A simple non-linear global-local finite element methodology for composite structures

A simple non-linear global-local finite element methodology is presented. A global coarse model, using 2-D shell elements, is solved non-linearly and the displacements and rotations around a region of interest are applied, as displacement boundary conditions, to a refined local 3-D model using Kirchhoff plate assumptions. The global elements' shape functions are used to interpolate between nodes. The local model is then solved non-linearly with an incremental scheme independent of that used for the global model.

Local-field and excitonic effects in the optical response of alpha-alumina

This paper introduces key ingredients of the dielectric response of a-alumina that go beyond an independent-particle (IP) treatment of the valence-electron excitations. The optical-response functions were calculated from first-principles both at the Bethe-Salpeter and the random-phase approximation (RPA) levels. Excitonic effects obtained within the Bethe-Salpeter framework were found essential for reproducing the low-energy part of the experimental spectra (below 15 eV) and the bound exciton in particular. For higher energies, local-field effects introduced through the RPA modified considerably the IP results and provided a satisfactory account of the reflectivity spectra and of the position and shape of the dominant bulk plasmon resonance in the electron energy-loss spectra.

Macroscopic limit of time-dependent density-functional theory for adiabatic local approximations of the exchange-correlation kernel

Time-dependent density-functional theory is a rather accurate and efficient way to compute electronic excitations for finite systems. However, in the macroscopic limit (systems of increasing size), for the usual adiabatic random-phase, local-density, or generalized-gradient approximations, one recovers the Kohn-Sham independent-particle picture, and thus the incorrect band gap. To clarify this trend, we investigate the macroscopic limit of the exchange-correlation kernel in such approximations by means of an algebraical analysis complemented with numerical studies of a one-dimensional tight-binding model. We link the failure to shift the Kohn-Sham spectrum of these approximate kernels to the fact that the corresponding operators in the transition space act only on a finite subspace.

On the required shape corrections to the local density and generalized gradient approximations to the Kohn-Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

It is well known that shape corrections have to be applied to the local-density (LDA) and generalized gradient (GGA) approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential (BP-GRAC) and the statistical averaging of (model) orbital potentials (SAOP), versus LDA and GGA potentials, in molecular response calculations of the static average polarizability alpha, the Cauchy coefficient S-4, and the static average hyperpolarizability beta. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr (BLYP), and Becke-Perdew (BP) characteristically underestimate contributions to alpha and S-4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N-2 molecule shows, that both SAOP and BP-GRAC yield reliable energies omega(i) and oscillator strengths f(i) of individual excitations, so that they reproduce well the spectral structure of alpha and S-4.(C) 2002 American Institute of Physics.

Investigating local relationships between trace elements in soils and cancer data

Medical geology research has recognised a number of potentially toxic elements (PTEs), such as arsenic, cobalt, chromium, copper, nickel, lead, vanadium, uranium and zinc, known to influence human disease by their respective deficiency or toxicity. As the impact of infectious diseases has decreased and the population ages, so cancer has become the most common cause of death in developed countries including Northern Ireland. This research explores the relationship between environmental exposure to potentially toxic elements in soil and cancer disease data across Northern Ireland. The incidence of twelve different cancer types (lung, stomach, leukaemia, oesophagus, colorectal, bladder, kidney, breast, mesothelioma, melanoma and non melanoma(NM) both basal and squamous, were examined in the form of twenty-five coded datasets comprising aggregates over the 12 year period from 1993 to 2006. A local modelling technique,geographically weighted regression (GWR) is usedto explore the relationship between environmental exposure and cancer disease data. The results show comparisons of the geographical incidence of certain cancers (stomach and NM squamous skin cancer) in relation to concentrations of certain PTEs (arsenic levels in soils and radon were identified). Findings from the research have implications for regional human health risk assessments.

Local framings

Framings provide a way to construct Quillen functors from simplicial sets to any given model category. A more structured set- up studies stable frames giving Quillen functors from spectra to stable model categories. We will investigate how this is compatible with Bousfield localisation to gain insight into the deeper structure of the stable homotopy category. We further show how these techniques relate to rigidity questions and how they can be used to study algebraic model categories.

Long-range synchronization and local desynchronization of alpha oscillations during visual short-term memory retention in children

Local alpha-band synchronization has been associated with both cortical idling and active inhibition. Recent evidence, however, suggests that long-range alpha synchronization increases functional coupling between cortical regions. We demonstrate increased long-range alpha and beta band phase synchronization during short-term memory retention in children 6-10 years of age. Furthermore, whereas alpha-band synchronization between posterior cortex and other regions is increased during retention, local alpha-band synchronization over posterior cortex is reduced. This constitutes a functional dissociation for alpha synchronization across local and long-range cortical scales. We interpret long-range synchronization as reflecting functional integration within a network of frontal and visual cortical regions. Local desynchronization of alpha rhythms over posterior cortex, conversely, likely arises because of increased engagement of visual cortex during retention.