Pegs and Ropes: Geometry at Stonehenge

A recent computer-aided-design investigation of the Neolithic 56 Aubrey Hole circuit at Stonehenge has led to the discovery of an astonishingly simple geometrical construction for drawing an approximately regular 56-sided polygon, feasible with a compass and straightedge. In the present work, we prove analytically that the aforementioned construction yields as a byproduct, an extremely accurate method for approximating a regular heptagon, and we quantify the accuracy that prehistoric surveyors may have ideally attained using simple pegs and ropes. We compare this method with previous approximations, and argue that it is likely to be at the same time the simplest and most accurate. Implications of our findings are discussed

Evaporite-karst processes, landforms, and environmental problems

Evaporite karst is widespread, but relatively unknown when compared with carbonate karst; this special issue addresses that lack of familiarity. Evaporite rocks have much higher solubilities and faster dissolution rates than carbonate rocks and they also commonly have lower mechanical strengths and more ductile reheologies. Many of these factors are dependent on the local hydrogeology, and when combined they can result in areas where karst features evolve on a human time scale, rather than a geological timescale. Karst collapse and subsidence are common in such areas, making them problematical for the local population. The evaporite-karst environment is very sensitive to changes in the local hydrology and hydrogeology, so that human factors such as groundwater extraction, drainage, and irrigation can act as triggering events for karst collapses. Some evaporite-karst features such as caves and saline springs have been beneficially exploited, but most of them, including sinkholes, subsidence, and groundwater degradation, pose a threat to the local environment and a hazard to development. The papers in this special issue of Environmental Geology arose from a successful session on Evaporite Karst convened by us at the Sixth International Conference on Geomorphology. This was held in Zaragoza, Spain, in September 2005 and was organised by Zaragoza University and the International Association of Geomorphologists (IAG; http://www.geomorph.org/). Authors of the twenty-eight presented abstracts were invited to submit full papers to this special issue. Nineteen papers were proposed and sixteen papers have been accepted and are published here

Identification, prediction and mitigation of sinkhole hazards in evaporite karst areas

Abstract Sinkholes usually have a higher probability of occurrence and a greater genetic diversity in evaporite terrains than in carbonate karst areas. This is because evaporites have a higher solubility, and commonly a lower mechanical strength. Subsidence damage resulting from evaporite dissolution generates substantial losses throughout the world, but the causes are only well-understood in a few areas. To deal with these hazards, a phased approach is needed for sinkhole identification, investigation, prediction, and mitigation. Identification techniques include field surveys, and geomorphological mapping combined with accounts from local people and historical sources. Detailed sinkhole maps can be constructed from sequential historical maps, recent topographical maps and digital elevation models (DEMs) complemented with building-damage surveying, remote sensing, and high-resolution geodetic surveys. On a more detailed level, information from exposed paleosubsidence features (paleokarst), speleological explorations, geophysical investigations, trenching, dating techniques, and boreholes, may help to recognize dissolution and subsidence features. Information on the hydrogeological pathways including caves, springs and swallow holes, are particularly important especially when corroborated by tracer tests. These diverse data sources make a valuable database - the karst inventory. From this dataset, sinkhole susceptibility zonations (relative probability) may be produced based on the spatial and temporal distribution of the features and good knowledge of the local geology. Sinkhole distribution can be investigated by spatial distribution analysis techniques including studies of preferential elongation, alignment and nearest neighbor analysis. More objective susceptibility models may be obtained by analyzing the statistical relationships between the known sinkholes and the conditioning factors, such as weather conditions. Chronological information on sinkhole formation is required to estimate the probability of occurrence of sinkholes (number of sinkholes/km² year). Such spatial and temporal predictions, derived from limited records and based on the assumption that past sinkhole activity may be extrapolated to the future, are non-corroborated hypotheses. Validation methods allow us to assess the predictive capability of the susceptibility maps and to transform them into probability maps. Avoiding the most hazardous areas by preventive planning is the safest strategy for development in sinkhole-prone areas. Corrective measures could be to reduce the dissolution activity and subsidence processes, but these are difficult. A more practical solution for safe development is to reduce the vulnerability of the structures by using subsidence-proof designs

Towards observable signatures of other bubble universes

We evaluate the possibility of observable effects arising from collisions between vacuum bubbles in a universe undergoing false-vacuum eternal inflation. Contrary to conventional wisdom, we find that under certain assumptions most positions inside a bubble should have access to a large number of collision events. We calculate the expected number and angular size distribution of such collisions on an observer's "sky," finding that for typical observers the distribution is anisotropic and includes many bubbles, each of which will affect the majority of the observer's sky. After a qualitative discussion of the physics involved in collisions between arbitrary bubbles, we evaluate the implications of our results, and outline possible detectable effects. In an optimistic sense, then, the present paper constitutes a first step in an assessment of the possible effects of other bubble universes on the cosmic microwave background and other observables.Comment: 17 PRD-style pages including 13 embedded figures. Minor corrections to figures 4 and 7 and added discussion in Sec. III.E.2 and

