Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N(2)) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the "block" version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale Brownian dynamics simulations with hydrodynamic interactions.     

Evaluation of relative comparator and <Emphasis Type="Italic">k</Emphasis><Subscript>0</Subscript>-NAA for characterization of Aboriginal Australian ochre

Ochre is a significant material in Aboriginal Australian cultural expression from ceremonial uses to its application on many types of artifacts. However, ochre is a complex material, with associated surrounding minerals potentially challenging the overall analysis. In recent literature several studies have attempted to characterize ochre by a variety of techniques to understand procurement and trade. However, ochre is difficult to differentiate on major elemental or mineralogical composition and requires a detailed analysis of its geochemical “fingerprint”. Neutron activation analysis (NAA) provides the high sensitivity (sub-ppm), precision and accuracy in multi-elemental analysis required for ochre. The elements of interest for ochre generally include rare earth elements (REEs) and certain transition metal elements as well as arsenic and antimony. Data from relative comparator NAA (MURR, University of Missouri, USA) is compared with data from k ₀-NAA OPAL (ANSTO, Lucas Heights, Australia). A discussion of the two methods will be examined for their utility in “fingerprinting” the provenance of ochre. The continuing importance of NAA to archaeometry will also be discussed.     

Axially symmetric volume constrained anisotropic mean curvature flow

We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary components on two horizontal plates and its free energy is anisotropic and axially symmetric. For axially symmetric initial surfaces with sufficiently large volume in comparison with their initial surface energy, we show that the flow exists for all time. Numerical simulations of the curvature flow are presented.     

Cubic diophantine inequalities for split forms

Denote by \(s_0^{(r)}\) the least integer such that if \(s \geqslant s_0^{(r)}\) , and \(F\) is a cubic form with real coefficients in \(s\) variables that splits into \(r\) parts, then \(F\) takes arbitrarily small values at nonzero integral points. We bound \(s_0^{(r)}\) for \(r \leqslant 6\) .     

Almost sure explosion of solutions to stochastic differential equations

This paper is concerned with the problem of explosive solutions for a class of stochastic differential equations. Our main results are presented as two theorems. Theorem 1 is concerned with the existence of explosive solutions with positive probability under certain sufficient conditions. With some additional mild conditions, it is shown in Theorem 2 that the explosion will occur almost surely. The methods of auxiliary functions and cycles are used in the proofs. Several remarks about their applications are given.     

Spongipyran synthetic studies. Total synthesis of (+)-spongistatin 2

Evolution of a convergent synthetic strategy to access (+)-spongistatin 2 (2), a potent cytotoxic marine macrolide, is described. Highlights of the synthesis include: development of a multicomponent dithiane-mediated linchpin union tactic, devised and implemented specifically for construction of the spongistatin AB and CD spiro ring systems; application of a Ca^II ion controlled acid promoted equilibration to set the thermodynamically less stable axial-equatorial stereogenicity in the CD spiroketal; use of sulfone addition/Julia methylenation sequences to unite the AB and CD fragments and introduce the C(44)-C(51) side chain; and fragment union and final elaboration to (+)-spongistatin 2 (2) exploiting Wittig olefination to unite the advanced ABCD and EF fragments, followed by regioselective Yamaguchi macrolactonization and global deprotection. Correction of the CD spiro ring stereogenicity was subsequently achieved via acid equilibration in the presence of Ca^II ion to furnish (+)-spongistatin 2 (2). The synthesis proceeded with a longest linear sequence of 41 steps.     

Nanophotonic Ion Production from Silicon Microcolumn Arrays

Nanoantennas for ions : Silicon microcolumn arrays harvest light from a laser pulse to produce ions. The system behaves like a quasi‐periodic antenna array with ion yields that show profound dependence on the plane of polarization and the angle of incidence of the laser beam. Photonic ion sources promise to enable enhanced control of ion production on a micro‐ and nanometer scale and direct integration with miniaturized analytical devices.

     

Charge-density waves in pure and intercalated Nb3Te4

High-resolution transmission electron microscopy (HRTEM), resistivity measurements and electronic band structure calculations performed by means of the extended Hückel tight-binding method are presented for the quasi one-dimensional compounds A_xNb₃Te₄ (A = In, Tl, Zn, Ag, Hg). HRTEM and electron diffraction performed on pure Nb₃Te₄ at room- and liquid nitrogen temperatures, reveal both the basic structure and the low-temperature charge-density waves (CDWs) modulation. Resistivity vs. temperature plots show characteristic CDW anomalies, dependent on the type and concentration of the atoms, intercalated into the large hexagonal tunnels of the host structure. It is shown that intercalation of Tl and In results in a flattening of the corresponding Fermi surfaces and that CDW formation is largely dependent on the coincidence between the Fermi level E_F and a small peak in the density of states spectrum, mainly developed from the Nb dz² orbitals. This peak is positioned in a minimum between the filled and empty states of the spectrum and tends to split into a doublet as a consequence of intercalation.     

Syntheses and structures of N-polyfluorophenyl- and N,N′-bis(polyfluorophenyl)ethane-1,2-diaminato(1- or 2-)platinum(II) complexes

The reaction of [PtX₂(L)] (X = Cl, Br, I; L = NH₂CH₂CH₂NY₂; Y = Et, Me) with thallium(I) carbonate and a polyfluorobenzene (RF) in pyridine (py) yields the platinum(II) complexes, [Pt{N(R)CH₂CH₂NY₂}X(py)] (R = C₆F₅, 4-HC₆F₄, 4-BrC₆F₄, or 4-IC₆F₄, Y = Et (1), Me (2), X = Cl, Br or I) in an improved synthesis. From the reaction of [PtCl₂(H₂NCH₂)₂)] with Tl₂CO₃ and 1,2,3,4-tetrafluorobenzene or 2-bromo-1,3,4,5-tetrafluorobenzene in py, the new complexes [Pt(NRCH₂)₂(py)₂] (3) (R = C₆H₂F₃-2,3,6 and C₆HBrF₃-2,3,5,6) have been isolated but the latter preparation also gave product(s) with a 4-bromo-2,3,5-trifluorophenyl group. From an analogous preparation in 4-ethylpyridine (etpy), [Pt(N(4-HC₆F₄)CH₂)₂(etpy)₂] (4) was obtained. The X-ray crystal structures of (3) (R = C₆HBrF₃-2,3,5,6) and (4) were determined as well as that of the previously prepared (3) (R = 4-BrC₆F₄) and a more precise structure of (3) (R = 4-HC₆F₄) has been obtained.     

Performance of a biomimetic oxidation catalyst immobilized on silicon wafers: comparison with its gold congener

With the aim of extending the usefulness of an existing biomimetic catalytic system, cobalt porphyrin catalytic units with thiol linkers were heterogenized via chemical grafting to silicon wafers and utilized for the catalytic oxidation of hydroquinone to p-benzoquinone. Atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS) were used to analyze the morphology and composition of the heterogeneous catalyst. The results of the catalytic oxidation of hydroquinone obtained with porphyrins grafted on silicon were compared with those obtained earlier with the same catalyst in homogeneous phase and immobilized on gold. It was found that the catalysis could run over 400 h, without showing any sign of deactivation. The measured catalytic activity is at least 10 times higher than that measured under homogeneous conditions, but also 10 times lower than that observed with the catalytic unit immobilized on gold. The reasons of this discrepancy are discussed in term of substrate influence and overlayer organization. The silicon-immobilized catalyst has potential as an advanced functional material with applications in oxidative heterogeneous catalysis of organic reactions, as it combines long-term relatively high activity with low cost.