An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy

Published versio

Claw length recommendations for dairy cow foot trimming

The aim was to describe variation in length of the dorsal hoof wall in contact with the dermis for cows on a single farm, and hence, derive minimum appropriate claw lengths for routine foot trimming. The hind feet of 68 Holstein-Friesian dairy cows were collected post mortem, and the internal structures were visualised using x-ray mCT. The internal distance from the proximal limit of the wall horn to the distal tip of the dermis was measured from crosssectional sagittal images. A constant was added to allow for a minimum sole thickness of 5 mm and an average wall thickness of 8 mm. Data were evaluated using descriptive statistics and two-level linear regression models with claw nested within cow. Based on 219 claws, the recommended dorsal wall length from the proximal limit of hoof horn was up to 90 mm for 96 per cent of claws, and the median value was 83 mm. Dorsal wall length increased by 1 mm per year of age, yet 85 per cent of the null model variance remained unexplained. Overtrimming can have severe consequences; the authors propose that the minimum recommended claw length stated in training materials for all Holstein-Friesian cows should be increased to 90 mm

Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition gradient energy to capture solute trapping, and is therefore suited for studying phenomena where the width of the interface plays an important role. Derivation of the inhomogeneous free energy functional from a Taylor expansion of homogeneous free energy reveals how the interfacial properties of each component and phase may be specified under a mass constraint. A diffusion potential for components was defined away from the dilute solution limit, and a multi-obstacle barrier function was used to constrain phase fractions. The model was used to simulate solidification via nucleation, premelting at phase boundaries and triple junctions, the intrinsic instability of small particles, and solutal melting resulting from differing diffusivities in solid and liquid. The shape of metastable free energy surfaces is found to play an important role in microstructure evolution and may explain why some systems premelt at phase boundaries and phase triple junctions while others do not.Comment: 14 pages, 8 figure

On the stable discretization of strongly anisotropic phase field models with applications to crystal growth

We introduce unconditionally stable finite element approximations for anisotropic Allen--Cahn and Cahn--Hilliard equations. These equations frequently feature in phase field models that appear in materials science. On introducing the novel fully practical finite element approximations we prove their stability and demonstrate their applicability with some numerical results. We dedicate this article to the memory of our colleague and friend Christof Eck (1968--2011) in recognition of his fundamental contributions to phase field models.Comment: 20 pages, 8 figure

Indium coverage of the Si(111)- 7×3 -in surface

The indium coverage of the Si(111)-√7 × √3-In surface is investigated by means of x-ray photoelectron spectroscopy and first-principles density functional theory calculations. Both experimental and theoretical results indicate that the In coverage is a double layer rather than a single layer. Moreover, the atomic structure of the Si(111)-√7 × √3-In surface is discussed by comparing experimental with simulated scanning tunneling microscopy (STM) images and scanning tunneling spectra with the calculated density of states. Our structural assignment agrees with previous studies, except for the interpretation of experimental STM images

Associations between sole ulcer, white line disease and digital dermatitis and the milk yield of 1824 dairy cows on 30 dairy cow farms in England and Wales from February 2003–November 2004

The milk yields of 1824 cows were used to investigate the effect of lesion-specific causes of lameness, based on farmer treatment and diagnosis of lame cows, on milk yield. A three level hierarchical model of repeated test day yields within cows within herds was used to investigate the impact of lesion-specific causes of lameness (sole ulcer, white line disease, digital dermatitis and other causes) on milk yield before and after treatment compared with unaffected cows. Cattle which developed sole ulcer (SU) and white line disease (WLD) were higher yielding cattle before they were diagnosed. Their milk production fell to below that of the mean of unaffected cows before diagnosis and remained low after diagnosis. In cattle which developed digital dermatitis (DD) there was no significant difference in milk yield before treatment and a slightly raised milk yield immediately after treatment. The estimated milk loss attributable to SU and WLD was approximately 570kg and 370kg respectively. These results highlight that specific types of lameness vary by herds and within herds they are associated with higher yielding cattle. Consequently lesion-specific lameness reduction programmes targeting the cow and farm specific causes of lameness might be more effective than generic recommendations. They also highlight the importance of milk loss when estimating the economic impact of SU and WLD on the farms profitability

Isolation of digital dermatitis treponemes from hoof lesions in wild North American elk (Cervus elaphus) in Washington State, USA

Since 2008, a large increase in the numbers of cases of lameness have been seen in wild North American elk (Cervus elaphus) from Washington State, USA. The most recent cases manifested as foot lesions similar both clinically and pathologically to those seen in digital dermatitis (DD) in cattle and sheep, a disease with a bacterial etiopathogenesis. To determine whether the same bacteria considered responsible for DD are associated with elk lameness, lesion samples were subjected to bacterial isolation studies and PCR assays for three phylogroups of relevant DD treponemes. The DD treponemes were isolated from lesional tissues but not from control feet or other areas of the diseased foot (including the coronary band or interdigital space), suggesting that the bacteria are strongly associated with DD lesions and may therefore be causal. In addition, PCR analysis revealed that all three unique DD treponeme phylotypes were found in elk hoof disease, and in 23 of samples, all 3 DD-associated treponemes were present in lesions. Sequence analysis of the 16S rRNA gene showed that the elk lesion treponemes were phylogenetically almost identical to those isolated from cattle and sheep DD lesions. The isolates were particularly similar to two of the three culturable DD treponeme phylotypes: specifically, the Treponema medium/Treponema vincentii-like and Treponema phagedenis-like DD spirochetes. The third treponeme culturable phylogroup (Treponema pedis), although detected by PCR, was not isolated. This is the first report describing isolation of DD treponemes from a wildlife host, suggesting that the disease may be evolving to include a wider spectrum of cloven-hoofed animals. Copyright © 2015, American Society for Microbiology. All Rights Reserved

Stress- and diffusion-induced interface motion: Modelling and numerical simulations

Accepted versio