Strong convergence of the finite element method with truncated noise for semilinear parabolic stochastic equations with additive noise

We consider a semilinear parabolic PDE driven by additive noise. The equation is discretized in space by a standard piecewise linear finite element method. We show that the orthogonal expansion of the finite-dimensional Wiener process, that appears in the discretized problem, can be truncated severely without losing the asymptotic order of the method, provided that the kernel of the covariance operator of the Wiener process is smooth enough. For example, if the covariance operator is given by the Gauss kernel, then the number of terms to be kept is the quasi-logarithm of the number of terms in the original expansion. Then one can reduce the size of the corresponding linear algebra problem enormously and hence reduce the computational complexity, which is a key issue when stochastic problems are simulated.     

14.5% near-normal incidence reflectance of Cr/Sc x-ray multilayer mirrors for the water window

Cr/Sc multilayer mirrors, synthesized by ion-assisted magnetron sputter deposition, are proved to have a high near-normal reflectivity of R = 14.5% at a grazing angle of 87.5 degrees measured at the wavelength lambda = 3.11 nm, which is an improvement of more than 31% compared with previously published results. Elastic recoil detection analyses show that the mirrors contained as much as 15 at. % of N and traces of C and O. Soft x-ray reflectivity simulations reveal interface widths of sigma = 0.34 nm and an exceptionally small layer thickness drift of approximately 1.6 x 10(-5) nm/multilayer period throughout the stack. Simulations show that a reflectivity of R = 25.6% is attainable if impurities and layer thickness drift can be eliminated. The abrupt interfaces are achieved with ion assistance with a low ion energy of 24 eV and high ion-to-metal flux ratios of 7.1 and 23.1 during Cr and Sc sputter deposition, respectively. In addition, a near-normal incidence reflectivity of 5.5% for the C VI emission line (lambda = 3.374 nm) from a laser plasma source was verified.     

Fixed-point algorithms for frequency estimation and structured low rank approximation

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, i.e., frequency estimation. For the basic formulation of the fixed-point algorithm we show that it converges to the solution of a related minimization problem, namely the one obtained by replacing the original objective function with its convex envelope and keeping the structured matrix constraint unchanged.It often happens that this solution agrees with the solution to the original minimization problem, and we provide a simple criterion for when this is true. We also provide more general fixed-point algorithms that can be used to treat the problems of making weighted approximations by sums of exponentials given equally or unequally spaced sampling. We apply the method to the case of missing data, although the above mentioned convergence results do not hold in this case. However, it turns out that the method often gives perfect reconstruction (up to machine precision) in such cases. We also discuss multidimensional extensions, and illustrate how the proposed algorithms can be used to recover sums of exponentials in several variables, but when samples are available only along a curve.     

Enantioselective luminescence quenching of DNA light-switch [Ru(phen)2dppz]2+ by electron transfer to structural homologue [Ru(phendione)2dppz]2+

The quenching of the luminescence of [Ru(phen)(2)dppz](2+) by structural homologue [Ru(phendione)(2)dppz](2+), when both complexes are bound to DNA, has been studied for all four combinations of Delta and Lambda enantiomers. Flow linear dichroism spectroscopy (LD) indicates similar binding geometries for all the four compounds, with the dppz ligand fully intercalated between the DNA base pairs. A difference in the LD spectrum observed for the lowest-energy MLCT transition suggests that a transition, potentially related to the final localization of the excited electron to the dppz ligand in [Ru(phen)(2)dppz](2+), is overlaid by an orthogonally polarized transition in [Ru(phendione)(2)dppz](2+). This would be consistent with a low-lying LUMO of the phendione moiety of [Ru(phendione)(2)dppz](2+) that can accept the excited electron from [Ru(phen)(2)dppz](2+), thereby quenching the emission of the latter. The lifetime of excited Delta-[Ru(phen)(2)dppz](2+) is decreased moderately, from 664 to 427 ns, when bound simultaneously with the phendione complex to DNA. The 108 ns lifetime of opposite enantiomer, Lambda-[Ru(phen)(2)dppz](2+), is only shortened to 94 ns. These results are consistent with an average rate constant for electron transfer of approximately 1.10(6) s(-1) between the phenanthroline- and phendione-ruthenium complexes. At binding ratios close to saturation of DNA, the total emission of the two enantiomers is lowered equally much, but for the Lambda enantiomer, this is not paralleled by a decrease in luminescence lifetime. A binding isotherm simulation based on a generalized McGhee-von Hippel approach shows that the Delta enantiomer binds approximately 3 times stronger to DNA both for [Ru(phendione)(2)dppz](2+) and [Ru(phen)(2)dppz](2+). This explains the similar decrease in total emission, without the parallel decrease in lifetime for the Lambda enantiomer. The simulation also does not indicate any significant binding cooperativity, in contrast to the case when Delta-[Rh(phi)(2)bipy](3+) is used as quencher. The very slow electron transfer from [Ru(phen)(2)dppz](2+) to [Ru(phendione)(2)dppz](2+), compared to the case when [Rh(phi)(2)phen](3+) is the acceptor, can be explained by a much smaller driving free-energy difference.     

