Fracture Surfaces as Multiscaling Graphs

Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$ order moments of the height fluctuations across any distance $\ell$ scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.Comment: 4 pages, 5 figure

Railroads and micro-regional growth in Prussia

We study the effect of railroad access on urban population growth. Using GIS techniques, we match triennial population data for roughly 1000 cities in nineteenth-century Prussia to georeferenced maps of the German railroad network. We find positive short- and long-term effects of having a station on urban growth for different periods during 1840-1871. Causal effects of (potentially endogenous) railroad access on city growth are identified using instrumentalvariable and xed-effects estimation techniques. Our instrument identifies exogenous variation in railroad access by constructing straight-line corridors between terminal stations. Counterfactual models using pre-railroad growth yield no evidence in support of the hypothesis that railroads appeared as a consequence of a previous growth spurt

Estimating joint intensity, density and mean tracelength using circular scanlines and circular windows

The purpose of this thesis is to evaluate and demonstrate the performance of new circular scanline and circular window estimators of joint intensity, density and mean tracelength. The estimators are distribution independent and provide a rapid means of estimating parameters, because only counts of fracture trace intersections and/or trace endpoints are needed. These estimators defeat the problems of orientation bias, censoring and length bias, which plagued previous methods. Using synthetic patterns with known parameters, the estimators reliably match control values. When applied to nine different joint sets or pavements, the estimators also correctly estimate fracture characteristics. A 95% prediction interval is used to establish confidence in measurements by defining the likely range for new predicted values. Plots for prediction interval show that the interval for predicted values is reduced and hence, estimate quality improved more efficiently by using sampling schemes that increase radius rather than number of circles. Larger circles are more efficient because they effectively average out spatial heterogeneity. When estimating mean tracelength, reliability of estimates is also improved by sampling schemes that yield large counts of fracture endpoints. Analysis of synthetic patterns shows that for trace centers described by a Poisson process, sampling schemes that capture 20 endpoints, on average, are needed to produce reliable results. This value should not be applied literally to natural patterns, as they are not typically Poissonian, but this analysis emphasizes the benefits of large sample size. These estimators may be applied to any type of data set that consists of linear traces, including fault traces on a planar slice through a 3-d seismic reflection data cube

Temporal and phylogenetic evolution of the sauropod dinosaur body plan

The colossal size and body plan of sauropod dinosaurs are unparalleled in terrestrial vertebrates. However, to date, there have been only limited attempts to examine temporal and phylogenetic patterns in the sauropod bauplan. Here, we combine three-dimensional computational models with phylogenetic reconstructions to quantify the evolution of whole-body shape and body segment properties across the sauropod radiation. Limitations associated with the absence of soft tissue preservation in fossils result in large error bars about mean absolute body shape predictions. However, applying any consistent skeleton : body volume ratio to all taxa does yield changes in body shape that appear concurrent with major macroevolutionary events in sauropod history. A caudad shift in centre-of-mass (CoM) in Middle Triassic Saurischia, associated with the evolution of bipedalism in various dinosaur lineages, was reversed in Late Triassic sauropodomorphs. A craniad CoM shift coincided with the evolution of quadrupedalism in the Late Triassic, followed by a more striking craniad shift in Late Jurassic–Cretaceous titanosauriforms, which included the largest sauropods. These craniad CoM shifts are strongly correlated with neck enlargement, a key innovation in sauropod evolution and pivotal to their gigantism. By creating a much larger feeding envelope, neck elongation is thought to have increased feeding efficiency and opened up trophic niches that were inaccessible to other herbivores. However, we find that relative neck size and CoM position are not strongly correlated with inferred feeding habits. Instead the craniad CoM positions of titanosauriforms appear closely linked with locomotion and environmental distributions, potentially contributing to the continued success of this group until the end-Cretaceous, with all other sauropods having gone extinct by the early Late Cretaceous

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, succeeding to reproduce the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up with the proposition of new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.Comment: A review paper submitted to J. Stat. Phy

A method of detecting radio transients

Radio transients are sporadic signals and their detection requires that the backends of radio telescopes be equipped with the appropriate hardware and software to undertake this. Observational programs to detect transients can be dedicated or they can piggy-back on observations made by other programs. It is the single-dish single-transient (non-periodical) mode which is considered in this paper. Because neither the width of a transient nor the time of its arrival is known, a sequential analysis in the form of a cumulative sum (cusum) algorithm is proposed here. Computer simulations and real observation data processing are included to demonstrate the performance of the cusum. The use of the Hough transform is here proposed for the purpose of non-coherent de-dispersion. It is possible that the detected transients could be radio frequency interferences (RFI) and a procedure is proposed here which can distinguish between celestial signals and man-made RFI. This procedure is based on an analysis of the statistical properties of the signals