A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind

A fast and efficient numerical method based on the Gauss-Jacobi quadrature is described that is suitable for solving Fredholm singular integral equations of the second kind that are frequently encountered in fracture and contact mechanics. Here we concentrate on the case when the unknown function is singular at both ends of the interval. Quadrature formulae involve fixed nodal points and provide exact results for polynomials of degree 2n − 1, where n is the number of nodes. Finally, an application of the method to a plane problem involving complete contact is presented.     

Light-induced electron spin polarization in the ground state of water-soluble copper porphyrins

Light-induced spin-polarized transient EPR spectra are reported for several water-soluble copper porphyrins. The spectra are assigned to the doublet ground state, with emissive spin polarization resulting from photoexcitation and subsequent electronic relaxation. In contrast to other systems for which polarization of a doublet ground state has been observed, the exchange interactions in the copper porphyrins are strong and the geometry is fixed. It is proposed that intersystem crossing from the photoexcited trip-doublet to the trip-quartet state can lead to net polarization of the spin system and that this polarization is maintained during electronic decay, possibly via charge-transfer and exciplex states. The intensity of the observed spin polarization is essentially independent of the molecular orientation in the external field, but is strongly dependent on the nature of the charged peripheral groups. Possible reasons for this behavior are discussed.     

Hopping and optical absorption of electrons in nano-porous crystal 12CaO·7Al2O3

Recently it has been discovered that a nano-porous main group oxide 12CaO·7Al₂O₃ (C12A7) can be converted from a wide-gap insulator to a good transparent conductor. Using ab initio modelling we explain good conductivity of this material by very small barriers for hopping of localised electrons between neighbouring positive cages. We show that optical absorption of C12A7 in infrared region and at energies higher than 2.7 eV is due to inter-cage and intra-cage electron transitions, respectively. The proposed mechanisms can be useful in further search for conducting transparent media.     

Experimental evidence of a relationship between monomer plasma residence time and carboxyl group retention in acrylic acid plasma polymers

Decreasing carboxyl retention in deposits from the glow region of an acrylic acid plasma was measured by X-ray photoelectron spectroscopy and chemical derivatisation as the collection distance from the monomer vapour inlet was increased. Volatilisation of plasma polymerised acrylic acid was detected after trifluoroethanol derivatisation; this is correlated with evaporation of low molecular weight components observed previously.     

On a large-gain theorem

The aim of this paper is to give a general quantitative requirement which the loop gain must satisfy in order to stabilize a given unstable (possibly nonlinear and time-varying) plant, namely that the gain must exceed one.     

Decision Making Effectiveness in Wildfire Incident Management Teams

During large scale wildfires, suppression activities are carried out under the direction of an Incident Management Team (IMT). The aim of the research was to increase understanding of decision processes potentially related to IMT effectiveness. An IMT comprises four major functions: Command, Operations, Planning, and Logistics. Four methodologies were used to study IMT processes: computer simulation experiments; analyses of wildfire reports; interviews with IMT members; and cognitive ethnographic studies of IMTs. Three processes were important determinants of IMT effectiveness: information management and cognitive overload; matching component function goals to overall goals; and team metacognition to detect and counter task‐disruptive developments. These processes appear to be complex multi‐person analogues of individual Incident Command processes identified previously. The findings have implications for issues such as: creating IMTs; training IMTs; managing IMTs; and providing decision support to IMTs.     

A One-Dimensional Nonlocal Damage-Plasticity Model for Ductile Materials

This paper presents a new 1-D non-local damage-plasticity deformation model for ductile materials. It uses the thermodynamic framework described in Houlsby and Puzrin (2000) and holds, nevertheless, some similarities with Lemaitre’s (1971) approach. A 1D finite element (FE) model of a bar fixed at one end and loaded in tension at the other end is introduced. This simple model demonstrates how the approach can be implemented within the finite element framework, and that it is capable of capturing both the pre-peak hardening and post-peak softening (generally responsible for models instability) due to damage-induced stiffness and strength reduction characteristic of ductile materials. It is also shown that the approach has further advantages of achieving some degree of mesh independence, and of being able to capture deformation size effects. Finally, it is illustrated how the model permits the calculation of essential work of rupture (EWR), i.e. the specific energy per unit cross-sectional area that is needed to cause tensile failure of a specimen.     

Ugtracold Alkali Atoms in Optical Lattices: A New Type of Quantum Crystals?

Similarities between alkali gases in optical lattices with non-integer occupation of the lattice sites and quantum crystals are explored. The analogy with the vacancy liquid provides an agternative explanation to the Mott transition for the recent experiment on the phase transition in the lattice. The vacancy liquid can undergo BEC with T _c within experimental reach. Direct and vacancy-assisted mechanisms of the band motion for hyperfine impurities are discussed. The presence of vacancies can resugt in the spatial decomposition of the system into pure hyperfine components. Below BEC for the vacancies, the impurity component resembles ³He in ³He-Hell mixtures.