Hybrid finite element–finite volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks

The generation of computational meshes of complex geological objects is a challenge: their shape needs to be retained, resolution has to adapt to local detail, and variations of material properties in the objects have to be represented. Also mesh refinement and adaptation must be sufficient to resolve variations in the computed variable(s). Here, we present an unstructured hybrid finite element, node‐centred finite‐volume discretization suitable for solving fluid flow, reactive transport, and mechanical partial differential equations on a complex geometry with inhomogeneous material domains. We show that resulting meshes accurately capture free‐form material interfaces as defined by non‐uniform rational B‐spline curves and surfaces. The mesh discretization error is analysed for the elliptic pressure equation and an error metric is introduced to guide mesh refinement. Finite elements and finite volumes are represented in parametric space and integrations are conducted numerically. Subsequently, integral properties are mapped to physical space using Jacobian transformations. This method even retains its validity when the mesh is deformed. The resulting generic formulation is demonstrated for a transport calculation performed on a complex discrete fracture model.     

The Judicial Bookshelf

"In law, also, men make a difference," ¹ counseled Felix Frankfurter the year before his appointment to the Supreme Court. Frankfurter highlighted one of the three critical components of judicial decision-making in constitutional law: alongside the text of the Constitution itself and the cases that pose various questions for decision are the women and men who answer those questions. Those answers, as Frankfurter believed, are invariably influenced by the values Justices bring with them to the Bench. Yet he was expressing no newfound truth, but an awareness that had been apparent for a long time. "Impressed with a conviction that the true administration of justice is the firmest pillar of good government," President George Washington wrote future Attorney General Edmund Randolph in 1789, "I have considered the first arrangement of the judicial department as essential to the happiness of our country and the stability of its political system." To be sure, the Court's role in the political system was unclear, but Washington realized the impact the Court might have in the young Republic. This required, he told Randolph, "the selection of the fittest characters to expound the laws and dispense justice." ² And as he filled the six seats Congress had authorized for the Supreme Court, the first President made sure that each nominee was a strong supporter of the new Constitution.     

Shape matters: assessing regional variation of Bell Beaker projectile points in Central Europe using geometric morphometrics

Despite the large-scale expansion of Bell Beaker phenomenon, there is a tension between the normative Bell Beaker material culture categories and their local objectification in the form of real artefacts. Stone projectile points provide an opportunity to evaluate how much was the general category of such a point influenced by regional and local factors. The aim of this paper is to explore shape and size variation of Central European Bell Beaker projectile points from Moravia (Czech Republic) to elucidate factors responsible for this variation. The sample consists of 194 projectile points from 54 Central European Bell Beaker sites (2500–2300/2200 BC) distributed in Morava River catchment. The size and shape of projectile points were studied by landmark-based geometric morphometrics and expressed as shape groups, which have been assessed in terms of their spatial distribution, raw material, and reutilization. Although several shape categories of points were identified, there is a strong degree of uniformity in the research sample. The dominant shape category (75.4 % of points) was pervasive across geographic space and was not significantly affected either by raw material or reutilization. A lower degree of reutilization of points is interpreted as a consequence of a non-utilitarian role of projectile points, which represented a critical component of Bell Beaker mortuary practices.     

Neutron activation analysis of stone from the Chadron Formation and a Clovis Site on the Great Plains

Cryptocrystalline silicates from the Chadron Formation were widely used by prehistoric human groups in the Great Plains of North America. There are two documented quarry areas: Flattop Butte in Colorado and the White River Badlands of South Dakota. Cryptocrystalline silicates from these sources are visually indistinguishable, making it difficult to determine the sources of artefacts found at archaeological sites. In this investigation, neutron activation analysis is used to distinguish the two sources. This technique also identifies lithic material from the Clovis-age Eckles site in Kansas as being from Flattop Butte.