Using delays and time-varying gains to improve the static output feedback stabilizability of linear systems: a comparison

We address the output feedback stabilization problem of linearfinite-dimensional SISO systems. Limitations of static time-invariantoutput feedback on stabilizability are well known. We investigateand compare the possibilities of two recently proposed simplemodifications/generalizations of static time-invariant outputfeedback to remove such limitations. The first approach consistsof introducing a time-delay in the control law, which can betreated as an additional control parameter. The second approachconsists of making the gain time-varying. We show that bothapproaches are complementary. Existing theoretical results arebrought together in a unifying framework. Numerical proceduresfor the construction of the controllers are provided. Robustnessw.r.t. both parametric and delay uncertainty are dealt with.As an illustration the stabilizability of all second-order systemsis completely determined.     

Interpretation of “the wave function of the Universe”

Hawking and Hartle interpreted their wave function of the universe as giving the probability for the universe to appear from nothing. However, this is not a correct interpretation, since the normalization presupposes a universe, not nothing. Transition probabilities require a measure on the initial state and a physical result requires a physical initial state.     

Density functional study of methyl chemisorption on polycyclic aromatic hydrocarbons.

The reactions of methyl radicals with large (up to C(96)H(24)) polycyclic aromatic hydrocarbons (PAHs) are studied by density functional calculations to shed light on the experimentally observed deposition of carbon on highly oriented pyrolytic graphite (HOPG), which occurs when hot HOPG (decorated by nanometre-sized defects) is exposed to methyl radicals. The equilibrium structures of the reaction products, together with transition structures for PAHs up to the size of phenanthroperylene, are determined using the density functionals B3LYP, TPSSh, BP86 and TPSS. The structures are analysed by computing the pi orbital axis vector (POAV) and the altitude of the reactive carbon above the molecular plane of the PAH. The strongest C-CH(3) bonds are found at the edges of the PAHs, where the s character of the C orbital involved in the bond is roughly 25 % (sp(3) hybrid orbital). Carbon atoms inside the PAH form bonds with the methyl radical through atomic orbitals with about 16 % s character in the POAV analysis. These bonds are much weaker than those at the edges of the PAH, while the reactive carbon has moved about 40 pm above the molecular plane. At the edges, the PAH carbon atoms do not leave the molecular plane to this extent. The computed barrier heights and geometrical parameters of the transition structures are in agreement with Hammond's postulate, and the relative energies of all of the equilibrium structures can be rationalized by Hückel molecular orbital (HMO) theory.     

Improved Spectral Coverage and Fluorescence Quenching in Donor–acceptor Systems Involving Indolo[3‐2‐b]carbazole and Boron‐dipyrromethene or Diketopyrrolopyrrole

A novel π‐conjugated triad and a polymer incorporating indolo[3,2‐b]‐carbazole (ICZ) and 4,4‐difluoro‐4‐bora‐3a,4a‐diaza‐s‐indacene (BODIPY) were synthesized via a Sonogashira coupling. Compared to the parent BODIPY the absorption and fluorescence spectrum were for both compounds broader and redshifted. The redshift of the fluorescence and the decrease of the fluorescence quantum yield and decay time upon increasing solvent polarity were attributed to the formation of a partial charge‐transfer state. Upon excitation in the ICZ absorption band the ICZ fluorescence was quenched in both compounds mainly due to energy transfer to the BODIPY moiety. In a similar ICZ–π–DPP polymer (where DPP is diketopyrrolopyrrole), a smaller redshift of the absorption and fluorescence spectra compared to the parent DPP was observed. A less efficient quenching of the ICZ fluorescence in the ICZ–π–DPP polymer could be related to the unfavorable orientation of the transition dipoles of ICZ and DPP. The rate constant for energy transfer was for all compounds an order of magnitude smaller than predicted by Förster theory. While in a solid film of the triad a further redshift of the absorption maximum of nearly 100 nm was observed, no such shift was observed for the ICZ–π–BODIPY polymer.     

Diastereoselective Strategies towards Thia[n]helicenes

In the present study, we have investigated different strategies for diastereoselective synthesis of thia[n]helicenes. We describe the introduction of different chiral auxiliaries at various positions and investigated their effect in the photocyclization reaction. Different chiral groups were placed at the sterically hindered position of the helical core and their interactions with various solvents and metals like copper were investigated. The use of Cu^I salts has led to high diastereoselectivity in the photocyclization process and we were successful in obtaining the thia[5]helicene in enantiomerically pure form in good yield. The single diastereomer obtained was characterized by X‐ray crystallography. From the study of the barrier of racemization of these thia[5]helicenes, the stability was found to be comparable to unsubstituted tetrathia[7]helicenes and substituted diazadithia[7]helicenes. This approach provides an easy access to enantiopure helicenes.     

