Convergence Theory for Preconditioned Eigenvalue Solvers in a Nutshell

Preconditioned iterative methods for numerical solution of large matrix eigenvalue problems are increasingly gaining importance in various application areas, ranging from material sciences to data mining. Some of them, e.g., those using multilevel preconditioning for elliptic differential operators or graph Laplacian eigenvalue problems, exhibit almost optimal complexity in practice; i.e., their computational costs to calculate a fixed number of eigenvalues and eigenvectors grow linearly with the matrix problem size. Theoretical justification of their optimality requires convergence rate bounds that do not deteriorate with the increase of the problem size. Such bounds were pioneered by E. D’yakonov over three decades ago, but to date only a handful have been derived, mostly for symmetric eigenvalue problems. Just a few of known bounds are sharp. One of them is proved in doi: 10.1016/S0024-3795(01)00461-X for the simplest preconditioned eigensolver with a fixed step size. The original proof has been greatly simplified and shortened in doi: 10.1137/080727567 by using a gradient flow integration approach. In the present work, we give an even more succinct proof, using novel ideas based on Karush–Kuhn–Tucker theory and nonlinear programming.     

Vibrational and thermodynamic properties of Ar, N2, O2, H2 and CO adsorbed and condensed into (H,Na)-Y zeolite cages as studied by variable temperature IR spectroscopy

The adsorption of Ar, H2, O2, N2 and CO on (H,Na)-Y zeolite (Si/Al = 2.9, H+/Na+ approximately 5) has been studied at variable-temperature (90-20 K) and sub-atmospheric pressure (0-40 mbar) by FTIR spectroscopy. Unprecedented filling conditions of the zeolite cavities were attained, which allowed the investigation of very weakly adsorbed species and of condensed, liquid-like or solid-like, phases. Two pressure regimes were singled out, characterized by: (i) specific interaction at low pressure of the probe molecules (P) with the internal Br?nsted and Lewis sites, and (ii) multilayer adsorption at higher pressure. In the case of CO the perturbation of the protonic sites located inside the sodalite cages was also observed. As the molecule is too large to penetrate the sodalite cage, the perturbation is thought to involve a proton jump tunneling mechanism. The adsorption energy for the (HF)OH...P (P = Ar, H2, O2, N2 and CO) specific interaction involving the high frequency Br?nsted acid sites exposed in the supercages was derived following the VTIR (variable temperature infrared spectroscopy) method described by E. Garrone and C. Otero Areán (Chem. Soc. Rev., 2005, 34, 846).     

Structural and electronic properties of group III Rich In0.53Ga0.47As(001)

The structural and electronic properties of group III rich In_0.53Ga_0.47As(001) have been studied using scanning tunneling microscopy/spectroscopy (STM/STS). At room temperature (300 K), STM images show that the In_0.53Ga_0.47As(001)–(4 × 2) reconstruction is comprised of undimerized In/Ga atoms in the top layer. Quantitative comparison of the In_0.53Ga_0.47As(001)–(4 × 2) and InAs(001)–(4 × 2) shows the reconstructions are almost identical, but In_0.53Ga_0.47As(001)–(4 × 2) has at least a 4× higher surface defect density even on the best samples. At low temperature (77 K), STM images show that the most probable In_0.53Ga_0.47As(001) reconstruction is comprised of one In/Ga dimer and two undimerized In/Ga atoms in the top layer in a double (4 × 2) unit cell. Density functional theory (DFT) simulations at elevated temperature are consistent with the experimentally observed 300 K structure being a thermal superposition of three structures. DFT molecular dynamics (MD) show the row dimer formation and breaking is facilitated by the very large motions of tricoodinated row edge As atoms and z motion of In/Ga row atoms induced changes in As–In/Ga–As bond angles at elevated temperature. STS results show there is a surface dipole or the pinning states near the valence band (VB) for 300 K In_0.53Ga_0.47As(001)–(4 × 2) surface consistent with DFT calculations. DFT calculations of the band-decomposed charge density indicate that the strained unbuckled trough dimers being responsible for the surface pinning.     

