Crystallisation in a granular material

The athermal and dissipative nature of packings of grains is still challenging our understanding of their compaction as well as their crystallisation. For instance, some beads poured in a container get jammed in random disordered con gurations, which cannot be denser than 64%, the random closed packing (RCP) limit. Remarkably it has been suggested that the RCP bound is saturated with dense patterns of beads aggregated into polytetrahedral structures. Yet when a suitable vibration is applied, a packing of beads might start to order and some regular patterns appear. We present new experiments on the crystallisation of the packing of beads. By extending tapping techniques, we have obtained packings with volume fractions φ ranging from the RCP to the crystal (φ = 0.74). Computing tomography has been used to scan the internal structure of large packings (≈200,000 beads). Voronoi and Delaunay space partitions on the grain centres were performed to characterise the structural rearrangements during the crystallisation. This allows us to describe statistical properties of the local volume uctuations and the evolution of the densest patterns of beads. In terms of statistical description, a parameter based on the volume uctuations discloses different regimes during the transition. In terms of geometry, we con rm that polytetrahedral dense clusters are ubiquitous at the RCP. We describe some intrinsic features of these clusters such as rings of tetrahedra and show how they disappear as the crystal grows. This experiment enlightens how an athermal system jammed in a complex frustrated con guration is gradually converted into a periodic crystal

Mapping permeability in low-resolution micro-CT images: A multiscale statistical approach

We investigate the possibility of predicting permeability in low-resolution X-ray microcomputed tomography (µCT). Lower-resolution whole core images give greater sample coverage and are therefore more representative of heterogeneous systems; however, the lower resolution causes connecting pore throats to be represented by intermediate gray scale values and limits information on pore system geometry, rendering such images inadequate for direct permeability simulation. We present an imaging and computation workflow aimed at predicting absolute permeability for sample volumes that are too large to allow direct computation. The workflow involves computing permeability from high-resolution µCT images, along with a series of rock characteristics (notably open pore fraction, pore size, and formation factor) from spatially registered low-resolution images. Multiple linear regression models correlating permeability to rock characteristics provide a means of predicting and mapping permeability variations in larger scale low-resolution images. Results show excellent agreement between permeability predictions made from 16 and 64 µm/voxel images of 25 mm diameter 80 mm tall core samples of heterogeneous sandstone for which 5 µm/voxel resolution is required to compute permeability directly. The statistical model used at the lowest resolution of 64 µm/voxel (similar to typical whole core image resolutions) includes open pore fraction and formation factor as predictor characteristics. Although binarized images at this resolution do not completely capture the pore system, we infer that these characteristics implicitly contain information about the critical fluid flow pathways. Three-dimensional permeability mapping in larger-scale lower resolution images by means of statistical predictions provides input data for subsequent permeability upscaling and the computation of effective permeability at the core scale

Topological Persistence for Relating Microstructure and Capillary Fluid Trapping in Sandstones

Results from a series of two‐phase fluid flow experiments in Leopard, Berea, and Bentheimer sandstones are presented. Fluid configurations are characterized using laboratory‐based and synchrotron based 3‐D X‐ray computed tomography. All flow experiments are conducted under capillary‐dominated conditions. We conduct geometry‐topology analysis via persistent homology and compare this to standard topological and watershed‐partition‐based pore‐network statistics. Metrics identified as predictors of nonwetting fluid trapping are calculated from the different analytical methods and are compared to levels of trapping measured during drainage‐imbibition cycles in the experiments. Metrics calculated from pore networks (i.e., pore body‐throat aspect ratio and coordination number) and topological analysis (Euler characteristic) do not correlate well with trapping in these samples. In contrast, a new metric derived from the persistent homology analysis, which incorporates counts of topological features as well as their length scale and spatial distribution, correlates very well (R2 = 0.97) to trapping for all systems. This correlation encompasses a wide range of porous media and initial fluid configurations, and also applies to data sets of different imaging and image processing protocols.We gratefully acknowledge funding from the member companies of the ANU/UNSW Digicore Research Consortium, as well as the Australian Research Council. Adrian Sheppard is supported by Discovery Project DP160104995, Vanessa Robins is supported by ARC Future Fellowship FT140100604, and Anna Herring is supported by ARC Discovery Early Career Fellowship DE180100082

Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory

We show how discrete Morse theory provides a rigorous and unifying foundation for defining skeletons and partitions of grayscale digital images. We model a grayscale image as a cubical complex with a real-valued function defined on its vertices (the voxel values). This function is extended to a discrete gradient vector field using the algorithm presented in Robins, Wood, Sheppard TPAMI 33:1646 (2011). In the current paper we define basins (the building blocks of a partition) and segments of the skeleton using the stable and unstable sets associated with critical cells. The natural connection between Morse theory and homology allows us to prove the topological validity of these constructions; for example, that the skeleton is homotopic to the initial object. We simplify the basins and skeletons via Morse-theoretic cancellation of critical cells in the discrete gradient vector field using a strategy informed by persistent homology. Simple working Python code for our algorithms for efficient vector field traversal is included. Example data are taken from micro-CT images of porous materials, an application area where accurate topological models of pore connectivity are vital for fluid-flow modelling

