Integral-equation theories and Mayer-sampling Monte Carlo: a tandem approach for computing virial coefficients of simple fluids

Mayer-sampling Monte Carlo (MSMC) has enabled computation of higher-order virial coefficients than previously possible for a variety of potential models, but it is not required for computation of the entire virial coefficient for models that are spherically symmetric: approximations that result from the hypernetted-chain (HNC) or Percus–Yevick (PY) integral-equation theories in conjunction with the compressibility equation (c) or virial equation (v) can be computed quickly by fast Fourier transforms. For the fourth and fifth virial coefficients of the Lennard–Jones potential (with parameters σ and ε), we demonstrate that the corrections to each of the four approximations (HNC(c), HNC(v), PY(c), and PY(v)) are faster to compute to a desired precision by MSMC than the full coefficient itself, with the exception of the PY(v) correction at fifth order, and that the optimal decomposition with regard to precision can be identified using a fraction of the steps required to obtain precise virial coefficients. At reduced temperatures kT/ε greater than 4, the PY(c) correction is fastest to compute by MSMC at both fourth and fifth orders. For lower temperatures, the HNC(v) decomposition is most efficient at fourth order, while the HNC(c) decomposition is most efficient at fifth order. These results are specific to the Lennard–Jones potential, but the method for determining the optimal decomposition is applicable to any spherically symmetric potential.     

Nontrivial Solutions of p-Superlinear p-Laplacian Problems

We obtain nontrivial solutions for a class of p-Laplacian problems that are p-superlinear at infinity and nonresonant at zero. The proof is based on showing that the associated variational function has a (generalized) local linking near the origin and makes use of a new sequence of min-max eigenvalues of the p-Laplacian defined using the Yang index.     

The role of index bonds in universal currency hedging

This study examines the demand for index bonds and their role in hedging risky asset returns against currency risks in a complete market where equity is not hedged against inflation risk. Avellaneda's uncertain volatility model with non-constant coefficients to describe equity price variation, forward price variation, index bond price variation and rate of inflation, together with Merton's intertemporal portfolio choice model, are utilized to enable an investor to choose an optimal portfolio consisting of equity, nominal bonds and index bonds when the rate of inflation is uncertain. A hedge ratio is universal if investors in different countries hedge against currency risk to the same extent. Three universal hedge ratios (UHRs) are defined with respect to the investor's total demand for index bonds, hedging risky asset returns (i.e. equity and nominal bonds) against currency risk, which are not held for hedging purposes. These UHRs are hedge positions in foreign index bond portfolios, stated as a fraction of the national market portfolio. At equilibrium all the three UHRs are comparable to Black's corrected equilibrium hedging ratio. The Cameron-Martin-Girsanov theorem is applied to show that the Radon-Nikodym derivative given under a P -martingale, the investor's exchange rate (product of the two currencies) is a martingale. Therefore the investors can agree on a common hedging strategy to trade exchange rate risk irrespective of investor nationality. This makes the choice of the measurement currency irrelevant and the hedge ratio universal without affecting their values.     

Reductive decomposition of a diazonium intermediate by dithiothreitol affects the determination of NOS turnover rates

Accurate determination of nitrite either as such or as the breakdown product of nitric oxide (NO) is critical in a host of enzymatic reactions in various settings addressing structure-function relationships, as well as mechanisms and kinetics of molecular operation of enzymes. The most common way to quantify nitrite, for instance in nitric oxide synthase (NOS) mechanistic investigations, is the spectrophotometric assay based on the Griess reaction through external standard calibration. This assay is based on a two-step diazotization reaction, in which a cationic diazonium derivative of sulfanilamide is formed as intermediate before the final absorbing azo-product. We show that this intermediate is very sensitive to reducing agents that may be transferred from the reaction media under investigation. The interaction of this vital intermediate with the reducing agent, dithiothreitol (DTT), which is widely used in NOS reactions, is characterized by both electrochemical and spectroscopic means. The effect of DTT on the performance of external calibration, both in sample recovery studies and in actual NOS reactions, is presented. Finally an alternative method of standard additions, which partially compensates for the accuracy and sensitivity problems of external calibration, is proposed and discussed.     

A comparative study of aqueous DMSO mixtures by computer simulations and integral equation theories

ABSTRACT

Several computer simulation studies of aqueous-dimethylsulfoxide with different force field models, and conducted by different authors, point out to an anomalous depressing of second and third neighbour correlations of the water–water radial distribution functions. This seemingly universal feature can be interpreted as the formation of linear water clusters. We test here the ability of liquid state integral equation theories to reproduce this feature. It is found that the incorporation of the water bridge diagram function is required to reproduce this feature. These theories are generally unable to properly reproduce atom–atom distribution functions. However, the near-ideal Kirkwood–Buff integrals are relatively well reproduced. We compute the X-ray scattering function and compare with available experimental results, with the particular focus to explain why these data do not reproduce the cluster pre-peak observed in the water–water structure factor.     

Investigating molecular charge transfer complexes with a low temperature scanning tunneling microscope

Electron donor-acceptor molecular charge transfer complexes (CTCs) formed by alpha-sexithiophene (6T) and tetrafluoro-tetracyano-quinodimethane (F4TCNQ) on a Au(111) surface are investigated by scanning tunneling microscopy, spectroscopy, and spectroscopic imaging at 6 K. New hybrid molecular orbitals are formed in the CTCs, and the highest occupied molecular orbital of the CTC is mainly located on the electron accepting F4TCNQ while the lowest unoccupied molecular orbital is predominantly positioned on the electron donating 6T. We observed the conductance switching of F4TCNQ inside CTCs, which may find potential applications in novel molecular device operations.     

Geometric structure of dimension functions of certain continuous fields

For a continuous field of C^?-algebras A, we give a criterion to ensure that the stable rank of A is one. In the particular case of a trivial field this leads to a characterization of stable rank one, completing accomplishments by Nagisa, Osaka and Phillips. Further, for certain continuous fields of C^?-algebras, we study when the Cuntz semigroup satisfies the Riesz interpolation property, and we also analyze the structure of its functionals. As an application, we obtain a positive answer to a conjecture posed by Blackadar and Handelman in a variety of situations.     

Spectroscopic study of the penetration depth of grafted polystyrene onto poly(tetrafluoroethylene‐co‐perfluoropropylvinylether) substrates. 1. Effect of grafting conditions

This study concerns the radiation grafting of styrene onto poly(tetrafluoroethylene‐co‐perfluoropropylvinylether) (PFA) substrates and the penetration depth of the graft. Grafting was obtained by the simultaneous irradiation method, and the spectroscopic analysis was made with the micro‐Raman technique. Effects of grafting conditions such as the type of solvent, dose rate, and irradiation dose on the grafting yield were investigated. Of the different solvents used, the most efficient in terms of increasing grafting yield were dichloromethane, benzene, and methanol, respectively. A mixture of methanol and dichloromethane used as a solvent for styrene achieved a higher degree of grafting and concentration of grafted polystyrene onto the surface of PFA substrates than solutions of the monomer in the separate solvents. The degree of grafting increased with increasing radiation dose up to 500 kGy, stabilizing above this dose. However, the grafting yield decreased with an increase in the dose rate. The increase in the overall grafting yield was accompanied by a proportional increase in the penetration depth of the grafts into the substrate. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3191–3199, 2002     

Inference on the variance and smoothing of the paths of diffusions

We give a hypothesis testing method to fit the diffusion coefficient σ of a d-dimensional stochastic differential equation on the basis of the observation of certain functionals of regularizations of the solution.