Fatigue-Life Prediction Methodology Using Small-Crack Theory

This paper reviews the capabilities of a plasticity-induced crack-closure model to predict fatigue lives of metallic materials using 'small-crack theory' for various materials and loading conditions. Crack-tip constraint factors, to account for three-dimensional state-of-stress effects, were selected to correlate large-crack growth rate data as a function of the effective-stress-intensity factor range (delta K(eff)) under constant-amplitude loading. Some modifications to the delta k(eff)-rate relations were needed in the near-threshold regime to fit measured small-crack growth rate behavior and fatigue endurance limits. The model was then used to calculate small- and large-crack growth rates, and to predict total fatigue lives, for notched and un-notched specimens made of two aluminum alloys and a steel under constant-amplitude and spectrum loading. Fatigue lives were calculated using the crack-growth relations and microstructural features like those that initiated cracks for the aluminum alloys and steel for edge-notched specimens. An equivalent-initial-flaw-size concept was used to calculate fatigue lives in other cases. Results from the tests and analyses agreed well

Links Between Acceleration, Melting, and Supraglacial Lake Drainage of the Western Greenland Ice Sheet

The impact of increasing summer melt on the dynamics and stability of the Greenland Ice Sheet is not fully understood. Mounting evidence suggests seasonal evolution of subglacial drainage mitigates or counteracts the ability of surface runoff to increase basal sliding. Here, we compare subdaily ice velocity and uplift derived from nine Global Positioning System stations in the upper ablation zone in west Greenland to surface melt and supraglacial lake drainage during summer 2007. Starting around day 173, we observe speedups of 6-41% above spring velocity lasting approximately 40 days accompanied by sustained surface uplift at most stations, followed by a late summer slowdown. After initial speedup, we see a spatially uniform velocity response across the ablation zone and strong diurnal velocity variations during periods of melting. Most lake drainages were undetectable in the velocity record, and those that were detected only perturbed velocities for approximately 1 day, suggesting preexisting drainage systems could efficiently drain large volumes of water. The dynamic response to melt forcing appears to 1) be driven by changes in subglacial storage of water that is delivered in diurnal and episodic pulses, and 2) decrease over the course of the summer, presumably as the subglacial drainage system evolves to greater efficiency. The relationship between hydrology and ice dynamics observed is similar to that observed on mountain glaciers, suggesting that seasonally large water pressures under the ice sheet largely compensate for the greater ice thickness considered here. Thus, increases in summer melting may not guarantee faster seasonal ice flow

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Teachers as leaders in a knowledge society: encouraging signs of a new professionalism

[Abstract]: Challenges confronting schools worldwide are greater than ever,and, likewise, many teachers possess capabilities, talents, and formal credentials more sophisticated than ever. However, the responsibility and authority accorded to teachers have not grown significantly, nor has the image of teaching as a profession advanced significantly. The question becomes, what are the implications for the image and status of the teaching profession as the concept of knowledge society takes a firm hold in the industrialized world? This article addresses the philosophical underpinnings of teacher leadership manifested in case studies where schools sought to achieve the generation of new knowledge as part of a process of whole-school revitalization. Specifically, this article reports on Australian research that has illuminated the work of teacher leaders engaged in the IDEAS project, a joint school revitalization initiative of the University of Southern Queensland and the Queensland Department of Education and the Arts

System size resonance in coupled noisy systems and in the Ising model

We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensembles -- lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance.Comment: 4 page

Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011

Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality

We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In particular, we give bounds on the first negative Lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time. We then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum and relate the scaling exponent to the scaling of quantities like avalanche size, duration, density of active sites, etc ...Comment: 33 pages, 6 figures, 1 table (to appear

Phase transitions in a spin-1 model with plaquette interaction on the square lattice

An extension of the Blume-Emery-Griffiths model with a plaquette four-spin interaction term, on the square lattice, is investigated by means of the cluster variation method in the square approximation. The ground state of the model, for negative plaquette interaction, exhibits several new phases, including frustrated ones. At finite temperature we obtain a quite rich phase diagram with two new phases, a ferrimagnetic and a weakly ferromagnetic one, and several multicritical points