Orientational disorder in some molecular solids in relation to the boson peak in glasses

Orientational disorder in some molecular solids is discussed in relation to the emphasis placed on transverse vibrational modes in glasses as the origin of the observed boson peak in two very recent contributions in Nature Materials. In particular, facts are here presented for (i) CH₄, (ii) C₆₀ and (iii) ethanol in their solid phases for (a) specific heat and (b) neutron scattering. The results for ethanol in particular do not fit in with the interpretation of the boson peak in terms of transverse acoustic phonons in disordered systems. Glasses will therefore have to be separated into at least two classes where the physical interpretation of the boson peak is concerned.     

A piezoelectric immunosensor for the determination of pesticide residues and metabolites in fruit juices

A quartz crystal microbalance (QCM) immunosensor was developed for the determination of the insecticide carbaryl and 3,5,6-trichloro-2-pyridinol (TCP), the main metabolite of the insecticide chlorpyrifos and of the herbicide triclopyr. The detection was based on a competitive conjugate-immobilized immunoassay format using monoclonal antibodies (MAbs). Hapten conjugates were covalently immobilized, via thioctic acid self-assembled monolayer (SAM), onto the gold electrode sensitive surface of the quartz crystal. This covalent immobilization allowed the reusability of the modified electrode surface for at least one hundred and fifty assays without significant loss of sensitivity. The piezoimmunosensor showed detection limits (analyte concentrations producing 10% inhibition of the maximum signal) of 11 and 7 μg l⁻¹ for carbaryl and TCP, respectively. The sensitivity attained (I₅₀ value) was around 30 μg l⁻¹ for both compounds. Linear working ranges were 15-53 μg l⁻¹ for carbaryl and 13-83 μg l⁻¹ for TCP. Each complete assay cycle took 20 min. The good sensitivity, specificity, and reusability achieved, together with the short response time, allowed the application of this immunosensor to the determination of carbaryl and TCP in fruits and vegetables at European regulatory levels, with high precision and accuracy.     

Lattice-ordered triangular matrix algebras

In this article we give some necessary and sufficient conditions for a lattice-ordered semigroup algebra to be isomorphic to a lattice-ordered triangular matrix algebra.     

Configurations of flags and representations of surface groups in complex hyperbolic geometry

In this work, we describe a set of coordinates on the PU(2,1)-representation variety of the fundamental group of an oriented punctured surface Σ with negative Euler characteristic. The main technical tool we use is a set of geometric invariants of a triple of flags in the complex hyperbolic plane H²_{\mathbb C}{\bf H^2_{\mathbb {C}}} . We establish a bijection between a set of decorations of an ideal triangulation of Σ and a subset of the PU(2,1)-representation variety of π ₁(Σ).     

A Fleming–Viot Particle Representation¶of the Dirichlet Laplacian

We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N→∞ to the first eigenfunction of the Laplacian in D with the same boundary conditions. Received: 11 November 1999 / Accepted: 19 May 2000     

Explicit density–potential relation for 4-electron atoms in 2-orbital S states

An explicit relation is derived between the one-body potential energy and the electron density for the ground state of the Be atom in a nonrelativistic framework. This same relation applies to any four-electron atomic ion (or to Be itself) in a state where the electrons occupy two doubly filled orbitals. The relation is interpreted as an exact Hartree-like model of the Hohenberg–Kohn theorem within the general context of N electrons and a potential that is not necessarily spherically symmetrical.     

Metal-insulator transition in hydrogen and in expanded alkali metals

Two methods are considered for testing the stability of an electron gas to formation of bound states round a pair of protons. In the first, the screened potential for the two protons is set up as a superposition, which is appropriate in a very high density electron gas. The condition for bound state formation is then examined in the two-centre problem. The density thus obtained is in the right density range to accord with the experiment of Hawke et al. for producing cold metallic hydrogen.This has encouraged us to attempt a more ambitious calculation, namely the investigation of the Heitler-London energy of a model H₂ molecule with screened electron-nuclear and electron-electron interactions, the screening being again through appropriate introduction of the Thomas-Fermi screening radius. The merit of this second model is that the theory contains the Heitler-London value of the dissociation energy of the free H₂ molecule in the limit when the density of the electron gas tends to zero. This feature, the binding energy of the diatomic and its importance in distinguishing the metal-insulator transition in hydrogen from those expected to occur in expanded alkali metals is stressed. The second point we stress is that, in both the models discussed above, there is a close connection with the one-centre criterion for bound state formation. Though we have not carried out detailed two-centre calculations for expanded alkali metals, nevertheless some discussion is given of the one-centre bound state criterion in these metals.Some remarks are also made on the dielectric function of molecular crystals, in relation to the insulator-metal transition.     

Complexity and criticality in fusion, space and astrophysical plasmas

Techniques from complexity and criticality theory have fruitful applications to a wide range of natural and laboratory plasma systems. Here we review examples that have direct observational relevance, spanning fusion, the Earth's magnetosphere, the sun and astrophysical accretion disks. The complex systems techniques range from sandpiles to a novel loop-based dynamical model, together with modern approaches to model-independent data analysis.