In Situ Total X‐Ray Scattering Study of WO3 Nanoparticle Formation under Hydrothermal Conditions

Pair distribution function analysis of in situ total scattering data recorded during formation of WO₃ nanocrystals under hydrothermal conditions reveal that a complex precursor structure exists in solution. The WO₆ polyhedra of the precursor cluster undergo reorientation before forming the nanocrystal. This reorientation is the critical element in the formation of different hexagonal polymporphs of WO₃.     

A Remark on the Equivalence between Poisson and Gaussian Stochastic Partial Differential Equations

We discuss the connection between Gaussian and Poisson noise Wick-type stochastic partial differential equations.     

The Heston stochastic volatility model in Hilbert space

We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein–Uhlenbeck process with itself. The volatility process is then defined by a Cholesky decomposition of the variance process. We define a Hilbert-valued Ornstein–Uhlenbeck process with Wiener noise perturbed by this stochastic volatility, and compute the characteristic functional and covariance operator of this process. This process is then applied to the modeling of forward curves in energy and commodity markets. Finally, we compute the dynamics of the tensor Heston volatility model when the generator is bounded, and study its projection down to the real line for comparison with the classical Heston dynamics.     

How to construct a multiple regression model for data with missing elements and outlying objects

The aim of this study is to show the usefulness of robust multiple regression techniques implemented in the expectation maximization framework in order to model successfully data containing missing elements and outlying objects. In particular, results from a comparative study of partial least squares and partial robust M-regression models implemented in the expectation maximization algorithm are presented. The performances of the proposed approaches are illustrated on simulated data with and without outliers, containing different percentages of missing elements and on a real data set. The obtained results suggest that the proposed methodology can be used for constructing satisfactory regression models in terms of their trimmed root mean squared errors.     

Relevance of the slowly varying electron gas to atoms, molecules, and solids

We present a Thomas-Fermi-inspired density scaling under which electron densities of atomic, molecular, or condensed matter become both large and slowly varying, so that semiclassical approximations and second-order density gradient expansions are asymptotically exact for the kinetic and exchange energies. Thus, even for atoms and molecules, density-functional approximations should recover the universal second-order gradient expansions in this limit. We also explain why common generalized gradient approximations for exchange do not.     

Optimization of photoplate evaluation in spark-source mass spectrometry

In spark-source mass spectrometry with photoplate detection, errors caused by densitometric measurements and the linearization of the blackening data are very important for the ultimate accuracy achieved. Two methods are described for the determination of the linearization parameters in the Hull equation by least-squares optimization of the known abundance ratio of isotope pairs.     

Modeling of Two-Phase Flow in Fractured Porous Media on Unstructured Non-Uniformly Coarsened Grids

In this article, we investigate two strategies for coarsening fractured geological models. The first approach, which generates grids that resolve the fractures, is referred to as explicit fracture-matrix separation (EFMS). The second approach is based on a non-uniform coarsening strategy introduced in Aarnes et al. (Adv Water Resour 30(11):2177–2193, 2007a). A series of two-phase flow simulations where the saturation is modeled on the respective coarse grids are performed. The accuracy of the resulting solutions is examined, and the robustness of the two strategies is assessed with respect to number of fractures, degree of coarsening, well locations, phase viscosities, and fracture permeability. The numerical results show that saturation solutions obtained on the non-uniform coarse grids are consistently more accurate than the corresponding saturation solutions obtained on the EFMS grids. The numerical results also reveal that it is much easier to tune the upscaling factor with the non-uniform coarsening approach.     

Aqueous microemulsions of a fluorinated surfactant and oil studied by PFG-NMR: transformation from threadlike to spherical micelles

The aqueous microemulsion system consisting of the fluorinated surfactant tetraethylammonium perfluorooctylsulfonate (TEAFOS) and the fluorinated oil 1H-perfluorohexane (PFH) has been investigated using the pulsed field gradient NMR self-diffusion method on both 1H and 19F. Neat TEAFOS(aq) builds threadlike micelles from rather low surfactant concentrations up to ca. 80 mmol kg(-1). The addition of PFH to TEAFOS(aq) solutions induces a transition from threadlike micelles to spherical micelles solubilizing the oil. In this paper, information from the self-diffusion coefficients of oil (PFH), surfactant counterion (TEA+), surfactant ion (FOS-), and water (HDO) during the transition is presented.     

Continuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Equations

Using the maximum principle for semicontinuous functions (Differential Integral Equations3 (1990), 1001-1014; Bull. Amer. Math. Soc. (N.S)27 (1992), 1-67), we establish a general “continuous dependence on the non- linearities” estimate for viscosity solutions of fully nonlinear degenerate parabolic equations with time- and space-dependent nonlinearities. Our result generalizes a result by Souganidis (J. Differential Equations56 (1985), 345-390) for first- order Hamilton-Jacobi equations and a recent result by Cockburn et al. (J. Differential Equations170 (2001), 180-187) for a class of degenerate parabolic second-order equations. We apply this result to a rather general class of equations and obtain: (i) Explicit continuous dependence estimates. (ii) L^∞ and Hölder regularity estimates. (iii) A rate of convergence for the vanishing viscosity method. Finally, we illustrate results (i)-(iii) on the Hamilton-Jacobi- Bellman partial differential equation associated with optimal control of a degenerate diffusion process over a finite horizon. For this equation such results are usually derived via probabilistic arguments, which we avoid entirely here.