An expedient route to diaza-spirocycles utilizing a sequential multicomponent α-aminoallylation/ring-closing metathesis strategy

A general method for the preparation of diaza-spirocycles is reported. This method used an olefin metathesis in order to construct the desired spirocyclic framework. Beginning with commercially available protected amino ketones, this strategy ultimately produced pharmacologically relevant diaza-scaffolds in an efficient and high-yielding process.     

The synthesis of 6-trifluoroethyl-l-lysine: a method to introduce functionality at C-6 of l-lysine

Described is a method of introducing trifluoroalkyl groups at C-6 of lysine. This chemistry has the potential to introduce a variety of functionality at C-6 of lysine.     

How many black holes fit on the head of a pin?

The Bekenstein–Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole “molecules” of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations. Fourth Award in the 2007 Essay Competition of the Gravity Research Foundation.     

A power-law distribution for tenure lengths of sports managers

We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.     

The Silicon Backplane Design for an LCOS Polarization-Insensitive Phase Hologram SLM

Polarization-insensitivity is achieved in a reflective spatial light modulator by laying a quarter-wave plate (QWP) at the incident wavelength directly over the mirror pixels of a silicon backplane, and forming a nematic Freedrickcz cell over the QWP to modulate the reflected phase. To achieve the highest drive voltage from the available silicon process, a switched voltage common front electrode design is described, with variable amplitude square wave drive to the pixels to maintain constant root-mean-square drive and minimize phase fluctuations during the dc balance refresh cycle. The silicon has been fabricated and liquid-crystal-on-silicon cells both with and without the QWP assembled; applications include optically transparent switches for optical networks, beam steering for add-drop multiplexers for wavelength-division-multiplexing telecommunications, television multicast, and holographic projection.     

Defect clusters in titanium-substituted spinel-related lithium ferrite

The cation distribution in spinel-related titanium-substituted lithium ferrite, Li_0.5+0.5xFe_2.5−1.5xTi_xO₄ has been explored using interatomic potential and ab initio calculations. The results suggest that the cation distribution with Ti⁴⁺ substituting for Fe³⁺ on octahedral B sites and excess Li⁺ substituting for Fe³⁺ on tetrahedral A sites is stabilised by the formation of clusters of two octahedrally coordinated Ti⁴⁺ ions and one tetrahedrally coordinated Li⁺ ion linked through a common oxygen.     

Mesh selection for stiff two-point boundary value problems

This paper is concerned with the mesh selection algorithm of COLSYS, a well known collocation code for solving systems of boundary value problems. COLSYS was originally designed to solve non-stiff and mildly stiff problems only. In this paper we show that its performance for solving extremely stiff problems can be considerably improved by modifying its error estimation and mesh selection algorithms. Numerical examples indicate the superiority of the modified algorithm.Dedicated to John Butcher on the occasion of his sixtieth birthday     

Raman spectroscopy of acoustic phonons in periodic and Fibonacci superlattices

Results of Raman scattering experiments on (a) periodic superlattices made up of GaAs/In_xGa_1−xAs layers with high indium concentrations, (b) GaAs/Ga_1−xAl_xAs Fibonacci superlattices, are presented. We discuss the observed peak positions and intensities using the continuum theory of acoustic wave propagation in layered media and the photo-elastic coupling model.     

An adaptive pruning algorithm for the discrete L-curve criterion

We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log–log plot of corresponding residual norms and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algorithms and demonstrate its robustness by numerical examples.