correlated Gaussian process is used to model random rough surfaces.The algorithm is based on a network description of the fracture aperture field. The network is constructed from the identification of critical points (saddles and maxima) of the aperture field. The invasion potential is determined from examining drainage process in a flat mini-channel. A direct comparison between numerical prediction and experimental visualizations on an identical geometry has been performed for one realization of an artificial fracture with a moderate fractional contact area of about 0.3. A good agreement is found between predictions and observations

Robotic manipulation of a rotating chain

This paper considers the problem of manipulating a uniformly rotating chain: the chain is rotated at a constant angular speed around a fixed axis using a robotic manipulator. Manipulation is quasi-static in the sense that transitions are slow enough for the chain to be always in "rotational" equilibrium. The curve traced by the chain in a rotating plane -- its shape function -- can be determined by a simple force analysis, yet it possesses complex multi-solutions behavior typical of non-linear systems. We prove that the configuration space of the uniformly rotating chain is homeomorphic to a two-dimensional surface embedded in $\mathbb{R}^3$. Using that representation, we devise a manipulation strategy for transiting between different rotation modes in a stable and controlled manner. We demonstrate the strategy on a physical robotic arm manipulating a rotating chain. Finally, we discuss how the ideas developed here might find fruitful applications in the study of other flexible objects, such as elastic rods or concentric tubes.Comment: 12 pages, 9 figure

Efficient control of accelerator maps

Recently, the Hamiltonian Control Theory was used in [Boreux et al.] to increase the dynamic aperture of a ring particle accelerator having a localized thin sextupole magnet. In this letter, these results are extended by proving that a simplified version of the obtained general control term leads to significant improvements of the dynamic aperture of the uncontrolled model. In addition, the dynamics of flat beams based on the same accelerator model can be significantly improved by a reduced controlled term applied in only 1 degree of freedom