Three-dimensional effects on cracked discs and plates under nominal Mode III loading

The existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, threedimensional effects are sometimes ignored in situations where they may be important. The purpose of the present contribution is to review the study carried out by the same authors in some recent investigations, in which a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic discs and plates has been analysed by means of accurate 3D finite element (FE) models. The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked components under anti-plane loading. The influence of plate bending is increasingly important as the thickness decreases. It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. Discussion on whether KIII tends to zero or infinity as a corner point is approached is futile because KIII is meaningless at a corner point. The intensity of the local stress and strain state through the thickness of the cracked components has been evaluated by using the strain energy density (SED) averaged over a control volume embracing the crack tip. The SED has been considered as a parameter able to control fracture in some previous contributions and can easily take into account also coupled three-dimensional effects. Calculation of the SED shows that the position of the maximum SED in the discs case is a function of the thickness. In the plates case instead the position of the maximum SED is independent of plate thickness, contrary to disc results

Crack paths and the linear elastic analysis of cracked bodies

The linear elastic analysis of cracked bodies is a Twentieth Century development, with the firstpapers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 thatwidespread application to practical engineering problems became possible. Linear elastic fracture mechanics(LEFM) developed rapidly in the 1960s, with application to brittle fracture and fatigue crack growth. The firstapplication of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969.Finite element analysis had a significant influence on the development of LEFM. Corner point singularities wereinvestigated in the late 1970s. It was soon found that the existence of corner point effects made interpretationof calculated stress intensity factors difficult and their validity questionable. In 1998 it was shown that theassumption that crack growth is in mode I leads to geometric constraints on permissible fatigue crack paths.Current open questions are. The need for a new field parameter, probably a singularity, to describe the stressesat surfaces. How best to allow for the influence of corner point singularities in three dimensional numericalpredictions of fatigue crack paths. Adequate description of fatigue crack path stability

Three-dimensional effects on cracked components under anti-plane loading

The existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, threedimensional effects are sometimes ignored in situations where they may be important. The purpose of the present investigation is to study by means of accurate 3D finite element (FE) models a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic plates. An extended version of the present work has recently been published in the literature. The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked components under anti-plane loading. The influence of plate bending is increasingly important as the thickness decreases. It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. Discussion on whether KIII tends to zero or infinity as a corner point is approached is futile because KIII is meaningless at a corner point. The intensity of the local stress and strain state through the thickness of the cracked components has been evaluated by using the strain energy density (SED) averaged over a control volume embracing the crack tip. The SED has been considered as a parameter able to control fracture in some previous contributions and can easily take into account also coupled three-dimensional effects. Calculation of the SED shows that the position of the maximum SED is independent of plate thickness. Both for thin plates and for thick ones the maximum SED is close to the lateral surface, where the maximum intensity of the coupled mode II takes place

Disordered Electrons in a Strong Magnetic Field: Transfer Matrix Approaches to the Statistics of the Local Density of States

We present two novel approaches to establish the local density of states as an order parameter field for the Anderson transition problem. We first demonstrate for 2D quantum Hall systems the validity of conformal scaling relations which are characteristic of order parameter fields. Second we show the equivalence between the critical statistics of eigenvectors of the Hamiltonian and of the transfer matrix, respectively. Based on this equivalence we obtain the order parameter exponent $\alpha_0\approx 3.4$ for 3D quantum Hall systems.Comment: 4 pages, 3 Postscript figures, corrected scale in Fig.

THE ANOMALOUS DIFFUSION IN HIGH MAGNETIC FIELD AND THE QUASIPARTICLE DENSITY OF STATES

We consider a disordered two-dimensional electronic system in the limit of high magnetic field at the metal-insulator transition. Density of states close to the Fermi level acquires a divergent correction to the lowest order in electron-electron interaction and shows a new power-law dependence on the energy, with the power given by the anomalous diffusion exponent $\eta$. This should be observable in the tunneling experiment with double-well GaAs heterostructure of the mobility $\propto 10^{4}V/s$ at temperatures of $\propto 10 mK$ and voltages of $\propto 1 \mu V$.Comment: 12 pages, LATEX, one figure available at request, accepted for publication in Phys. Rev.

