Branching Instabilities in Rapid Fracture: Dynamics and Geometry

We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation of the static ones. The results of this model are in good agreement with a sizeable quantity of experimental data.Comment: 9 pages, 11 figure

Four Measures of the Intracluster Medium Temperature and Their Relation to a Cluster's Dynamical State

We employ an ensemble of hydrodynamic cluster simulations to create spatially and spectrally resolved images of quality comparable to Chandra's expected performance. Emission from simulation mass elements is represented using the XSPEC mekal program assuming 0.3 solar metallicity, and the resulting spectra are fit with a single-temperature model. Despite significant departures from isothermality in the cluster gas, single-temperature models produce acceptable fits to 20,000 source photon spectra. The spectral fit temperature T_s is generally lower than the mass weighted average temperature T_m due to the influence of soft line emission from cooler gas being accreted as part of the hierarchical clustering process. In a Chandra-like bandpass of 0.5 to 9.5 keV we find a nearly uniform fractional bias of (T_m-T_s)/T_s = 20% with occasional large deviations in smaller clusters. In the more traditional 2.0 to 9.5 keV bandpass, the fractional deviation is scale-dependent and on average follows the relation (T_m-T_s)/T_s = 0.2 log(T_m). This bias results in a spectral mass-temperature relationship with slope about 1.6, intermediate between the virial relation M ~ T_m^{3/2} and the observed relation M_{ICM} ~ T^2. Imaging each cluster in the ensemble at 16 epochs in its evolutionary history, we catalogue merger events with mass ratios exceeding 10% in order to investigate the relationship between spectral temperature and proximity to a major merger event. Clusters that are very cool relative to the mean mass-temperature relationship lie preferentially close to a merger, suggesting a viable observational method to cull a subset of dynamically young clusters from the general population.Comment: 34 pages, including 2 tables and 14 figures (one in color). Compiled using LaTeX 2.09 with graphics package and aaspp4 style. The simulated spectral data files used in this paper are available for public consumption at http://redshift.stanford.edu/bfm

Stress-driven phase transformation and the roughening of solid-solid interfaces

The application of stress to multiphase solid-liquid systems often results in morphological instabilities. Here we propose a solid-solid phase transformation model for roughening instability in the interface between two porous materials with different porosities under normal compression stresses. This instability is triggered by a finite jump in the free energy density across the interface, and it leads to the formation of finger-like structures aligned with the principal direction of compaction. The model is proposed as an explanation for the roughening of stylolites - irregular interfaces associated with the compaction of sedimentary rocks that fluctuate about a plane perpendicular to the principal direction of compaction.Comment: (4 pages, 4 figures

Intransitivity and coexistence in four species cyclic games

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We consider here a generalization with four species, the minimum number of species allowing other interactions beyond the single loop (one predator, one prey). We show that, contrary to the mean field prediction, on a square lattice the model presents a transition, as the parameter setting the rate at which one species invades another changes, from a coexistence to a state in which one species gets extinct. Such a dependence on the invasion rates shows that the interaction graph structure alone is not enough to predict the outcome of such models. In addition, different invasion rates permit to tune the level of transitiveness, indicating that for the coexistence of all species to persist, there must be a minimum amount of intransitivity.Comment: Final, published versio

Should patients with abnormal liver function tests in primary care be tested for chronic viral hepatitis: cost minimisation analysis based on a comprehensively tested cohort

Background Liver function tests (LFTs) are ordered in large numbers in primary care, and the Birmingham and Lambeth Liver Evaluation Testing Strategies (BALLETS) study was set up to assess their usefulness in patients with no pre-existing or self-evident liver disease. All patients were tested for chronic viral hepatitis thereby providing an opportunity to compare various strategies for detection of this serious treatable disease. Methods This study uses data from the BALLETS cohort to compare various testing strategies for viral hepatitis in patients who had received an abnormal LFT result. The aim was to inform a strategy for identification of patients with chronic viral hepatitis. We used a cost-minimisation analysis to define a base case and then calculated the incremental cost per case detected to inform a strategy that could guide testing for chronic viral hepatitis. Results Of the 1,236 study patients with an abnormal LFT, 13 had chronic viral hepatitis (nine hepatitis B and four hepatitis C). The strategy advocated by the current guidelines (repeating the LFT with a view to testing for specific disease if it remained abnormal) was less efficient (more expensive per case detected) than a simple policy of testing all patients for viral hepatitis without repeating LFTs. A more selective strategy of viral testing all patients for viral hepatitis if they were born in countries where viral hepatitis was prevalent provided high efficiency with little loss of sensitivity. A notably high alanine aminotransferase (ALT) level (greater than twice the upper limit of normal) on the initial ALT test had high predictive value, but was insensitive, missing half the cases of viral infection. Conclusions Based on this analysis and on widely accepted clinical principles, a "fast and frugal" heuristic was produced to guide general practitioners with respect to diagnosing cases of viral hepatitis in asymptomatic patients with abnormal LFTs. It recommends testing all patients where a clear clinical indication of infection is present (e.g. evidence of intravenous drug use), followed by testing all patients who originated from countries where viral hepatitis is prevalent, and finally testing those who have a notably raised ALT level (more than twice the upper limit of normal). Patients not picked up by this efficient algorithm had a risk of chronic viral hepatitis that is lower than the general population

Placental transfer of the polybrominated diphenyl ethers BDE-47, BDE-99 and BDE-209 in a human placenta perfusion system: an experimental study

<p>Abstract</p> <p>Background</p> <p>Polybrominated diphenyl ethers (PBDEs) have been widely used as flame retardants in consumer products. PBDEs may affect thyroid hormone homeostasis, which can result in irreversible damage of cognitive performance, motor skills and altered behaviour. Thus, in utero exposure is of very high concern due to critical windows in fetal development.</p> <p>Methods</p> <p>A human ex vivo placenta perfusion system was used to study the kinetics and extent of the placental transfer of BDE-47, BDE-99 and BDE-209 during four-hour perfusions. The PBDEs were added to the maternal circulation and monitored in the maternal and fetal compartments. In addition, the perfused cotyledon, the surrounding placental tissue as well as pre-perfusion placental tissue and umbilical cord plasma were also analysed. The PBDE analysis included Soxhlet extraction, clean-up by adsorption chromatography and GC-MS analysis.</p> <p>Results and Discussion</p> <p>Placental transfer of BDE-47 was faster and more extensive than for BDE-99. The fetal-maternal ratios (FM-ratio) after four hours of perfusion were 0.47 and 0.25 for BDE-47 and BDE-99, respectively, while the indicative permeability coefficient (IPC) measured after 60 minutes of perfusion was 0.26 h^-1and 0.10 h^-1, respectively. The transport of BDE-209 seemed to be limited. These differences between the congeners may be related to the degree of bromination. Significant accumulation was observed for all congeners in the perfused cotyledon as well as in the surrounding placental tissue.</p> <p>Conclusion</p> <p>The transport of BDE-47 and BDE-99 indicates in utero exposure to these congeners. Although the transport of BDE-209 was limited, however, possible metabolic debromination may lead to products which are both more toxic and transportable. Our study demonstrates fetal exposure to PBDEs, which should be included in risk assessment of PBDE exposure of women of child-bearing age.</p