Stochastic models for the completeness of stratigraphic sections

Properties of stratigraphic completeness are determined here from a Brownian motion model of sediment accumulation. This avoids flaws inherent in application of a discrete-time random walk to the time span, rather than thickness, of sediment layers. Both discrete and continuous models show that the concept of stratigraphic completeness is meaningful only when the time scale is specified. From the discrete model, not surprisingly, completeness improves with increasing relative frequency and average thickness of depositional increments and the error of completeness estimation should decrease for longer sections. The continuous model shows that two dimensionless products determine the probability that a given time interval will be recorded by some preserved sediment. The first is the ratio of the age of the interval to its time span; the second is the product of the square root of the time span and ratio of the mean to the standard deviation of accumulation rate. Expected completeness is the average of these probabilities for all successive intervals of the given time span. For long sections, completeness may be estimated from the second dimensionless product alone. The two dimensionless products are sufficient to predict the relationship of accumulation rate to time span, the distribution of bed thickness, and the weak association of completeness and section thickness.     

The buckling of plastic oblate hemi-ellipsoidal dome shells under external hydrostatic pressure

The paper presents a theoretical and an experimental investigation into the buckling of seven oblate hemi-ellipsoidal dome shells under external hydrostatic pressure. Four of the shells were made in glass reinforced plastic and three were made from a thermosetting plastic called solid urethane plastic. All the vessels were tested to destruction. The theoretical study was made with the aid of a non-linear finite element solution, where both geometrical and material non-linearity were allowed for. Good agreement was found between experiment and theory for all the vessels. The very oblate domes failed axisymmetrically. Theoretical convergence was good for the more oblate domes but it was not as good as for the less oblate domes. This may have been because the less oblate domes did not fail in a classical axisymmetric manner as was expected. This work is of much importance in ocean engineering.     

Galaxy destruction and diffuse light in clusters

Deep images of the Centaurus and Coma clusters reveal two spectacular arcs of diffuse light that stretch for over 100 kpc, yet are just a few kiloparsecs wide. At a surface brightness of m _b ∼27–28 mag arcsec⁻² , the Centaurus arc is the most striking example known of structure in the diffuse light component of a rich galaxy cluster. We use numerical simulations to show that the Centaurus feature can be reproduced by the tidal debris of a spiral galaxy that has been tidally disrupted by the gravitational potential of NGC 4709. The surface brightness and narrow dimensions of the diffuse light suggest that the disc was corotating with its orbital path past pericentre. Features this prominent in clusters will be relatively rare, although at fainter surface brightness levels the diffuse light will reveal a wealth of structure. Deeper imaging surveys may be able to trace this feature for several times its presently observed extent, and somewhere along the tidal debris, a fraction of the original stellar component of the disc will remain bound, but transformed into a faint spheroidal galaxy. It should be possible to confirm the galactic origin of the Centaurus arc by observing planetary nebulae along its length with redshifts close to that of NGC 4709.     

Theoretical issues in the ‘food desert’ debate and ways forward

Food is essential to life—yet the spatial and economic configuration of the conventional food system does not meet nutritional needs and exacerbates issues of food insecurity. Relevant options for policy change have been explored in light of evaluations of geographic disparities in food access, but the dominant ‘food desert’ discourse often focuses uncritically on insufficient conceptions of access. Understanding the complexity of food deserts is important for moving into meaningful policy action. We present a theoretical position to inspire future empirical research. The ecological model recognizes both endogenous and built environment factors in shaping health. Interventions in the food environment, however, often concentrate exclusively on structural determinants of health (e.g. retail-based initiatives). Yet retail-based interventions are difficult to implement due to governance systems which limit the ability of government bodies to influence private retail development. As well, recognizing the complexity of debates over the influence of structure and agency, we apply structuration theory to food deserts. Behavioral economics further informs both structural and behavioral determinants of health. This approach sidesteps the issue of victim-blaming, as all consumers are viewed as ‘predictably irrational’ in decision-making. In combining these theories, we challenge methodological and theoretical assumptions by showing the complexity of food desert interventions. Policy recommendations focus on behavioral determinants of health and the opportunities for empowerment through local food systems. These recommendations recognize the limits of translating research into policy and in devising effective food based interventions, and are sensitive to social, economic, and political constraints uncovered throughout the paper.