Geometrical frustration in amorphous and partially crystallized packings of spheres

We study the persistence of a geometrically frustrated local order inside partially crystallized packings of equal-sized spheres. Measurements by x-ray tomography reveal previously unseen grain scale rearrangements occurring inside large three-dimensional packings as they crystallize. Three successive structural transitions are detected by a statistical description of the local volume fluctuations. These compaction regimes are related to the disappearance of densely packed tetrahedral patterns of beads. Amorphous packings of monodisperse spheres are saturated with these tetrahedral clusters at Bernal's limiting density (ϕ≈64%). But, no periodic lattice can be built upon these patterns; they are geometrically frustrated and are thus condemned to vanish while the crystallization occurs. Remarkably, crystallization-induced grain rearrangements can be interpreted in terms of the evolution of key topological features of these aggregates

Ecological and Management Implications of Climate Change Induced Shifts in the Phenology of Alewife (Alosa pseudoharengus)

Climate change is causing species to shift their phenology, or the timing of recurring life events such as migration and reproduction, in variable and complex ways. This can potentially result in mismatches or asynchronies in food and habitat resources that negatively impact individual fitness, population dynamics, and ecosystem function. This project seeks to improve our understanding of shifts in the timing of seasonal migration and spawning of adult anadromous alewife, Alosa psuedoherengus in seven natal stream systems within the state of Massachusetts: Acushnet, Agawam, Herring, Jones, Nemasket, Stoney Brook, and Town Brook Rivers. Initial analyses examined if and how the direction and magnitude of annual spawning run initiation, peak and end dates have shifted over recent decades. Preliminary results suggest that changes in alewife migration timing are not consistent across runs within Massachusetts. Trends from an overall analysis of all sites show a shift of earlier timing in run initiation dates and a shift towards later run end dates. Ongoing work seeks to evaluate the extent of estuarine habitat availability around each of the seven run sites; this will be accomplished by measuring the area of continuous wetland habitat downstream from alewife spawning ponds. Additionally, shifts in the timing of alewife migration in relation to environmental conditions such as river and sea surface temperature, river flow and winter conditions will be evaluated. Project results will help managers assess the vulnerability of alewife and other coastal species to the interactive effects of environmental and anthropogenic stressors influencing their populations across the region

Iterative reconstruction optimisations for high angle cone-beam micro-CT

We address several acquisition questions that have arisen for the high cone-angle helical-scanning micro-CT facility developed at the Australian National University. These challenges are generally known in medical and industrial cone-beam scanners but can be neglected in these systems. For our large datasets, with more than 2048³ voxels, minimising the number of operations (or iterations) is crucial. Large cone-angles enable high signal-to-noise ratio imaging and a large helical pitch to be used. This introduces two challenges: (i) non-uniform resolution throughout the reconstruction, (ii) over-scan beyond the region-of-interest significantly increases required reconstructed volume size. Challenge (i) can be addressed by using a double-helix or lower pitch helix but both solutions slow down iterations. Challenge (ii) can also be improved by using a lower pitch helix but results in more projections slowing down iterations. This may be overcome using less projections per revolution but leads to more iterations required. Here we assume a given total time for acquisition and a given reconstruction technique (SART) and seek to identify the optimal trajectory and number of projections per revolution in order to produce the best tomogram, minimise reconstruction time required, and minimise memory requirements

An adaptive volumetric flux boundary condition for lattice Boltzmann methods

This paper presents a spatially and temporally adaptive boundary condition to specify the volumetric flow rate for lattice Boltzmann methods. The approach differs from standard velocity boundary conditions because it allows the velocity to vary over the boundary region provided that the total flux through the boundary satisfies a prescribed constraint, which is a typical scenario for laboratory experimental studies. This condition allows the boundary pressure to adjust dynamically to yield a specified boundary flow rate as a means to avoid unphysical mismatch between the boundary velocity and the interior flow field that can arise when a standard velocity boundary condition is applied. The method is validated for simulation of one- and two-fluid flow in complex materials, with conditions determined to match typical experiments used to study flow in porous media.This work was supported by Army Research Office grant W911NF-14-1-02877 and National Science Foundation grant 1619767. An award of computer time was provided by the Department of Energy INCITE program. This research also used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DEAC05-00OR22725. Z.L. acknowledges the Australian Government Research Training Program (RTP) Scholarship and the Robert and Helen Crompton travel fund. A.P.S. acknowledges the support of an Australian Research Council Future Fellowship through project FT100100470. This research also used resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government