The projective method for solving linear matrix inequalities

Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.     

A new approach to micropatterning: application of potential-assisted ion transfer at the liquid-liquid interface for the local metal deposition

A new approach to micropatterning is demonstrated. The approach is based on driving an electrochemical process at the solid-liquid interface through the formation of a flux of ions from a micropipet that is held in close proximity to the surface. The flux of ions is generated by the so-called potential assisted ion transfer at the interface between two immiscible electrolyte solutions (ITIES). As a model system, the local deposition of silver was examined. Specifically, a constant potential, which was applied to a micropipet filled with an aqueous solution of silver ions, caused the transfer of Ag(+) into the outer nitrobenzene (NB) solution that consisted of an electrolyte, tetrabutylammonium tetrakis[4-chlorophenyl]borate (TBATPBCl). To facilitate the transfer of silver ions a macrocyclic ligand, that is, dibenzo-24-crown-8 (DB24C8), was added to the organic phase. The Faradaic current of this micro-ITIES was used as a means of controlling the tip-surface distance in scanning electrochemical microscopy (SECM) and depositing silver microstructures on a gold substrate.     

Hydro­gen‐bonded supramolecular lattice of the 1:3:4 complex between [5,10,15,20‐meso‐tetrakis(4‐hydroxy­phenyl)­porphyrinato‐κ4N]­zinc(II), dibenzo‐24‐crown‐8 and methanol

The title compound, [5,10,15,20‐meso‐tetrakis(4‐hydroxy­phenyl)­porphyrinato‐κ⁴N]­zinc(II) tris(dibenzo‐24‐crown‐8) methanol tetrasolvate, [Zn(C₄₄H₂₈N₄O₄)]·3C₂₄H₃₂O₈·4CH₄O, was synthesized and its molecular structure precisely charac­terized by low‐temperature single‐crystal analysis. All the components are involved in hydrogen bonding with each other, thus forming an extensively hydrogen‐bonded supramolecular lattice. The functionalized porphyrin moiety coordinates both equatorially and axially to the neighboring species.     

On safe tractable approximations of chance constraints

A natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem, where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 − ?. While being attractive from modeling viewpoint, chance constrained problems “as they are” are, in general, computationally intractable. In this survey paper, we overview several simulation-based and simulation-free computationally tractable approximations of chance constrained convex programs, primarily, those of chance constrained linear, conic quadratic and semidefinite programming.     

Palladium Complexes of Corroles and Sapphyrins

Palladium complexes of corrole and sapphyrin were prepared in high yield and fully characterized. The corrole provides a tetradentate/trianionic square planar coordination sphere for Pd^II, charge balanced by pyridinium. Both one and two Pd^II ions may be accommodated by the pentapyrrolic skeleton of the sapphyrin, and in each case the macrocycle acts as bidentate/monoanionic ligand and the inner-sphere square planar geometry is completed by allyl anions coordinated in an η³ fashion. NMR spectroscopy and X-ray crystallography data analyses uncovered the presence of interesting stereoisomers due to the flexibility of the ally ligands and also the pyrrole ring(s) that is/are not involved in metal binding.     

High Charge Delocalization and Conjugation in Oligofuran Molecular Wires

The extent of charge delocalization and of conjugation in oligofurans and oligothiophenes was studied by using mixed valence systems comprising oligofurans and oligothiophenes capped at both ends by ferrocenyl redox units. Using electrochemical, spectral, and computational tools, we find strong charge delocalization in ferrocene‐capped oligofurans which was stronger than in the corresponding oligothiophene systems. Spectroscopic studies suggest that the electronic coupling integral (H_ab) is roughly 30–50 % greater for oligofuran‐bridged systems, indicating better energy matching between ferrocene units and oligofurans. The distance decay constant (damping factor), β, is similar for oligofurans (0.066 A^?1) and oligothiophenes (0.070 A^?1), which suggests a similar extent of delocalization in the bridge, despite the higher HOMO–LUMO gap in oligofurans. Computational studies indicate a slightly larger extent of delocalization in furan‐bridged systems compared with thiophene‐bridged systems, which is consistent with oligofurans being significantly more rigid and less aromatic than oligothiophenes. High charge delocalization in oligofurans, combined with the previously reported strong fluorescence, high mobility, and high rigidity of oligofuran‐based materials makes them attractive candidates for organic electronic applications.     

Micrometer scale gel patterns

A novel method for fabricating micrometer sized gel patterns is described. The presented method involves spin-coating a pre-gel solution on a surface that was chemically treated to modulate its surface energy, creating highly hydrophobic areas on a hydrophilic substrate. Following spin-coating, the gel solution self organizes on the hydrophilic sites. This method offers the advantages of high resolution, self-alignment to pre-patterned electrodes, and a simple straightforward fabrication process. Minimum feature size achieved was approximately 20 μm. The characteristic shrinking and swelling times of gel patterns were measured and found to be around 0.6 s for swelling and 2 s for shrinking (for a 60 μm diameter gel) in agreement with the reduced response time expected for scaled down gel patterns. These results suggest the suitability of these gel patterns as valves or actuators in microfluidic devices. Micron-size gel patterns were also incorporated into microfluidic channels thus demonstrating a new approach to create simple, affordable, microfluidic devices, which incorporate “smart” hydrogels as building elements in a simple fashion.