Structure of trans-1,4-polybutadiene synthesized with a new catalyst system

Abstract

The structure, phase composition, and temperature behavior of two trans-1,4-polybutadienes (TPBs) were studied by means of x-ray scattering and differential scanning calorimetry (DSC) techniques. The two samples examined were (1) PB synthesized using an immobilized titanium-magnesium catalyst and (2) a random copolymer based on PB prepared with a homogeneous vanadium-containing catalyst used as a reference material. It was found that the nascent structure of the first PB involves three phases: crystalline, mesomorphic (low-temperature form), and amorphous. In the vicinity of 65°C, a first-order phase transition occurs. The system becomes biphasic and contains the high-temperature form of the mesophase, as well as the amorphous phase, component. Above 165°C, the polymer melts to form a single-phase isotropic melt with a structure typical of liquids. The lateral dimension of crystallites reversibly changes at the crystal-mesophase transition. It is suggested that during annealing of the mesophase formed by cooling of the isotropic melt, the chains acquire an extended conformation. Loss of regularity of the structure of macromolecules of TPB causes a reduction of phase transition temperatures, an increase of the imperfection of the crystalline phase, and a contraction of the temperature range of existence of the mesophase.     

On the Boolean Model of Wiener Sausages

The Boolean model of Wiener sausages is a random closed set that can be thought of as a random collection of parallel neighborhoods of independent Wiener paths in space. It describes e.g. the target detection area of a network of sensors moving according to the Brownian dynamics whose initial locations are chosen in the medium at random. In the paper, the capacity functional of this Boolean model is given. Moreover, the one- and two-point coverage probabilities as well as the contact distribution function and the specific surface area are studied. In and , the one- and two-point coverage probabilities are calculated numerically by Monte Carlo simulations and as a solution of the heat conduction problem. The corresponding approximation formulae are given and the error of approximation is analyzed. Research supported by the grant GACR 201/06/0302.     

Chemosensory performance of molecularly imprinted fluorescent conjugated polymer materials

Fluorescent conjugated polymers are an attractive basis for the design of low detection limit sensing devices owing to their intrinsic signal amplification capability. A simple and universal method to rationally control or fine-tune the chemodetection selectivity of conjugated polymer materials toward a desired analytical target would further benefit their applications. In a quest of such a method we investigated a general approach to cross-linked molecularly imprinted fluorescent conjugated polymer (MICP) materials that possess an intrinsic capability for signal transduction and have potential to enhance selectivity and sensitivity of sensor devices based on conjugated polymers. To study these capabilities, we prepared an MICP material for the detection of 2,4,6-trinitrotoluene and related nitroaromatic compounds. We found the imprinting effect in this material to be based on analyte shape/size recognition being substantial and generally overcoming other competing thermodynamically determined trends. The described molecularly imprinted fluorescent conjugated polymers show remarkable air stability and photostability, high fluorescence quantum yield, and reversible analyte binding and therefore are advantageous for sensing applications due to the ability to "preprogram" their detection selectivity through a choice of an imprinted template.     

Hemicarceplexes That Release Guests upon Irradiation

Cleavage of one of the four bridging units in the two new types of hemicarceplexes presented here is sufficient to effect immediate guest release into the chloroform solvent (shown schematically on the right). The thermal stability and photoactivity of these hemicarceplexes indicate that incarceration is potentially useful for the controlled delivery of drugs.     

Electropolymerizable 2,2'-Carboranyldithiophenes. Structure-Property Investigations of the Corresponding Conducting Polymer Films by Electrochemistry, UV-Visible Spectroscopy and Conducting Probe Atomic Force Microscopy

Carborane-functionalized conducting polymer films have been electrogenerated in dichloromethane from the anodic oxidation of ortho- (1), meta- (3) and para-carborane (4) isomers linked to two 2-thienyl units. The corresponding electrochemical response was characterized by a broad reversible redox system corresponding to the p-doping/undoping of the polythiophene backbone, the formal potential of which increased in the order poly(1) < poly(3) < poly(4), from ca. 0.50 to 1.15 V vs Ag/Ag(+) 10(-2) M. From further UV-visible spectroscopy analysis, the optical band gap was estimated at 1.8, 2.0 and 2.2 eV for poly(1), poly(3) and poly(4), respectively. The more conjugated and electroconductive character of poly(1) is ascribed to a more planar conformation of the conjugated backbone resulting from an intramolecular β-β' cyclization reaction in the monomer, consequently yielding a fused conjugated polymer. Molecular modeling calculations using the DFT method support this hypothesis. The surface topography and maps of the conductive domains of the electropolymerized films were evaluated by conducting probe AFM. The three polymers exhibit fairly similar morphological characteristics and a surface roughness of ~2 nm. Current-voltage (I-V) characteristics of conducting AFM tip-carborane polymer-ITO junctions showed that poly(1) had the highest conductivity.