Efficient three-component synthesis of tetrahydrothieno[3,2-f]quinolines

An efficient one-pot method for the synthesis of tetrahydrothieno[3,2-f]quinolines is described, using the imino Diels-Alder reaction between ethyl-5-aminobenzothiophene-2-carboxylate, aromatic aldehydes and cyclic enol ethers. Furthermore, hydroxyalkyl-substituted tetrahydrothieno[3,2-f]quinolines were synthesized in good yields, by performing the same imino Diels-Alder reaction in absence of aldehydes. The intramolecular aza-Diels-Alder reaction of 5-aminobenzothiophene with o-(allyloxy)benzaldehyde was also performed resulting in the fully oxidized thienoquinoline derivative.     

Acceleration of self-consistent-field convergence by combining conventional diagonalization and a diagonalization-free procedure

A new scheme that combines conventional matrix diagonalization with the recently proposed diagonalization-free algorithm has been developed to obtain the density matrix for the next self-consistent-field iteration from the Fock matrix of the current iteration. In this manner, the advantages of the two methods are combined. The more rapid convergence of the diagonalization-free algorithm for density matrices rather close to self consistence and the more robust convergence of the conventional matrix diagonalization further away from self-consistence. The scheme has been implemented in the one- and two-component self-consistent-field procedures in the program system TURBOMOLE. The number of iterations is typically reduced by about 10%, but savings are usually much larger for slowly converging cases.     

Interactions between block copolymers and single-walled carbon nanotubes in aqueous solutions: a small-angle neutron scattering study

The amphiphilic copolymers of the Pluronic family are known to be excellent dispersants for single-walled carbon nanotubes (SWCNT) in water, especially F108 and F127, which have rather long end-blocks of poly(ethylene oxide) (PEO). In this study, the structure of the CNT/polymer hybrid formed in water is evaluated by measurements of small-angle neutron scattering (SANS) with contrast variation, as supported by cryo-transmission electron microscopy (cryo-TEM) imaging. The homogeneous, stable, inklike dispersions exhibited very small isolated bundles of carbon nanotubes in cryo-TEM images. SANS experiments were conducted at different D(2)O/H(2)O content of the dispersing solvent. The data for both systems showed surprisingly minimal intensity values at 70% D(2)O solvent composition, which is much higher than the expected value of 17% D(2)O that is based on the scattering length density (SLD) of PEO. At this near match point, the data exhibited a q(-1) power law relation of intensity to the scattering vector (q), indicating rodlike entities. Two models are evaluated, as extensions to Pederson's block copolymer micelles models. One is loosely adsorbed polymer chains on a rodlike CNT bundle. In the other, the hydrophobic block is considered to form a continuous hydrated shell on the CNT surface, whereas the hydrophilic blocks emanate into the solvent. Both models were found to fit the experimental data reasonably well. The model fit required special considerations of the tight association of water molecules around PEO chains and slight isotopic selectivity.     

Looped structure of flowerlike micelles revealed by 1H NMR relaxometry and light scattering

We present experimental proof that so-called "flowerlike micelles" exist and that they have some distinctly different properties compared to their "starlike" counterparts. Amphiphilic AB diblock and BAB triblock copolymers consisting of poly(ethylene glycol) (PEG) as hydrophilic A block and thermosensitive poly(N-isopropylacrylamide) (pNIPAm) B block(s) were synthesized via atom transfer radical polymerization (ATRP). In aqueous solutions, both block copolymer types form micelles above the cloud point of pNIPAm. Static and dynamic light scattering measurements in combination with NMR relaxation experiments proved the existence of flowerlike micelles based on pNIPAm(16kDa)-PEG(4kDa)-pNIPAm(16kDa) which had a smaller radius and lower mass and aggregation number than starlike micelles based on mPEG(2kDa)-pNIPAm(16kDa). Furthermore, the PEG surface density was much lower for the flowerlike micelles, which we attribute to the looped configuration of the hydrophilic PEG block. (1)H NMR relaxation measurements showed biphasic T(2) relaxation for PEG, indicating rigid PEG segments close to the micelle core and more flexible distal segments. Even the flexible distal segments were shown to have a lower mobility in the flowerlike micelles compared to the starlike micelles, indicating strain due to loop formation. Taken together, it is demonstrated that self-assemblies of BAB triblock copolymers have their hydrophilic block in a looped conformation and thus indeed adopt a flowerlike conformation.     

Electrowetting without electrolysis on self-healing dielectrics

An electrowetting system with protection against dielectric breakdown is presented. It comprises an electrolyte and a Parylene-C film deposited on an aluminum electrode. The system demonstrates virtually instantaneous self-healing (within 100 ms) after dielectric breakdown under both DC and certain AC electrowetting conditions. DC current response during electrowetting on intentionally damaged Parylene-C is presented. Also presented is a characterization of DC offset voltages and duty cycle percentages required for electrolysis free AC electrowetting between 10 Hz and 4 kHz.