Triassic stratigraphy and sedimentology in central England

The Triassic rocks of Central England consist of three major stratigraphic units: Sherwood Sandstone Group, Mercia Mudstone Group, and Penarth Group. The lower part of the Sherwood Sandstone Group represented by the Kidderminster, Cannock Chase, and Polesworth Formations represents pebbly braided river deposits carried by a major fluvial system flowing to the North-Northwest. The upper part of the Sherwood Sandstone Group includes the Wildmoor and Bromsgrove Sandstone Formations, the deposits of a sandy alluvial system. The Mercia Mudstone Group represents quiet-water deposits of marginal palya type which were subjected to occasional marine flooding. The overlying Penarth Group represent shallow marine and lagoonal environment associated with the Rhaetian marine transgression. The mineralogy of the Triassic sandstones indicates that the main source was from medium to low rank metamorphic rocks with additional supplies from igneous and metamorphic rocks. The study of size-composition trends shows that the climate was semiarid in early Triassic time and became more humid later. The Triassic sandstones show a variety of diagenetic features typical of continental red beds; these include: 1. the dissolution of unstable ferromagnesian silicates, 2. the replacement of detrital grains by clay, 3. the pseudomorphism of biotite by haematite, and 4. the formation of a suite of authigenic minerals including quartz, illite, mixed-layer illite-montmorillonite, kaolinite, k-feldspar, haematite, titanium oxide and later carbonate cement. Palaeomagnetic studies of selected samples show that the magnetization is muticomponent with the various components being carried by different textural phases of haematite.

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

Representing spray zone with cross flow as a well-mixed compartment in a high shear granulator

The spray zone is an important region to control nucleation of granules in a high shear granulator. In this study, a spray zone with cross flow is quantified as a well-mixed compartment in a high shear granulator. Granulation kinetics is quantitatively derived at both particle-scale and spray zone-scale. Two spatial decay rates, DGSDR (droplet-granule spatial decay rate) ζDG and DPSDR (droplet-primary particle spatial decay rate) ζDP, which are functions of volume fraction and diameter of particulate species within the powder bed, are defined to simplify the deduction. It is concluded that in cross flow, explicit analytical results show that the droplet concentration is subject to exponential decay with depth which produces a numerically infinite depth of spray zone in a real penetration process. In a well-mixed spray zone, the depth of the spray zone is 4/(ζDG + ζDP) and π2/3(ζDG + ζDP) in cuboid and cylinder shape, respectively. The first-order droplet-based collision rates of, nucleation rate B0 and rewetting rate RW0 are uncorrelated with the flow pattern and shape of the spray zone. The second-order droplet-based collision rate, nucleated granule-granule collision rate RGG, is correlated with the mixing pattern. Finally, a real formulation case of a high shear granulation process is used to estimate the size of the spray zone. The results show that the spray zone is a thin layer at the powder bed surface. We present, for the first time, the spray zone as a well-mixed compartment. The granulation kinetics of a well-mixed spray zone could be integrated into a Population Balance Model (PBM), particularly to aid development of a distributed model for product quality prediction.