Copolymerization of ethylene and styrene to a nearly-alternating crystalline copolymer

An almost alternating stereoregular copolymer can be obtained by copolymerizing ethylene and styrene with the catalyst ethylenebis(1-indenyl)zirconium dichloride activated by methylaluminoxane at −25°C. The regular microstructure pointed out by the NMR spectrum allows the copolymer to crystallize as shown by calorimetric and X-ray diffraction measurements.     

Recursive Conditional Moment Equations for Advective Transport in Randomly Heterogeneous Velocity Fields

Flow and transport parameters such as hydraulic conductivity, seepage velocity, and dispersivity have been traditionally viewed as well-defined local quantities that can be assigned unique values at each point in space-time. Yet in practice these parameters can be deduced from measurements only at selected locations where their values depend on the scale (support volume) and mode (instruments and procedure) of measurement. Quite often, the support of the measurements is uncertain and the data are corrupted by experimental and interpretive errors. Estimating the parameters at points where measurements are not available entails an additional random error. These errors and uncertainties render the parameters random and the corresponding flow and transport equations stochastic. The stochastic flow and transport equations can be solved numerically by conditional Monte Carlo simulation. However, this procedure is computationally demanding and lacks well-established convergence criteria. An alternative to such simulation is provided by conditional moment equations, which yield corresponding predictions of flow and transport deterministically. These equations are typically integro-differential and include nonlocal parameters that depend on more than one point in space-time. The traditional concept of a REV (representative elementary volume) is neither necessary nor relevant for their validity or application. The parameters are nonunique in that they depend not only on local medium properties but also on the information one has about these properties (scale, location, quantity, and quality of data). Darcy's law and Fick's analogy are generally not obeyed by the flow and transport predictors except in special cases or as localized approximations. Such approximations yield familiar-looking differential equations which, however, acquire a non-traditional meaning in that their parameters (hydraulic conductivity, seepage velocity, dispersivity) and state variables (hydraulic head, concentration) are information-dependent and therefore, inherently nonunique. Nonlocal equations contain information about predictive uncertainty, localized equations do not. We have shown previously (Guadagnini and Neuman, 1997, 1998, 1999a, b) how to solve conditional moment equations of steady-state flow numerically on the basis of recursive approximations similar to those developed for transient flow by Tartakovsky and Neuman (1998, 1999). Our solution yields conditional moments of velocity, which are required for the numerical computation of conditional moments associated with transport. In this paper, we lay the theoretical groundwork for such computations by developing exact integro-differential expressions for second conditional moments, and recursive approximations for all conditional moments, of advective transport in a manner that complements earlier work along these lines by Neuman (1993).     

Consequences of the non-abelian anomaly in supersymmetric theories

In supersymmetric theories, the anomalous interactions involving the Goldstone supermultiplets are found not to be determined from symmetry considerations alone: they depend also on the dynamical details of the model. The origin of the unexpected results lies in the presence of the massless fermionic superpartners of the Goldstone bosons. For example, the decay π⁰ → γγ is found to be suppressed in supersymmetric QCD (SQCD). Low-energy effective actions with the correct symmetry properties are constructed, taking SQCD as an illustrative example. The axion decay a → γγ in a supersymmetric composite model might be suppressed with the same mechanism that works for π⁰ → γγ in SQCD.     

Finite‐difference schemes for transport‐dominated equations using special collocation nodes

We introduce finite‐difference schemes based on a special upwind‐type collocation grid, in order to obtain approximations of the solution of linear transport‐dominated advection‐diffusion problems. The method is well suited when the diffusion parameter is very small compared to the discretization parameter. A theory is developed and many numerical experiments are shown. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

A Study on Diflunisal: Solubility,Acid Constants and Complex Formation with Calcium(II) and Magnesium(II)

The properties of diflunisal, a widely used analgesic, were studied in physiologic solutions, 0.15 mol·dm^?3 NaCl. Solubility and protonation constants were determined and its behavior as ligand towards Ca(II) and Mg(II) was investigated. Solubility and protonation constants of diflunisal at 25 °C and 0.15 mol·dm^?3 were obtained from electromotive force measurements of galvanic cells using coulometric titrations. The experimental data yielded the solubility, s, of –log₁₀ s = 3.86 ± 0.02 and the protonation constants log₁₀ K ₁ = 11.98 ± 0.10 and log₁₀ K ₂ = 3.86 ± 0.03. Equilibria between diflunisal and Ca(II) and Mg(II) were investigated by means of electromotive force measurements and by comparing solubilities of diflunisal in the presence and absence of Ca(II) or Mg(II), respectively. Experimental data were explained by assuming the formation of 1:1 complexes for Ca(II) and Mg(II) along with evaluating the relative stability constants.