On the spectrum of stiffness matrices arising from isogeometric analysis

We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, conditioning (extremal behavior), spectral distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain (compact) subset of \(\mathbb C\) . All the analysis is related to the notion of symbol in the Toeplitz setting and is carried out both for the cases of 1D and 2D problems.     

Detecting perfect powers by factoring into coprimes

This paper presents an algorithm that, given an integer , finds the largest integer such that is a th power. A previous algorithm by the first author took time where ; more precisely, time ; conjecturally, time . The new algorithm takes time . It relies on relatively complicated subroutines--specifically, on the first author's fast algorithm to factor integers into coprimes--but it allows a proof of the bound without much background; the previous proof of relied on transcendental number theory.

The computation of is the first step, and occasionally the bottleneck, in many number-theoretic algorithms: the Agrawal-Kayal-Saxena primality test, for example, and the number-field sieve for integer factorization.

     

High-resolution small-angle x-ray diffraction study of long-range order in hard-sphere colloidal crystals

The long-range order parameters in single crystals of hard colloidal spheres grown in sediments of colloid-polymer mixtures are determined using synchrotron small-angle x-ray diffraction with a resolution of 10(-6) of the wave vector. The interplanar positional order derived from the width of lattice reflections extends over at least 500 lattice planes. The lattice planes are orientationally correlated within approximately 0.1 degrees throughout the crystals, whereas the stacking of hexagonal planes remains random.     

Analysis of the phase transitions in alkyl-mica by density and pressure profiles

In a previous work [Heinz, Castelijns, and Suter, J. Am. Chem. Soc. 115, 9500 (2003)], we developed an accurate force field and simulated the phase transitions in C18-mica (octadecyltrimethylammonium-mica) as well as the absence of such transitions in 2C18-mica (dioctadecyldimethylammonium-mica) between room temperature and 100 degrees C. Here we analyze (i) average z coordinates of the carbon atoms and interdigitation of the hydrocarbon bilayers, (ii) density profiles, and (iii) pressure profiles of the structures along all Cartesian axes. In C18-mica, the standard deviation in the z coordinate for the chain atoms is high and more than doubles in the disordered phase. The order-disorder transition is accompanied by a change in the orientation of the ammonium head group, as well as decreasing tensile and shear stress in the disordered phase. In 2C18-mica, the standard deviation in the z coordinate for the chain atoms is low and does not increase remarkably on heating. The backbones display a highly regular structure, which is slightly obscured by rotations in the C18 backbones and minor head group displacements at 100 degrees C. Close contacts between the bulky head groups with sidearms cause significant local pressure which is in part not relieved at 100 degrees C. An increase of the basal-plane spacing at higher temperature is found in both systems due to larger separation between the two hydrocarbon layers and an increased z spacing between adjacent chain atoms (=decreased tilt of the chains relative to the surface normal), and, in C18-mica only, a stronger upward orientation of the C18 chain at the ammonium head group. The likelihood for chain interdigitation between the two hydrocarbon layers is 24%-30% for C18-mica, and 65%-26% for 2C18-mica (for 20-100 degrees C).     

Combined in Silico and in Vitro Approaches To Uncover the Oxidation and Schiff Base Reaction of Baicalein as an Inhibitor of Amyloid Protein Aggregation

The oxidized form of baicalein ( BA ) leads to covalent binding with human amyloid proteins. Such adducts hamper the aggregation and deposition of fibrils. A novel reaction of BA with pentylamine ( PA ) as a model for the lysine side chain is described. This is the first study addressing the atomistic details of a Schiff base reaction with the trihydroxylated moiety of BA . Nuclear magnetic resonance and mass spectrometry approaches clearly indicate the formation of dehydrobaicalein in solution as well as its condensation with PA under aerobic conditions, yielding regioselectively C6-substituted products. The combined results suggest initial ion pair formation between BA and PA , followed by a redox chain reaction: the initiation by oxygen/air; an o-quinone-based chain involving oxidation and reduction steps; and extra off-chain formation of a doubly oxidized product. These mechanistic details support the anti-amyloid activity of BA and endorse its trihydroxyphenyl moiety as a pharmacophore for drug-design studies.     

Simulation of 59Co NMR chemical shifts in aqueous solution

59Co chemical shifts were computed at the GIAO-B3LYP level for [Co(CN)6]3-, [Co(H2O)6]3+, [Co(NH3)6]3+, and [Co(CO)4]- in water. The aqueous solutions were modeled by Car-Parrinello molecular dynamics (CPMD) simulations, or by propagation on a hybrid quantum-mechanical/molecular-mechanical Born-Oppenheimer surface (QM/MM-BOMD). Mean absolute deviations from experiment obtained with these methods are on the order of 400 and 600 ppm, respectively, over a total delta(59Co) range of about 18,000 ppm. The effect of the solvent on delta(59Co) is mostly indirect, resulting primarily from substantial metal-ligand bond contractions on going from the gas phase to the bulk. The simulated solvent effects on geometries and delta(59Co) values are well reproduced by using a polarizable continuum model (PCM), based on optimization and perturbational evaluation of quantum-mechanical zero-point corrections.