Sten Andersson is 80

There is a special collection of contribution in the August 2012 issue of Structural Chemistry honoring the Swedish crystallographer Sten Andersson. This Encomium emphasizes the exemplary characteristics of his oeuvre.     

Enumeration of polycarborane isomers: especially dicarboranes

Various sorts of isomer enumeration problems are addressed in the context of polycarboranes, with special illustrative focus on the case of dicarboranes, for which then various numerical results are given. A systematic and general Pólya-theoretic methodology is used to make the computations, including some new techniques being applicable to a wide range of nano-structures built from a framework of like local subunits.     

First-order transitions in spherical models: Finite-size scaling

Finite-size behavior near the first-order phase boundary of ferromagnetic spherical models is investigated for block- and cylinder-shaped systems ind dimensions. The bulk thermodynamic singularities are rounded and, asymptotically for large size, obey appropriate scaling laws. Both short-range interactions and long-range couplings, decaying like 1/r^d+ with >0, are analyzed: the short-range results agree precisely with a recently developed scaling theory forO(n) symmetric systems in the limitn. More generally, the scaling functions are universal, depending only on . Explicit aspects of the shape and interactions enter only in the spin wave or Goldstone mode contributions which appear, technically, as corrections to scaling. An appendix analyzes the truncation error in the approximation, by many-fold sums, of multivariate integrals with integrands diverging like [_ja_{j j} ² ]^- as 0.     

Metal nanoslit lenses with polarization-selective design

We present comprehensive studies on thin diffraction lenses made of arrays of subwavelength, parallel nanoslits in a gold film. Such a nanoslit lens can operate either as a conventional convex or concave lens. The lenses can be designed to focus linearly polarized light with polarization either perpendicular (TM-lens) or parallel to the slits (TE-lens), while the orthogonal polarization diverges when passing through the lens. The designs of each lens are initially built on the dispersion relations for wave propagation through a parallel-plate waveguide. Both TM- and TE-lenses were realized experimentally, and full-wave numerical simulations fully support the experimental results.     

On the coherent inelastic processes in collisions of elementary particles with nuclei at ultrarelativistic energies

The coherent inelastic processes of the type a → b, which may take place in the interaction of hadrons and γ quanta with nuclei at very high energies (the nucleus remains the same), are theoretically investigated. Analytical formulas for the effective cross-section σ_coh(a→b) are obtained.     

Morphology-dependent photonic circuit elements

We theoretically propose and experimentally demonstrate the design of a novel one-dimensional ringlike macroscopic optical circuit element. The similarity between morphologies of an optical planar waveguide and a whispering-gallery axially symmetric solid-state resonator is used.     

A simple method to measure 13CH2 heteronuclear dipolar cross-correlation spectral densities

Here, we report a method to simultaneously determine CH2 cross-correlation spectral densities and T1 relaxation times in the laboratory and rotating frames. To accomplish this, we have employed an indirect approach that is based on measurement of differences in relaxation rates acquired with and without cross-correlation terms. The new method, which can be employed using multidimensional NMR and standard relaxation pulse sequences, is validated experimentally by investigation of a selectively 13C-enriched hexadecapeptide and the uniformly 13C-enriched immunoglobulin-binding domain of streptococcal protein G (GB1). Use of this approach makes determination of CH2 cross-correlation spectral densities in uniformly 13C-enriched proteins now routine and provides novel information concerning their internal motions.     

The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA1(1)

The universal quantumR-matrix is obtained in the case of the affine Kac-Moody Lie algebra sl(2).     

Improved Lower Bounds for the Critical Probability of Oriented Bond Percolation in Two Dimensions

We present a coupled decreasing sequence of random walks on Z that dominate the edge process of oriented bond percolation in two dimensions. Using the concept of random walk in a strip, we describe an algorithm that generates an increasing sequence of lower bounds that converges to the critical probability of oriented percolation p_c. From the 7th term on, these lower bounds improve upon 0.6298, the best rigorous lower bound at present, establishing 0.63328 as a rigorous lower bound for p_c. Finally, a Monte Carlo simulation technique is presented; the use thereof establishes 0.64450 as a non-rigorous five-digit-precision (lower) estimate for p_c. Mathematics Subject Classification (1991): 60K35 Supported by CNPq (grant N.301637/91-1). Supported by a grant from CNPq.