Zinc‐Catalyzed Borylation of Primary,Secondary and Tertiary Alkyl Halides with Alkoxy Diboron Reagents at Room Temperature

A new catalytic system based on a Zn^II NHC precursor has been developed for the cross‐coupling reaction of alkyl halides with diboron reagents, which represents a novel use of a Group XII catalyst for C? X borylation. This approach gives borylations of unactivated primary, secondary, and tertiary alkyl halides at room temperature to furnish alkyl boronates, with good functional‐group compatibility, under mild conditions. Preliminary mechanistic investigations demonstrated that this borylation reaction seems to involve one‐electron processes.     

An Iterative Divergent Approach to Conjugated Starburst Borane Dendrimers

Using a new divergent approach, conjugated triarylborane dendrimers were synthesized up to the 2^nd generation. The synthetic strategy consists of three steps: 1) functionalization, via iridium catalyzed C−H borylation; 2) activation, via fluorination of the generated boronate ester with K[HF₂] or [N(nBu₄)][HF₂]; and 3) expansion, via reaction of the trifluoroborate salts with aryl Grignard reagents. The concept was also shown to be viable for a convergent approach. All but one of the conjugated borane dendrimers exhibit multiple, distinct and reversible reduction potentials, making them potentially interesting materials for applications in molecular accumulators. Based on their photophysical properties, the 1^st generation dendrimers exhibit good conjugation over the whole system. However, the conjugation does not increase further upon expansion to the 2^nd generation, but the molar extinction coefficients increase linearly with the number of triarylborane subunits, suggesting a potential application as photonic antennas.     

Dispersive mixing in immiscible polymer blends

Dispersive mixing of immiscible polymer blends as well as polymer systems containing solids is achieved in compounding equipment at two stages of the system's processing experience: first, while one or more of the polymer components are melting, and second, after all polymer components have melted. That is, the first mode of dispersive mixing occurs during the melting mechanism of “dissipative mix melting” (Ref. 1), while the second is melt-melt mixing. During the compounding of a given blend system, there are a number of processing parameters that can be changed in order to improve mixing. These range from machine operating variables to the addition of processing aids. If such processing changes fail to produce the desired morphology, the most common change to consider is the screw geometry. This, in practice involves a trial and error procedure, or the use of an existing database built from prior experience. The role which the thermomechanical and rheological properties of the blend component play in dissipative mix melting and melt-melt mixing has not yet been well understood. The reason for this is that although most blend systems have components which are strongly non-Newtonian and strongly viscoelastic, the thinking and rules of thumb for mixing such materials has been heavily influenced by the analysis of G. I. Taylor (Ref. 2), who in 1932 addressed the phenomenon of the dispersion of a single Newtonian droplet by a Newtonian matrix flowing in laminar shear flow. This paper addresses the strong role that the rheology of blend components, under processing conditions, play in laminar dispersive mixing of polymer blends. From a practical point of view, if the dispersion mechanisms and rates of dispersion depend on the component rheology, then such knowledge can lead us to the selection of advantageous mixing element designs and processing conditions. The experimental results were obtained in dispersive mixing carried out in devices developed in the Polymer Mixing Study (Ref. 3). Such model devices include the Couette Flow Intensive Mixer (CIM) (Ref. 4), where a constant shear stress is applied on the blend components and the Twin Screw Mixing Element Evaluator (TSMEE) (Ref. 5), where the mixing flows are those encountered in actual mixing/compounding operations. The TSMEE will be described in the body of this paper together with its on- and off-line morphology determination capabilities and its in-line rheology sensor. The low-density polyethylene (LDPE) and polystyrene (PS) polymers studied were selected because they cover a wide spectrum of rheological properties.     

Monitor for displaying real-time images of low energy ion beams

Analytical Chemistry Division. Oak Ridge National Laboratory. Oak Ridge, Tennessee, USA A monitor that provides real-time images of low energy (< 50 eV) ion beams has been designed, constructed, and tested. The cross-sectional image of the beam at the entrance aperture of the monitor is magnified by a factor of 6.5 and displayed on a CRT, following current amplification by using a dual microchannel plate assembly. The monitor provides unambiguous information regarding the cross section of any low energy ion beam. Anplication in the design and testing of quadrupole-based mass spectrometers is emphasized,     

The many limits of mixed means

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a ₀,b ₀ we define

A recurrence relation for the square root

The behavior of the sequence x_{n + 1} = x_n(3N − x_n²)/2N is studied for N > 0 and varying real x₀. When 0 < x₀ < (3N)^1/2 the sequence converges quadratically to N^1/2. When x₀ > (5N)^1/2 the sequence oscillates infinitely. There is an increasing sequence β_r, with β₋₁ = (3N)^1/2 which converges to (5N)^1/2 and is such that when β_r < x₀ < β_{r + 1} the sequence {x_n} converges to (−1)^rN^1/2. For x₀ = 0, β₋₁, β₀,… the sequence converges to 0. For x₀ = (5N)^1/2 the sequence oscillates: x_n = (−1)ⁿ(5N)^1/2. The behavior for negative x₀ is obtained by symmetry.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

Enumeration of non-crossing pairings on bit strings

A non-crossing pairing on a bit string is a matching of 1s and 0s in the string with the property that the pairing diagram has no crossings. For an arbitrary bit-string w=p₁¹q₁⁰…pr¹qr⁰, let φ(w) be the number of such pairings. This enumeration problem arises when calculating moments in the theory of random matrices and free probability, and we are interested in determining useful formulas and asymptotic estimates for φ(w). Our main results include explicit formulas in the “symmetric” case where each pi=qi, as well as upper and lower bounds for φ(w) that are uniform across all words of fixed length and fixed r. In addition, we offer more refined conjectural expressions for the upper bounds. Our proofs follow from the construction of combinatorial mappings from the set of non-crossing pairings into certain generalized “Catalan” structures that include labeled trees and lattice paths.     

Scattering of plane guided waves obliquely incident on a straight feature with uniform cross-section

A frequency-domain finite element (FE) method is presented for modeling the scattering of plane guided waves incident on an infinitely-long, straight feature with uniform cross-section in a planar host waveguide. The method utilizes a mesh of 2-dimensional finite elements with harmonic shape functions in the perpendicular direction. The model domain comprises a cross-section through the feature and short lengths of the adjoining host waveguide. A spatial frequency equal to the wavenumber of the desired incident mode multiplied by the sine of the desired incidence angle is prescribed for the element shape functions. An integral representation of the incident mode is used to determine a suitable system of harmonic forces to uniquely excite that mode. These are applied at nodes through the thickness of the host waveguide on one side of the feature. The displacement field is measured at nodes through the thickness of the host waveguide on either side of the feature and decomposed into reflected and transmitted modes. The cases of guided wave transmission in a featureless waveguide and the reflection of guided waves from a free-edge are examined as validation cases. Finally, the results for transmission at an adhesively-bonded stiffener are presented and compared with experimental measurements.     

Thermodynamic Formalism for Contracting Lorenz Flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential [^( j)]_t(x,y,z):=-tlogJ_(x,y,z)^cu\hat{ \varphi }_{t}(x,y,z):=-t\log J_{(x,y,z)}^{cu} for the contracting Lorenz flow and for t in an interval containing [0,1]. We also analyse the Lyapunov spectrum of the flow in terms of the pressure.