Numerical calculation for the flow of submerged bodies under a free surface

The flow field generated by a Rankine body moving under a free surface in afinite-depth water is calculated by potential theory. Velocity field generated by a source located at the origin is calculated first by using highly efficient and adaptive quadratures of the QUADPACK library. This solution is used for generating the flow around a Rankine body by locating a source and an equal strength sink along the body axis. Results agree well with the existing literature.     

Isotopic composition of xenon in petroleum from the shell bullwinkle field

We have measured the abundance and isotopic composition of xenon in petroleum samples from the Shell Bullwinkle Field off the coast of Louisiana. We used an oxidation and purification procedure designed to insure complete extraction and clean up of xenon from the petroleum. The xenon isotopic composition was found to be similar to the atmospheric value for one petroleum sample. While the results of the second sample suggest possible enrichment of the heavier isotopes, the errors associated with these excesses preclude a definitive statement to that effect. No monoisotopic enrichment in¹²⁹Xe was detected in either sample, the presence of which might have allowed us to deduce the petroleum age. Our results represent only the second xenon measurement from petroleum, and the concentrations are within the range of values published in the earlier report.     

Advances in travel geometry and urban modelling

Urban travel geometry is a generalization of patterns of movement in cities and regions where route configuration and prevailing traffic speeds constrain or direct movement in distinctive and repeatable patterns. In this paper we use these properties to construct time surfaces on which distance equates to the time of travel in the urban plane. Such surfaces can be two- or three-dimensional and are useful in the study of urban structure, locational analysis, transport planning and traffic management. A particular niche addressed in this paper is non-conformal time surface transformations in which speed or the cost of travel is constrained according to co-ordinate directions. It is argued that such models may be more suited to gridded and orbital-radial cities than previously used conformal transformations. After explaining the rationale behind the approach, a mathematical basis is developed and several calibrated examples are provided based on regions in the UK. The paper concludes with some examples of potential applications, and an annex provides a detailed mathematical framework. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mimetic Finite Difference Methods for Diffusion Equations

This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous anisotropic materials. These difference operators satisfy the fundamental identities, conservation laws and theorems of vector and tensor calculus on nonorthogonal, nonsmooth, structured and unstructured computational grids. We provide explicit approximations for equations in two dimensions with discontinuous anisotropic diffusion tensors. We mention the similarities and differences between the new methods and mixed finite element or hybrid mixed finite element methods.     

SATURATION MAGNETIZATION MEASUREMENTS OF CARBONACEOUS CHONDRITES

The saturation magnetization of some carbonaceous chondrites was studied using a Faraday balance. The Faraday balance was shown to be an accurate (± 3%), reliable technique for measuring saturation magnetization by comparison with vibrating-sample magnetometer measurements on the same samples. Hyman and Rowe (1983) previously used these saturation magnetization measurements to measure the magnetite content of the five CI chondrites. Here, we present measurements on the magnetite contents of some CM2, CV3 and a CV5 chondrites. The method was also used to measure the content of metallic nickel-iron in Ornans, 3.4 ± 0.3%. Of the CM2 chondrites examined, only Bells, Essebi and Haripura had magnetite contents over about 1% by weight. A number of CV chondrites have magnetite between 2.3 and 13%, with little or no metallic iron. Leoville and Vigarano contain both magnetite and metallic iron, complicating the saturation magnetization results. Arch and Allende have very little metallic iron or magnetite, probably < 1% of either. This technique measures only ferrimagnetic magnetite; superparamagnetic magnetite with particle size < 300Å is ignored.     

Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

Mathematical Geosciences - We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic...     

Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

We propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. The method allows for the level of accuracy to be a user-controlled parameter.