Generalized motion by mean curvature as a macroscopic limit of stochastic ising models with long range interactions and Glauber dynamics

We study themacroscopic limit of an appropriately rescaledstochastic Ising model withlong range interactions evolving withGlauber dynamics as well as the correspondingmean field equation, which is nonlinear and nonlocal. In the limit we obtain an interface evolving with normal velocity k, wherek isthe mean curvature and thetransport coefficient is identified by aneffective Green-Kubo type formula. The above assertions are valid for all positive times, the motion of the interface being interpreted in theviscosity sense after the onset of the geometric singularities.Supported by ONRPartially supported by NSF, ARO, ONR and the Alfred P. Sloan Foundation     

Validation of a HPLC/MS method for simultaneous quantification of clonidine,morphine and its metabolites in human plasma

A high‐performance liquid chromatography–tandem mass spectrometry method was developed and validated for the simultaneous quantification of morphine, morphine's major metabolites morphine‐3‐glucuronide and morphine‐6‐glucuronide, and clonidine, to support the pharmacokinetic analysis of an ongoing double‐blinded randomized clinical trial that compares the use of morphine and clonidine in infants diagnosed with neonatal abstinence syndrome. Plasma samples were processed by solid‐phase extraction and separated on an Inertsil ODS‐3 (4 μm) column using an 0.1% formic acid in water–0.1% formic acid in methanol gradient. Detection of the analytes was conducted in the positive multiple reaction monitoring mode. The range of quantitation was 1–1000 ng/mL for morphine, morphine‐3‐glucuronide and morphine‐6‐glucuronide, and 0.25–100 ng/mL for clonidine. Intra‐day and inter‐day accuracy and precision were ≤15% for all analytes across the quantitation range. Extraction recovery rates were ≥94% for morphine, ≥90% for M3G, ≥87% for M6G and ≥ 79% for clonidine. Matrix effect ranged from 85–94% for clonidine to 101–106% for M3G. The method fulfilled all predetermined acceptance criteria and required only 100 μL of starting plasma volume. Furthermore, it was successfully applied to 30 clinical trial plasma samples.     

Waiting Time for an Almost Perfect Run and Applications in Statistical Process Control

A natural and intuitively appealing generalization of the runs principle arises if instead of looking at fixed-length strings with all their positions occupied by successes, we allow the appearance of a small number of failures. Therefore, the focus is on clusters of consecutive trials which contain large proportion of successes. Such a formation is traditionally called “scan” or alternatively, due to the high concentration of successes within it, almost perfect (success) run. In the present paper, we study in detail the waiting time distribution for random variables related to the first occurrence of an almost perfect run in a sequence of Bernoulli trials. Using an appropriate Markov chain embedding approach we present an efficient recursive scheme that permits the construction of the associated transition probability matrix in an algorithmically efficient way. It is worth mentioning that, the suggested methodology, is applicable not only in the case of almost perfect runs, but can tackle the general discrete scan case as well. Two interesting applications in statistical process control are also discussed.     

Calculation of complex near-wall turbulent flows with a low-Reynolds-number k-ϵ model

An improved low-Reynolds-number k-? model has been formulated and tested against a range of DNS (direct numerical simulation) and experimental data for channel and complex shear layer flows. The model utilizes a new form of damping function adopted to account for both wall proximity effects and viscosity influences and a more flexible damping argument based on the gradient of the turbulent kinetic energy on the wall. Additionally, the extra production of the inhomogeneous part of the viscous dissipation near a wall has been added to the dissipation equation with significantly improved results. The proposed model was successfully applied to the calculation of a range of wall shear layers in zero, adverse and favourable pressure gradients as well as backward-facing-step separated flows.     

Symbiotic symmetries of the two-Higgs-doublet model

The new phenomenon of symbiotic symmetries   is described in the context of the Two-Higgs-Doublet Model (THDM). The quartic potential has two or more separate sectors with unequal symmetries, but these unequal symmetries persist even though the different sectors are renormalized by one another. We discuss all such symmetries of the THDM, consistent with the SU(2)×U(1)$\mathit{SU}(2)\times U(1)$ gauge interactions, using the Pauli formalism.     