Binding geometry and photophysical properties of DNA-threading binuclear ruthenium complexes

The DNA binding conformation and the photophysical properties of the semiflexible binuclear ruthenium complex [micro-bidppz(phen)4Ru2]4+ (2) were studied with optical spectroscopy and compared to the rigid, planar homologue in syn conformation [micro-dtpf(phen)4Ru2]4+ (3) and the parent "light-switch" complex [Ru(phen)2dppz]2+ (1). Comparison of calculated and observed absorption bands of the bridging ligand, bidppz, confirm earlier suggestions that 2 is significantly nonplanar, both free in solution and when intercalated into poly(dAdT)2, but the conclusion that the intercalated conformation is an anti rotamer is not substantiated by comparison of linear and circular dichroism spectra of 2 and 3. The behavior of the emission quantum yield as a function of temperature is similar for the two binuclear complexes 2 and 3 in different protic solvents, and a quantitative analysis suggests that, in solution, the solvent is more strongly hydrogen bonded to the excited state of 2 than to 1. However, the observation that for 2 the radiative rate constant increases to a value similar to 1 upon intercalation into DNA suggests that the difference between 1 and 2 in accepting hydrogen bonds is less pronounced when intercalated.     

Liquid crystalline phases and their dispersions in aqueous mixtures of glycerol monooleate and glyceryl monooleyl ether

The aqueous phase behavior of mixtures of 1-glycerol monooleate (GMO) and its ether analogue, 1-glyceryl monooleyl ether (GME) has been investigated by a combination of polarized microscopy, X-ray diffraction, and NMR techniques. Three phase diagrams of the ternary GMO/GME/water system have been constructed at 25, 40, and 55 degrees C. The results demonstrate that the increasing amount of GME favors the formation of the reversed phases, evidenced by the transformation of the lamellar and bicontinuous cubic liquid crystalline phases of the binary GMO/water system into reversed micellar or reversed hexagonal phases. For a particular liquid crystalline phase, increasing the GME content has no effect on the structural characteristics and hydration properties, thus suggesting ideal mixing with GMO. Investigations of dispersed nanoparticle samples using shear and a polymeric stabilizer, Pluronic F127, show the possibility of forming two different kinds of bicontinuous cubic phase nanoparticles by simply changing the GMO/GME ratio. Also NMR self-diffusion measurements confirm that the block copolymer, Pluronic F127, used to facilitate dispersion formation, is associated with nanoparticles and provides steric stabilization.     

Heat capacity and other thermodynamic properties of CoTe2 from 5 to 1 030 K and of CoTe2.315 from 300 to 1 040 K

The heat capacity of orthorhombic (marcasite-type structure) cobalt ditelluride has been measured from 5 to 1 030 K by adiabatic-shield calorimetry with alternate energy inputs and equilibrations. Above 900 K a marked increase in heat capacity occurs which probably signals a change in the composition of the CoTe₂-phase towards higher tellurium content. Values at 298.15 and 1 000 K in J K^–1 mol^–1 of the heat capacity (C _p,m), entropy [S _m ^° (T)–S _m ^° (0)], andGibbs energy function – [G _m ^° (T)–H _m ^° (0)]T ^–1 are 75.23, 114.5, 49.93, and 132.4, 216.2, 139.17, respectively. Consistent with the metallic behavior of CoTe₂, deviation of the heat capacity from theDebye T ³-law was found at low temperatures. Comparison with the heat capacity of FeTe₂ shows aSchottky-like deviation with a maximum of 7.3 J K^–1 mol^–1 at 80 K and evidences the influence of the additional 3 d-electron in cobalt compared to iron. Heat capacity measurements were made on CoTe_2.33 to ascertain the existence range of the CoTe_2+x -phase and the entropy of the associated structural disorder.The portion of this research done at Ann Arbor was supported in part by the Structural Chemistry and Chemical Thermodynamics Program of the Division of Chemistry of the National Science Foundation under Grant No. CHE-7710049.     

Determination of the activity of a molecular solute in saturated solution

Prediction of the solubility of a solid molecular compound in a solvent, as well as, estimation of the solution activity coefficient from experimental solubility data both require estimation of the activity of the solute in the saturated solution. The activity of the solute in the saturated solution is often defined using the pure melt at the same temperature as the thermodynamic reference. In chemical engineering literature also the activity of the solid is usually defined on the same reference state. However, far below the melting temperature, the properties of this reference state cannot be determined experimentally, and different simplifications and approximations are normally adopted. In the present work, a novel method is presented to determine the activity of the solute in the saturated solution (=ideal solubility) and the heat capacity difference between the pure supercooled melt and solid. The approach is based on rigorous thermodynamics, using standard experimental thermodynamic data at the melting temperature of the pure compound and solubility measurements in different solvents at various temperatures. The method is illustrated using data for ortho-, meta-, and para-hydroxybenzoic acid, salicylamide and paracetamol. The results show that complete neglect of the heat capacity terms may lead to estimations of the activity that are incorrect by a factor of 12. Other commonly used simplifications may lead to estimations that are only one-third of the correct value.