Coercivity of Combined Boundary Integral Equations in High‐Frequency Scattering

We prove that the standard second‐kind integral equation formulation of the exterior Dirichlet problem for the Helmholtz equation is coercive (i.e., sign‐definite) for all smooth convex domains when the wavenumber k is sufficiently large. (This integral equation involves the so‐called combined potential, or combined field, operator.) This coercivity result yields k‐explicit error estimates when the integral equation is solved using the Galerkin method, regardless of the particular approximation space used (and thus these error estimates apply to several hybrid numerical‐asymptotic methods developed recently). Coercivity also gives k‐explicit bounds on the number of GMRES iterations needed to achieve a prescribed accuracy when the integral equation is solved using the Galerkin method with standard piecewise‐polynomial subspaces. The coercivity result is obtained by using identities for the Helmholtz equation originally introduced by Morawetz in her work on the local energy decay of solutions to the wave equation. © 2015 Wiley Periodicals, Inc.     

Chaetopterus variopedatus Bioluminescence: A Review of Light Emission within a Species Complex

Chaetopterus variopedatus has been studied for over a century in terms of its physiology, ecology and life history. One focus of research is on its intrinsic bioluminescent emissions, which can be observed as a blue light emitted from the extremities of individual body segments, or as a secreted mucus. Even though research shows that C. variopedatus is a species complex miscategorized as a single species, all of the variants of this polychaete produce light, which has been investigated in terms of both physiology and biochemistry. Despite decades of study, there are still many questions about the luminescence reaction, and, as of yet, no clear function for light emission exists. This review summarizes the current knowledge on C. variopedatus luminescence in addition to briefly describing its morphology, life cycle and ecology. Possible functions for luminescence were discussed using observations of specimens found in Brazil, along with a comparison of previous studies of other luminescent organisms. Further study will provide a better understanding of how and why C. variopedatus produces luminescence, and purifying the protein and luciferin involved could lead to new bioanalytical applications, as this reaction is unique among all known luminescent systems.     

Cyanide Complexes Based on {Mo6I8}4+ and {W6I8}4+ Cluster Cores

Compounds based on new cyanide cluster anions [{Mo₆I₈}(CN)₆]^2–, trans-[{Mo₆I₈}(CN)₄(MeO)₂]^2– and trans-[{W₆I₈}(CN)₂(MeO)₄]²⁻ were synthesized using mechanochemical or solvothermal synthesis. The crystal and electronic structures as well as spectroscopic properties of the anions were investigated. It was found that the new compounds exhibit red luminescence upon excitation by UV light in the solid state and solutions, as other cluster complexes based on {Mo₆I₈}⁴⁺ and {W₆I₈}⁴⁺ cores do. The compounds can be recrystallized from aqueous methanol solutions; besides this, it was shown using NMR and UV-Vis spectroscopy that anions did not undergo hydrolysis in the solutions for a long time. These facts indicate that hydrolytic stabilization of {Mo₆I₈} and {W₆I₈} cluster cores can be achieved by coordination of cyanide ligands.     

On the equation of state for thermal polymer solutions and melts with attractive interaction

We perform Monte Carlo simulations of a lattice model for polymer melts, i. e., the bond fluctuation model in three dimensions. By using an energy parameter that prefers relatively long bonds, the model exhibits a glass transition at low temperatures, in close qualitative similarity to experiment. We modify this model by adding an attractive interaction of variable strength. We demonstrate that a small interaction strength has only a very small effect on the static properties of the melt. For a fixed strength of the potential, the chemical potential is measured by a modified particle-insertion method over a large range of temperatures and densities. The osmotic pressure is obtained by thermodynamic integration. In contrast to the original version our extended model exhibits a positive thermal expansion.     

Monte Carlo modelling of the polymer glass transition

We are proposing a lattice model with chemical input for the computer modelling of the polymer glass transition. The chemical input information is obtained by a coarse graining procedure applied to a microscopic model with full chemical detail. We use this information on Bisphenol-A-Polycarbonate to predict it's Vogel-Fulcher temperature out of a dynamic Monte Carlo Simulation. The microscopic structure of the lattice model is that of a genuine amorphous material, and the structural relaxation obeys the time temperature superposition.     

Brownian dynamics simulation of grafted polymer brushes

We present results of computer simulations by the method of Brownian dynamics of polymeric brushes attached to impenetrable planes. For testing both model and method we have used one polymer brush attached to a repulsive plane and compare some results with Monte Carlo results of Lai and Binder on the bond fluctuation model. We have also studied two polymeric brushes attached to two parallel planes at different distances between planes, and investigate the interplay between the interpenetration of the brushes and the configurational properties of the grafted chains.     

Macrocyclization of polymers via ring‐closing metathesis and azide/alkyne‐“click”‐reactions: An approach to cyclic polyisobutylenes

The end‐to‐end cyclization of telechelic polyisobutylenes (PIB's) toward cyclic polyisobutylenes is reported, using either ring‐closing metathesis (RCM) or the azide/alkyne‐“click”‐reaction. The first approach uses bisallyl‐telchelic PIB's (M_n = 1650, 3680, 9770 g mol^?1) and Grubbs 1st‐, 2nd‐, and 3rd‐generation catalyst leading to cyclic PIB's in 60–80% yield, with narrow polydispersities (M_w/M_n = 1.25). Azide/alkyne‐“click”‐reactions of bisalkyne‐telechelic PIB's (M_n = 3840 and 9820 g mol^?1) with excess of 1,11‐diazido‐undecane leads to the formation of mixtures of linear/cyclic PIB's under formation of oligomeric cycles. Subsequent reaction of the residual azide‐moieties in the linear PIB's with excess of alkyne‐telechelic PEO enables the chromatographic removal of the resulting linear PEO‐PIB‐block copolymers by column chromatography. Thus pure cyclic PIB's can be obtained using this double‐“click”‐method, devoid of linear contaminants. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 671–680, 2010     

Halophilic reactions of a stable silylene with chloro and bromocarbons

A number of disilanes have been synthesized from a stable silylene, 1 (N,N'-di-tert-butyl-1,3-diaza-2-silacyclopent-4-en-2-ylidene), and a variety of halocarbons. It is proposed that disilane formation is a result of an initial halophilic interaction between the silylene and halocarbon. Formation of disilanes from 1 and CCl4, 2a, CHCl3, 2b, CH2Cl2, 2c, benzyl chloride, 2d, and bromobenzene, 5, are described here. An X-ray crystal structure of 2b was determined.     

Scaling concepts for polymer brushes and their test with computer simulation

After a brief review of the scaling concepts for static and dynamic properties of polymer brushes in good solvents and Theta solvents, the Monte Carlo evidence is discussed. It is shown that under typical conditions the diameter of the last blob is of the order of 10-20% of the brush height, and therefore pronounced deviations from the self-consistent field predictions occur. In bad solvents, lateral microphase separation occurs leading to an irregular pattern of “dimples”. Particularly interesting is the response of brushes to shear deformation, and the interaction between two interpenetrating brushes. Recent attempts to understand the resulting shear forces via molecular-dynamics simulations are briefly described, and an outlook on related experiments is given. Dedicated to Prof. H.E. Stanley on the occasion of his 60th birthday Received 11 March 2002 and Received in final form 3 June 2002