Many-body potential for point defect clusters in Fe-C alloys

Modeling the consequences of crystalline defects requires efficient interaction sampling. Empirical potentials can identify relevant pathways if the energetics and configurations of competing defects are captured. Here, we develop such a potential for an alloy of arbitrary point defect concentration, body-centered cubic alpha-Fe supersaturated in C. This potential successfully calculates energetically favored defects, and predicts formation energies and configurations of multicarbon-multivacancy clusters that were not attainable with existing potentials or identified previously via ab initio methods.     

Mechanism of thermal transport in dilute nanocolloids

Thermal conduction modes in a nanocolloid (nanofluid) are quantitatively assessed by combining linear response theory with molecular dynamics simulations. The microscopic heat flux is decomposed into three additive fluctuation modes, namely, kinetic, potential, and collision. For low volume fractions (<1%) of nanosized platinum clusters which interact strongly with xenon host liquid, a significant thermal conductivity enhancement results from the self correlation in the potential flux. Our findings reveal a molecular-level mechanism for enhanced thermal conductivity in nanocolloids with short-ranged attraction and offer predictions that can be experimentally tested.     

Stochastic Motion by Mean Curvature

We prove the existence of a continuously time‐varying subset K(t) of R ⁿ such that its boundary ∂K(t), which is a hypersurface, has normal velocity formally equal to the (weighted) mean curvature plus a random driving force. This is the first result in such generality combining curvature motion and stochastic perturbations. Our result holds for any C ² convex surface energy. The K(t) can have topological changes. The randomness is introduced by means of stochastic flows of diffeomorphisms generated by Brownian vector fields which are white in time but smooth in space. We work in the context of geometric measure theory, using sets of finite perimeter to represent K(t). The evolution is obtained as a limit of a time‐stepping scheme. Variational minimizations are employed to approximate the curvature motion. Stochastic calculus is used to prove global energy estimates, which in turn give a tightness statement of the approximating evolutions. (Accepted December 22, 1997)     

Transport with a Very Low Density Contrast in Hele–Shaw Cell and Porous Medium: Evolution of the Mixing Zone

The optimal concentration of a blue dye solution with 'tracer' properties, enabling a pollutant to be marked was determined by the use of numerical, theoretical and experimental approaches. Experimental investigations were performed on a transparent Hele–Shaw cell and the concentration distribution was analyzed using an optical technique based on dye light absorption properties. The injected optimal concentration was established thanks to a theoretical and experimental study carried out on the output signal dynamics. Using the same experimental conditions, numerical simulations were performed. The very good agreement between the data (experimental and numerical) clarified that: (i) the choice of the blue dye optimal concentration was valid and (ii) the concentration-dependent density should not be neglected in flow and transport equations even if it concerns a so-called 'tracer'. Following this remark, a theoretical aspect was developed in order to determine the analogous conditions between a Hele–Shaw cell and a porous medium for the variable density transport phenomenon. The structure of the concentration-dependent dispersion tensor used in the numerical code was obtained by homogenizing the Stokes flow of a bi-component mixture. The numerical results show that, as long as the tracer density does not exceed a certain value, it is not necessary to take into account a density contrast in terms of the dispersion tensor. The classical form of the Taylor dispersion tensor can be used successfully.     

Crystalline Behavior and Structure of a Liquid Crystal Compound, 5‐{[4′‐(((Pentyl)oxy)‐4‐biphenylyl)carbonyl]oxy}‐1‐pentyne

Single crystals of two liquid crystal compounds, 5‐{[4′‐(((pentyl)oxy)‐4‐biphenylyl)carbonyl]oxy}‐1‐pentyne (A3EO5) and 5‐{[(4′‐nonyloxy‐4‐biphenylyl)carbonyl]oxy}‐1‐pentyne (A3EO9), have been prepared by solution growth technique. The morphologies and structures of A3EO5 and A3EO9 crystals were investigated by wide angle X‐ray diffraction (WXRD), atom force microscope (AFM) and transmission electron microscope (TEM). In contrast to the same series of compounds which have a longer alkyl tail, 5‐{[(4′‐heptoxy‐4‐biphenylyl)carbonyl]oxy}‐1‐pentyne (A3EO7), 5‐{[(4′‐heptoxy‐4‐biphenylyl)oxy]carbonyl}‐1‐pentyne (A3E′O7) and A3EO9, A3EO5 shows strikingly different crystalline behavior. The former three compounds have only one crystal form, whereas A3EO5 exhibits polymorphism. Specifically, A3EO5 crystals grown from toluene solution show two crystal forms. The first one is crystal I which adopts a monoclinic P112/m space group with unit cell parameters of a?5.79 Å, b?8.34 Å, c?43.92 Å, γ?96°, and the other one is crystal II which adopts a monoclinic P112 space group with unit cell parameters of a?5.55 Å, b?7.38 Å, c?31.75 Å, γ?94°. When using dioxane as the solvent to grow A3EO5 crystal, we can selectively obtain crystal I. A3EO5 melt‐grown crystals also have two crystal forms which derive from crystal I and crystal II, respectively. The different crystalline behavior of the compounds should correlate with their different electron dipole moment resulting from the different length of alkyl tail.     