Two Tunnels to Inflation

We investigate the formation via tunneling of inflating (false-vacuum) bubbles in a true-vacuum background, and the reverse process. Using effective potentials from the junction condition formalism, all true- and false-vacuum bubble solutions with positive interior and exterior cosmological constant, and arbitrary mass are catalogued. We find that tunneling through the same effective potential appears to describe two distinct processes: one in which the initial and final states are separated by a wormhole (the Farhi-Guth-Guven mechanism), and one in which they are either in the same hubble volume or separated by a cosmological horizon. In the zero-mass limit, the first process corresponds to the creation of an inhomogenous universe from nothing, while the second mechanism is equivalent to the nucleation of true- or false-vacuum Coleman-De Luccia bubbles. We compute the probabilities of both mechanisms in the WKB approximation using semi-classical Hamiltonian methods, and find that -- assuming both process are allowed -- neither mechanism dominates in all regimes.Comment: 16 PRD-style pages, 13 figures. PRD, in press. Revised to match published versio

Dynamics and instability of false vacuum bubbles

This paper examines the classical dynamics of false vacuum regions embedded in surrounding regions of true vacuum, in the thin-wall limit. The dynamics of all generally relativistically allowed solutions -- most but not all of which have been previously studied -- are derived, enumerated, and interpreted. We comment on the relation of these solutions to possible mechanisms whereby inflating regions may be spawned from non-inflating ones. We then calculate the dynamics of first order deviations from spherical symmetry, finding that many solutions are unstable to such aspherical perturbations. The parameter space in which the perturbations on bound solutions inevitably become nonlinear is mapped. This instability has consequences for the Farhi-Guth-Guven mechanism for baby universe production via quantum tunneling.Comment: 16 PRD-style pages including 11 embedded figures; accepted by PRD. Revised version includes new solution, discussion of 'thermal activation', added reference, fixed typo

Hurdles for Recent Measures in Eternal Inflation

In recent literature on eternal inflation, a number of measures have been introduced which attempt to assign probabilities to different pocket universes by counting the number of each type of pocket according to a specific procedure. We give an overview of the existing measures, pointing out some interesting connections and generic predictions. For example, pairs of vacua that undergo fast transitions between themselves will be strongly favored. The resultant implications for making predictions in a generic potential landscape are discussed. We also raise a number of issues concerning the types of transitions that observers in eternal inflation are able to experience.Comment: 15 PRD-style pages, 5 figures, expanded discussion of measures in Sec. II, added reference

Aqueous & Non-Aqueous Phase Tracer Migration Through Differing Soil Textures

The National Grid Transco Company sponsored this project in order to promote the understanding of NAPL migration through b-horizon soils and retarding effects upon non aqueous species migration. Soil structure and texture was also studied using conservative (Bromide) and non-conservative (Phosphate) tracers. Experimental data was produced using a laboratory ½ metre scale automated lysimeter designed and constn1cted at Plymouth. The tracers were compared before oil injection, to calibrate differences in soil texture, and after oil injection to detect any changes in the flow patterns caused by the oil injection. It was found that the Crediton, Sollom and Conway soils respectively offered least resistance to the tracers with the non-conservative tracer behaving much more unpredictably than the conservative tracer. After oil injection it could be seen that the oil had heavily retarded the ability of the tracers to migrate from the injection site. This retardation was identified as analogous to perturbations of the soil structure. Statistical analysis of the data showed that the experiments were all internally self consistent and visible patterns could be seen in the corrected data caused by inclusion of oil in the injection site. Methods of dispersal for the oil and tracer are suggested in the concluding chapter with references to the work of previous authors. Development of a hazard assessment framework was facilitated by the simulation of soil structures using a pedo transfer function developed at the National Soils Resource Institute. To allow the modelling of soils the Pore-Cor software had an annealed simplex algorithm integrated into the data inversion engine to allow the simulation of 3-D soil structures using 2-D data from pedo transfer functions or experimentally derived water retention curves. An extensive sensitivity analysis upon the model highlighted limitations, due to the data set the current pedo transfer function is based upon. It was suggested that inclusion of choices of different pedo transfer functions could be used to overcome this problem. A suitable framework was derived for the identification of priority soils using a validated computer model. Experimental data was compared to the simulated data in order to try and develop an understanding of practical upscaling of the data. The use of the "Scaleway" method is discussed in the concluding Chapter.Tbe National Grid Transco pl