New Class of Random Matrix Ensembles with Multifractal Eigenvectors

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three ensembles belong to a new class of critical RME with multifractal eigenfunction statistics and a universal critical spectral statitics. The generic form of the two-level correlation function for weak and extremely strong multifractality is suggested. Applications to the spectral statistics at the Anderson transition and for certain systems on the border of chaos and integrability is discussed.Comment: 4 pages RevTeX, resubmitte

Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $\eta$ and the spectral compressibility $\chi$ at the mobility edge, $\chi=\eta/2d$, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of an unitary network-model and represent a new method to investigate spectral properties of disordered systems.Comment: 5 pages, RevTeX, 3 figures, Postscript, strongly revised version to be published in PR

Exact Multifractality for Disordered N-Flavour Dirac Fermions in Two Dimensions

We present a nonperturbative calculation of all multifractal scaling exponents at strong disorder for critical wavefunctions of Dirac fermions interacting with a non-Abelian random vector potential in two dimensions. The results, valid for an arbitrary number of fermionic flavours, are obtained by deriving from Conformal Field Theory an effective Gaussian model for the wavefunction amplitudes and mapping to the thermodynamics of a single particle in a random potential. Our spectrum confirms that the wavefunctions remain delocalized in the presence of strong disorder.Comment: 4 pages, no figue

Level Curvature Distribution and the Structure of Eigenfunctions in Disordered Systems

The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the random matrix theory is calculated using the nonlinear supersymmetric sigma-model and compared to numerical simulations on the Anderson model. It is predicted analytically and confirmed numerically that the sign of the correction is different for T-breaking perturbations caused by a constant vector-potential equivalent to a phase twist in the boundary conditions, and those caused by a random magnetic field. In the former case it is shown using a nonperturbative approach that quasi-localized states in weakly disordered systems can cause the curvature distribution to be nonanalytic. In $2d$ systems the distribution function $P(K)$ has a branching point at K=0 that is related to the multifractality of the wave functions and thus should be a generic feature of all critical eigenstates. A relationship between the branching power and the multifractality exponent $d_{2}$ is suggested. Evidence of the branch-cut singularity is found in numerical simulations in $2d$ systems and at the Anderson transition point in $3d$ systems.Comment: 34 pages (RevTeX), 8 figures (postscript

Pharmacological screening using an FXN-EGFP cellular genomic reporter assay for the therapy of Friedreich ataxia

Copyright @ 2013 Li et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Friedreich ataxia (FRDA) is an autosomal recessive disorder characterized by neurodegeneration and cardiomyopathy. The presence of a GAA trinucleotide repeat expansion in the first intron of the FXN gene results in the inhibition of gene expression and an insufficiency of the mitochondrial protein frataxin. There is a correlation between expansion length, the amount of residual frataxin and the severity of disease. As the coding sequence is unaltered, pharmacological up-regulation of FXN expression may restore frataxin to therapeutic levels. To facilitate screening of compounds that modulate FXN expression in a physiologically relevant manner, we established a cellular genomic reporter assay consisting of a stable human cell line containing an FXN-EGFP fusion construct, in which the EGFP gene is fused in-frame with the entire normal human FXN gene present on a BAC clone. The cell line was used to establish a fluorometric cellular assay for use in high throughput screening (HTS) procedures. A small chemical library containing FDA-approved compounds and natural extracts was screened and analyzed. Compound hits identified by HTS were further evaluated by flow cytometry in the cellular genomic reporter assay. The effects on FXN mRNA and frataxin protein levels were measured in lymphoblast and fibroblast cell lines derived from individuals with FRDA and in a humanized GAA repeat expansion mouse model of FRDA. Compounds that were established to increase FXN gene expression and frataxin levels included several anti-cancer agents, the iron-chelator deferiprone and the phytoalexin resveratrol.Muscular Dystrophy Association (USA), the National Health and Medical Research Council (Australia), the Friedreich’s Ataxia Research Alliance (USA), the Brockhoff Foundation (Australia), the Friedreich Ataxia Research Association (Australasia), Seek A Miracle (USA) and the Victorian Government’s Operational Infrastructure Support Program