Ruthenium complexes of 1,4,7-trimethyl-1,4,7-triazacyclononane for atom and group transfer reactions

With support by macrocyclic tertiary amine ligand 1,4,7-trimethyl-1,4,7-triazacyclononane (Me₃tacn), a number of mononuclear metal–ligand multiple bonded complexes have been isolated. Starting with a brief summary of these complexes, the present review focuses on ruthenium-oxo and -imido complexes of Me₃tacn. A family of monooxoruthenium(IV) complexes [Ru^IV(Me₃tacn)O(N–N)]²⁺ (N–N = 2,2′-bipyridines) and a cis-dioxoruthenium(VI) complex cis-[Ru^VI(Me₃tacn)O₂(CF₃CO₂)]⁺ have been isolated, and the structures of [Ru^IV(Me₃tacn)O(bpy)](ClO₄)₂ (bpy = 2,2′-bipyridine) and cis-[Ru^VI(Me₃tacn)O₂(CF₃CO₂)]ClO₄ have been determined by X-ray crystallography. Oxidation of [Ru^III(Me₃tacn)(NHTs)₂(OH)] (Ts = p-toluenesulfonyl) with Ag⁺ and electrochemical oxidation of [Ru^III(Me₃tacn)(H₂L)](ClO₄)₂ (H₃L = α-(1-amino-1-methylethyl)-2-pyridinemethanol) are likely to generate ruthenium-imido complexes supported by Me₃tacn. DFT calculations on cis-[Ru^VI(Me₃tacn)O₂(CF₃CO₂)]⁺ and proposed ruthenium-imido complexes have been performed. Complexes [Ru^IV(Me₃tacn)O(N–N)]²⁺ are reactive toward alkene epoxidation, and cis-[Ru^VI(Me₃tacn)O₂(CF₃CO₂)]⁺ efficiently oxidizes various organic substrates including concerted [3+2] cycloaddition reactions with alkynes and alkenes to selectively afford α,β-diketones, cis-diols, or CC bond cleavage products. Related oxidation reactions catalyzed by ruthenium Me₃tacn complexes include epoxidation of alkenes, cis-dihydroxylation of alkenes, oxidation of alkanes, alcohols, aldehydes, and arenes, and oxidative cleavage of CC, CC, and C–C bonds, all of which exhibit high selectivity. Ruthenium Me₃tacn complexes are also active catalysts for amination of saturated C–H bonds.     

The relationship between redox enzyme activity and electrochemical potential-cellular and mechanistic implications from protein film electrochemistry

In protein film electrochemistry a redox protein of interest is studied as an electroactive film adsorbed on an electrode surface. For redox enzymes this configuration allows quantification of the relationship between catalytic activity and electrochemical potential. Considered as a function of enzyme environment, i.e., pH, substrate concentration etc., the activity-potential relationship provides a fingerprint of activity unique to a given enzyme. Here we consider the nature of the activity-potential relationship in terms of both its cellular impact and its origin in the structure and catalytic mechanism of the enzyme. We propose that the activity-potential relationship of a redox enzyme is tuned to facilitate cellular function and highlight opportunities to test this hypothesis through computational, structural, biochemical and cellular studies.     

A combinatorial formula for Macdonald polynomials

In this paper we use the combinatorics of alcove walks to give uniform combinatorial formulas for Macdonald polynomials for all Lie types. These formulas resemble the formulas of Haglund, Haiman and Loehr for Macdonald polynomials of type GLn. At q=0 these formulas specialize to the formula of Schwer for the Macdonald spherical function in terms of positively folded alcove walks and at q=t=0 these formulas specialize to the formula for the Weyl character in terms of the Littelmann path model (in the positively folded gallery form of Gaussent and Littelmann).     

Linearly implicit time discretization of non-linear parabolic equations

We give a stability and error analysis of linearly implicitone-step methods for time discretization of non-linear parabolicequations. We derive precise error bounds for Rosenbrock andW-methods, and we explain the error reduction by Richardsonextrapolation of the linearly implicit Euler method which occursin spite of the breakdown of asymptotic expansions. The parabolicequations are studied in a Hilbert space framework that includessemilinear and quasilinear parabolic equations, and also stiffreaction-diffusion equations with reactions at different timescales.