Synthesis of pentafluorophenylmethylamines via silicon Mannich reaction

[reaction: see text] The three-component coupling of aldehydes, secondary amines, and methoxytris(pentafluorophenyl)silane, MeOSi(C(6)F(5))(3), affording pentafluorophenylmethylamines has been described. The generation of the five-coordinate silicate intermediate is believed to be the key feature responsible for the efficiency of the reaction.     

Poincaré–Lelong Approach to Universality and Scaling of Correlations Between Zeros

This note is concerned with the scaling limit as N→∞ of n-point correlations between zeros of random holomorphic polynomials of degree N in m variables. More generally we study correlations between zeros of holomorphic sections of powers L ^N of any positive holomorphic line bundle L over a compact K?hler manifold. Distances are rescaled so that the average density of zeros is independent of N. Our main result is that the scaling limits of the correlation functions and, more generally, of the “correlation forms” are universal, i.e. independent of the bundle L, manifold M or point on M. Received: 17 March 1999 / Accepted: 5 August 1999     

The Whitney problem of existence of a linear extension operator

We prove that a linear bounded extension operator exists for the trace of C ^1·ω (R ⁿ )to an arbitrary closed subset of R ⁿ .The similar result is obtained for some other spaces of multivariate smooth functions. We also show that unlike the one-dimensional case treated by Whitney, for some trace spaces of multivariate smooth functions a linear bounded extension operator does not exist. The proofs are based on a relation between the problem under consideration and a similar problem for Lipschitz spaces defined on hyperbolic Riemannian manifolds.     

Diffusion of guest molecules in MCM-41 agglomerates

The pulsed field gradient nuclear magnetic resonance method has been used to study self-diffusion of cyclohexane in a commercial MCM-41 material at different external gas pressures from zero to saturated vapor pressure. It is found that the effective diffusivities exhibit three different regions with increasing pressure: decrease at low pressures, a sudden drop at intermediate pressures, and increase at higher pressures. In addition, in the region of irreversible adsorption (hysteresis loop) the diffusivities are also found to differ on the adsorption and the desorption branches. A simple analytical model taking account of different molecular ensembles with different transport properties due to the complex architecture of the porous structure is developed which provides a quantitative prediction of the experimental data. The analysis reveals that the effective diffusivity is predominantly controlled by the adsorption properties of the individual mesoporous MCM-41 crystallites which, in combination with high transport rates, provide a simple instrument for fine tuning of the transport properties by a subtle variation of the external conditions.     

Electronic coupling in the excited electronic state of stacked DNA base homodimers

The nature of the electronic coupling of stacked nucleic acid bases adenine (A), thymine (T), and cytosine (C), in A-A, T-T, and C-C complexes in their excited states was investigated; a different character of the electronic coupling for the T-T complex was shown.     

Branching of colloidal chains in capillary-confined nematics

We report on the observation of colloidal chain assembly and branching inside capillaries filled with a nematic liquid crystal. Because of the homeotropic anchoring of liquid crystalline molecules on the capillary and colloidal droplet surfaces, the assembly of droplets along the capillary axis is expected, producing a transformation of the nematic director field from an escape-radial to quasiradial configuration. However, the subsequent over time branching of the straight colloidal chains is counterintuitive. By numerical simulations, we demonstrate that chain branching can occur by overcoming an energy barrier and can at least dwell as a metastable configuration. Moreover, manipulation of colloidal chains by electric fields and their gradients demonstrates various regimes of chain behavior in electric fields.     

Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase

The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite N by Korepin and Izergin. The solution is based on the Yang–Baxter equations and it represents the free energy in terms of an N × N Hankel determinant. Paul Zinn–Justin observed that the Izergin– Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large N asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann–Hilbert approach and the Deift–Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called free fermion line. We prove the conjecture of Zinn–Justin that the partition function of the six-vertex model with DWBC has the asymptotics, as N → ∞, and we find the exact value of the exponent κ.The first author is supported in part by the National Science Foundation (NSF) Grant DMS-0354962.     

Quantitative modeling of laser speckle imaging

We have analyzed the image formation and dynamic properties in laser speckle imaging (LSI) both experimentally and with Monte Carlo simulation. We show for the case of a liquid inclusion that the spatial resolution and the signal itself are both significantly affected by scattering from the turbid environment. Multiple scattering leads to blurring of the dynamic inhomogeneity as detected by LSI. The presence of a nonfluctuating component of scattered light results in the significant increase in the measured image contrast and complicates the estimation of the relaxation time. We present a refined processing scheme that allows a correct estimation of the relaxation time from LSI data.