Identification of local extinction topology in axisymmetric bluff‐body diffusion flames with a reactedness‐mixture fraction presumed probability density function model

The effects of finite‐rate chemistry, such as partial extinctions and re‐ignitions, are investigated in turbulent non‐pre‐mixed reacting flows stabilized in the wake of an axisymmetric bluff‐body burner. A two‐dimensional large‐eddy simulation procedure is employed that uses a partial equilibrium/two‐scalar reactedness mixture fraction probability density function (PDF) combustion sub‐model, which is applied at the sub‐grid scale (SGS) level. An anisotropic sub‐grid eddy–viscosity and two equations for the SGS turbulence kinetic and scalar energies complete the SGS closure model. The scalar covariances required in the joint PDF formulation are obtained from an extended scale‐similarity assumption between the resolved and the sub‐grid fluctuations. Extinction due to strong turbulence/chemistry interactions is recognized with the help of a ‘critical’, locally variable, turbulent Damkohler number criterion, while transient localized extinctions and re‐ignitions are treated with a Lagrangian transport equation for a reactedness progress variable. Comparisons with available experimental data suggested that the formulated approach was capable of identifying the effects of large‐scale vortex structure activity, which were inherent in the reacting wake and dominant in the counterpart isothermal flows that otherwise would have been obscured if a standard time‐averaged procedure had been used. Additionally, the post‐extinction and re‐ignition behaviour and its time‐varying interaction with the large‐scale structure dynamics were more appropriately addressed within the context of the present time‐dependent method. Copyright © 2001 John Wiley & Sons, Ltd.     

Borohydride, azide, and chloride anions as terminal ligands on Fe/Mo/S clusters. Synthesis, structure and characterization of [(Cl4-cat)(PPr3) MoFe3S4(X)2]2(Bu4N)4 and [(Cl4-cat)(PPr3)MoFe3S4 (PPr3)(X)]2(Bu4N)2 (X = N3-, BH4-, Cl-) double-fused cubanes. NMR reactivity studies of [(Cl4-cat)(PPr3) MoFe3S4(BH4)2]2(Bu4N)4

Our explorations of the reactivity of Fe/Mo/S clusters of some relevance to the FeMoco nitrogenase have led to new double-fused cubane clusters with the Mo2Fe6S8 core as derivatives of the known (Cl4-cat)2Mo2Fe6S8(PPr3)6 (I) fused double cubane. The new clusters have been obtained by substitution reactions of the PPr3 ligands with Cl-, BH4-, and N3-. By careful control of the conditions of these reactions, the clusters [(Cl4-cat)(PPr3)MoFe3S4(BH4)2]2(Bu4N)4 (II), [(Cl4-cat)(PPr3)MoFe3S4(PPr3)(BH4)]2(Bu4N)2 (III), [(Cl4-cat)(PPr3)MoFe3S4(N3)2]2(Bu4N)4 (IV), [(Cl4-cat)(PPr3)MoFe3S4(PPr3)(N3)]2(Bu4N)2 (V), and [(Cl4-cat)(PPr3)MoFe3S4Cl2]2(Et4N)4 (VI) have been obtained and structurally characterized. A study of their electrochemistry shows that the reduction potentials for the derivatives of I are shifted to more positive values than those of I, suggesting a stabilization of the reduced clusters by the anionic ligands BH4- and N3-. Using 1H NMR spectroscopy, we have explored the lability of the BH4- ligand in II in coordinating solvents and its hydridic character, which is apparent in its reactivity toward proton sources such as MeOH or PhOH.     

Consecutive k-out-of-n systems with maintenance

A consective k-out-of-n system consists of n linearly or cycliccally ordered components such that the system fails if and only if at least k consecutive components fail. In this paper we consider a maintained system where each component is repaired independently of the others according to an exponential distribution. Assuming general lifetime distributions for system's components we prove a limit theorem for the time to first failure of both linear and circular systems.