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

Roughening of Fracture Surfaces: the Role of Plastic Deformations

Post mortem analysis of fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveal self affine graphs with an anomalous scaling exponent $\zeta\approx 0.8$. Attempts to use elasticity theory to explain this result failed, yielding exponent $\zeta\approx 0.5$ up to logarithms. We show that when the cracks propagate via plastic void formations in front of the tip, followed by void coalescence, the voids positions are positively correlated to yield exponents higher than 0.5.Comment: 4 pages, 6 figure

Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure

Jernbanekalenderen, 1912-1943/44

Fortsettelse av Norsk jernbanekalender; 1887-1910 ; fortsetter som Tjenestemenn ved statsbanen

Comparing the temperatures of galaxy clusters from hydro-N-body simulations to Chandra and XMM-Newton observations

Theoretical studies of the physical processes guiding the formation and evolution of galaxies and galaxy clusters in the X-ray are mainly based on the results of numerical hydrodynamical N-body simulations, which in turn are often directly compared to X-ray observations. Although trivial in principle, these comparisons are not always simple. We demonstrate that the projected spectroscopic temperature of thermally complex clusters obtained from X-ray observations is always lower than the emission-weighed temperature, which is widely used in the analysis of numerical simulations. We show that this temperature bias is mainly related to the fact that the emission-weighted temperature does not reflect the actual spectral properties of the observed source. This has important implications for the study of thermal structures in clusters, especially when strong temperature gradients, like shock fronts, are present. Because of this bias, in real observations shock fronts appear much weaker than what is predicted by emission-weighted temperature maps, and may even not be detected. This may explain why, although numerical simulations predict that shock fronts are a quite common feature in clusters of galaxies, to date there are very few observations of objects in which they are clearly seen. To fix this problem we propose a new formula, the spectroscopic-like temperature function, and show that, for temperature larger than 3 keV, it approximates the spectroscopic temperature better than few per cent, making simulations more directly comparable to observations.Comment: Submitted for publication in MNRAS; 15 pages, 10 color figures and 13 BW figures,mn2e.cls. High resolution figures available here: http://people.roma2.infn.it/~mazzotta/preprints/mazzotta.pd

Modern wildlife conservation initiatives and the pastoralist/hunter nomads of northwestern Tibet.

In 1993 the Tibet Autonomous Region (TAR) of China established the 300 000 km2 Chang Tang Nature Preserve on the northwestern Tibetan plateau, an action precipitated by rapidly diminishing populations of chiru (Tibetan antelope) and wild yak. Some 30 000 nomadic pastoralists use areas within this reserve for livestock grazing, with many having traditionally depended in part on hunting for supplementary subsistence and trade. Following a 1997 request from TAR leaders for international assistance in addressing the conservation issues associated with the creation of this reserve, the TAR Forestry Bureau and the Network for University Co-operation Tibet – Norway began a 3-year research collaboration program in 2000 to outline human-wildlife interactions and conservation priorities in the western part of the reserve. To date, four excursions (2-6 weeks each) have been made to the western Chang Tang region, and investigations of interactions between pastoralists and wildlife conservation objectives have been initiated in an area of about 5000 km2, including the 2300 km2 Aru basin located at 5000 m elevation at the northern edge of pastoralist inhabitation. The Aru site is unique in that nomads have only recently returned to this previously off-limits basin. But, as in surrounding areas, the people’s lives are undergoing changes recently influenced by the introduction of permanent winter houses, changing international trade in shahtoosh and cashmere wool, and a move towards stricter hunting regulations. The northwestern Chang Tang, with the Aru basin as a prime site, represents one of the last strongholds of the endangered chiru and wild yak, as well as home to Tibetan gazelle, kiang, Tibetan argali, blue sheep, wolf, snow leopard and brown bear. In autumn 2000, for example, with approximately 12 000 of the wild ungulates (mostly the migratory chiru) within the Aru basin along with some 8000 domestic livestock, issues of land use overlap and possible grazing competition are clear to both local nomads and reserve managers. Whereas livestock development actions elsewhere on the Tibetan plateau are promoting increased livestock production, they are doing so at the expense of wildlife, and such an approach will not be appropriate in areas where wildlife conservation is a major priority. Although some of the ongoing livestock development programs may be adapted to the western TAR, new approaches to pastoral development will have to be developed in the reserve. The ultimate goal of enhancing the nomads’ standard of living, while conserving this truly unique array of biodiversity, presents a daunting challenge

Void Formation and Roughening in Slow Fracture

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the resulting fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveals self-affine cracks with anomalous scaling exponent $\zeta\approx 0.8$ in 3-dimensions and $\zeta\approx 0.65$ in 2-dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2-dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.Comment: 15 pages, 20 figure

Competition between Diffusion and Fragmentation: An Important Evolutionary Process of Nature

We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we solve exactly in terms of Bessel functions. The stationary state is a universal Bessel distribution described by one parameter, which fits perfectly experimental data from two very different system of nature, namely, the distribution of ice crystal sizes from the Greenland ice sheet and the length distribution of alpha-helices in proteins.Comment: 4 pages, 3 figures, (minor changes