Modeling doline populations with logistic growth functions

Initiation and evolution of a large karst depression population consisting of parent and daughter dolines were spatially and temporally modeled using logistic growth functions. Logistic growth models are well suited for analyzing doline population initiation and evolution because they reflect the density‐dependent growth mechanisms present in the evolution of karst depressions. Seven assumptions based upon previous studies were refined into mathematical statements and tested using more than 2000 dolines from a subpopulation of both parent and daughter karst depressions on the Western Highland Rim and Pennyroyal Plain of Tennessee and Kentucky. Logistic growth models quantify the initiation and evolution of doline populations and interface well with recent models describing the evolution of three‐dimensional conduit systems. Logistic growth models should apply to modeling other doline populations in karst terranes with hydraulically efficient, three‐dimensional conduit systems. Copyright © 2006 John Wiley & Sons, Ltd.     

A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a discrete-in-time setting. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a continuous in-time setting for a strictly positive constrained specific storage coefficient. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation, and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

A time-distribution study of doline collapse: Framework for prediction

A temporal analysis of doline collapse on the Western Highland Rim (Tennessee) indicated one approach to estimating the probability of collapse in areas where the geologic and hydrologic criteria associated with collapse have been identified. The distribution of collapse was examined for trend, autocorrelation, and goodness of fit. The distribution of doline collapse during one 12-month period conformed to a Poisson distribution with a mean occurrence rate of λ=0.346 collapses per week and with the interoccurrence times being exponentially distributed (0.01 level). Although the proposed model is spatially and temporally restricted, it may provide an initial framework for estimating the probability of doline collapse in other karst terrains of similar geologic and hydrologic settings.     

Stresses in column-supported hyperboloidal shells subject to seismic loading

The computation of stresses within a finite element displacement method analysis of a shell of revolution is considered. The common procedure of applying the kinematic and constitutive laws to the displacement functions is examined and justified for models where the displacements are represented by high-order polynomial expansions. Also, two alternative computational formats within this technique are explored. The influence of the column-supported base condition on a hyperboloidal shell of revolution is studied with respect to the stresses calculated from a response spectrum analysis. These studies emphasize the importance of accurately modelling the base region of a column-supported shell such as a hyperbolic cooling tower.     

A suborbital payload for soft X-ray spectroscopy of extended sources

We present a suborbital rocket payload capable of performing soft X-ray spectroscopy on extended sources. The payload can reach resolutions of ??100 (??/ ????) over sources as large as 3.25° in diameter in the 17?C107 Å bandpass. This permits analysis of the overall energy balance of nearby supernova remnants and the detailed nature of the diffuse soft X-ray background. The main components of the instrument are: wire grid collimators, off-plane grating arrays and gaseous electron multiplier detectors. This payload is adaptable to longer duration orbital rockets given its comparatively simple pointing and telemetry requirements and an abundance of potential science targets.     

Risks of shifting baselines highlighted by anecdotal accounts of New Zealand's snapper (Pagrus auratus) fishery

Anecdotal data sources may constitute an important component of the information available about an exploited species, as record keeping may not have occurred until after exploitation began. Here, we aimed to fill any gaps in the exploitative history of the sparid snapper (Pagrus auratus), using social and historical research methods. Social research consisted of interviews with recreational fishers, focusing on the most and largest snapper they had caught. In addition, the diary‐logs of two recreational fishers were analysed. Historical research consisted of investigation of old books, photos, archives and unpublished sources unconventional to fishery science. Interviews with fishers demonstrated no or weak trends in snapper abundance or size, and were likely impeded by a lack of ability to detect change in a fish stock that may still be considered abundant. The fishers’ perception of change, however, largely reflected recent experiences (last c. 10 years), when biomass is understood to have increased, and mostly did not consider experiences before the 1980s. Alternatively, diary‐logs of fisher catch rates produced a pattern that matched formal stock assessments of snapper biomass, suggesting declines in abundance up until the 1990s and an increase in biomass after that time. Historical research, although more qualitative, had the ability to investigate periods where formal records were not kept and described a fishery vastly different from the current one. Snapper were easily caught, in great abundance and in unusual locations. Localised depletion of snapper was first noticed in the early 20th century, despite spectacular catches of snapper occurring after that time. Snapper behaviour was also likely different, with visual sightings of snapper by onlookers a common occurrence. Although predictions from stock assessment models are consistent with that of the anecdotes listed here (i.e., high biomass in the past), these anecdotes are valuable as they explain lost biomass in a perspective meaningful to all. This perspective may be valuable for managers trying to consider the non‐financial value of a shared fishery but, if unrecognised, represents a shifting baseline.     

Pediment response to drainage basin evolution in south-central Arizona

The Sonoran Desert portion of the Basin and Range physiographic province contains a number of streams that now flow across once-closed basins. We explore here the research questions of if and how granitic rock pediments respond to the transition from rimming endorheic basins to bordering through-flowing streams. Granitic rock pediments of the northern Usery and eastern McDowell Mountains once graded to the closed Miocene–Pliocene Pemberton basin that occupied the present-day location of the confluence of the Salt and Verde Rivers. The process of lake overflow, which integrated these rivers, first aggraded fill terraces that, in turn, caused aggradation of a mantle of transported grus on bedrock pediments. Subsequent episodic incision of the Salt and Verde rivers lowered the base level; this led to the development of erosional features such as rolling topography of a degrading pediment mantle; exposure of the former piedmont angle and its associated zones of enhanced bedrock decay and regolith carbonate; and exposure of spheroidally weathered bedrock and emerging tors, some of which experienced 20^th century erosion. The granitic pediments of the former Pemberton Basin, which now transport grus to the Salt and Verde rivers, have actively adjusted to aggradational and degradational events associated with drainage integration and do not appear to be inherited from an ancient wet climatic interval.