Three-Dimensional Elastic Compatibility: Twinning in Martensites

We show how the St.Venant compatibility relations for strain in three dimensions lead to twinning for the cubic to tetragonal transition in martensitic materials within a Ginzburg-Landau model in terms of the six components of the symmetric strain tensor. The compatibility constraints generate an anisotropic long-range interaction in the order parameter (deviatoric strain) components. In contrast to two dimensions, the free energy is characterized by a "landscape" of competing metastable states. We find a variety of textures, which result from the elastic frustration due to the effects of compatibility. Our results are also applicable to structural phase transitions in improper ferroelastics such as ferroelectrics and magnetoelastics, where strain acts as a secondary order parameter

Droplet Fluctuations in the Morphology and Kinetics of Martensites

We derive a coarse grained, free-energy functional which describes droplet configurations arising on nucleation of a product crystal within a parent. This involves a new `slow' vacancy mode that lives at the parent-product interface. A mode-coupling theory suggests that a {\it slow} quench from the parent phase produces an equilibrium product, while a {\it fast} quench produces a metastable martensite. In two dimensions, the martensite nuclei grow as `lens-shaped' strips having alternating twin domains, with well-defined front velocities. Several empirically known structural and kinetic relations drop out naturally from our theory.Comment: 4 pages, REVTEX, and 3 .eps figures, compressed and uuencoded, Submitted to Phys. Rev. Let

Cost-Effectiveness Analysis of Stereotactic Ablative Body Radiation Therapy Compared With Surgery and Radiofrequency Ablation in Two Patient Cohorts: Metastatic Liver Cancer and Hepatocellular Carcinoma

Aims: To compare the cost-effectiveness of stereotactic ablative body radiation therapy (SABR) with radiofrequency ablation and surgery in adult patients with metastatic liver cancer and hepatocellular carcinoma (HCC). / Materials and methods: Two patient cohorts were assessed: liver oligometastases and HCC. For each patient cohort, a decision analytic model was constructed to assess the cost-effectiveness of interventions over a 5-year horizon. A Markov process was embedded in the decision model to simulate the possible prognosis of cancer. Data on transition probabilities, survival, side-effects, quality of life and costs were obtained from published sources and the SABR Commissioning through Evaluation (CtE) scheme. The primary outcome was the incremental cost-effectiveness ratio with respect to quality-adjusted life-years. The robustness of the results was examined in a sensitivity analysis. Analyses were conducted from a National Health Service and Personal Social Services perspective. / Results: In the base case analysis, which assumed that all three interventions were associated with the same cancer progression rates and mortality rates, SABR was the most cost-effective intervention for both patient cohorts. This conclusion was sensitive to the cancer progression rate, mortality rate and cost of interventions. Assuming a willingness-to-pay threshold of £20 000 per quality-adjusted life-year, the probability that SABR is cost-effective was 57% and 50% in liver oligometastases and HCC, respectively. / Conclusions: Our results indicate a potential for SABR to be cost-effective for patients with liver oligometastases and HCC. This finding supports further investigation in clinical trials directly comparing SABR with surgery and radiofrequency ablation

Thermodynamics of volume collapse transitions in cerium and related compounds

We present a non-linear elastic model of a coherent transition with discontinuous volume change in an isotropic solid. The model reproduces the anomalous thermodynamics typical of coherent equilibrium including intrinsic hysteresis (for a pressure driven experiment) and a negative bulk modulus. The novelty of the model is that the statistical mechanics solution can be easily worked out. We find that coherency leads to an infinite-range density--density interaction, which drives classical critical behavior. The pressure width of the hysteresis loop shrinks with increasing temperature, ending at a critical point at a temperature related to the shear modulus. The bulk modulus softens with a 1/2 exponent at the transition even far from the critical point. Many well known features of the phase diagram of Ce and related systems are explained by the model.Comment: Acta Materialia, in pres

Disorder-Driven Pretransitional Tweed in Martensitic Transformations

Defying the conventional wisdom regarding first--order transitions, {\it solid--solid displacive transformations} are often accompanied by pronounced pretransitional phenomena. Generally, these phenomena are indicative of some mesoscopic lattice deformation that ``anticipates'' the upcoming phase transition. Among these precursive effects is the observation of the so-called ``tweed'' pattern in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. The predicted phase diagram and glassy behavior have been verified by numerical simulations, and diffraction patterns of simulated systems are found to compare well with experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.Comment: 43 pages in TeX, plus figures. Most figures supplied separately in uuencoded format. Three other figures available via anonymous ftp

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state

Modelling avalanches in martensites

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45612-6_

The SLUGGS survey: the mass distribution in early-type galaxies within five effective radii and beyond

We study mass distributions within and beyond 5 effective radii (Re) in 23 early-type galaxies from the SAGES Legacy Unifying Globulars and Galaxies Survey, using their globular cluster (GC) kinematic data. The data are obtained with Keck/DEep Imaging Multi-Object Spectrograph, and consist of line-of-sight velocities for ̃3500 GCs, measured with a high precision of ̃15 km s-1 per GC and extending out to ̃13 Re. We obtain the mass distribution in each galaxy using the tracer mass estimator of Watkins et al. and account for kinematic substructures, rotation of the GC systems and galaxy flattening in our mass estimates. The observed scatter between our mass estimates and results from the literature is less than 0.2 dex. The dark matter fraction within 5 Re (fDM) increases from ̃0.6 to ̃0.8 for low- and high-mass galaxies, respectively, with some intermediate-mass galaxies (M* ̃ 1011 M☉) having low fDM ̃ 0.3, which appears at odds with predictions from simple galaxy models. We show that these results are independent of the adopted orbital anisotropy, stellar mass-to-light (M/L) ratio, and the assumed slope of the gravitational potential. However, the low fDM in the ̃1011 M☉ galaxies agrees with the cosmological simulations of Wu et al. where the pristine dark matter distribution has been modified by baryons during the galaxy assembly process. We find hints that these M* ̃ 1011 M☉ galaxies with low fDM have very diffuse dark matter haloes, implying that they assembled late. Beyond 5 Re, the M/L gradients are steeper in the more massive galaxies and shallower in both low and intermediate mass galaxies

Implementation science protocol for a participatory, theory-informed implementation research programme in the context of health system strengthening in sub-Saharan Africa (ASSET-ImplementER).

Objectives ASSET (Health System Strengthening in sub-Saharan Africa) is a health system strengthening (HSS) programme involving eight work-packages (ie, a research study that addresses a specific need for HSS) that aims to develop solutions that support high-quality care. Here we present the protocol for the implementation science (IS) theme within ASSET (ASSET-ImplmentER) that aims to understand what HSS interventions work, for whom and how, and how IS methodologies can be adapted to improve the HSS interventions within resource-poor contexts. Settings Publicly funded health facilities in rural and urban areas in in Ethiopia, South Africa, Sierra Leone, and Zimbabwe. Participants Research staff including principal investigators, coinvestigators, field staff, PhD students, and research assistants. Interventions Work-packages use a mixed-methods effectiveness–effectiveness hybrid designs. At the end of the pre-implementation phase, a workshop is held whereby the IS theme, jointly with ASSET work-packages apply IS determinant frameworks to research findings to identify factors that influence the effectiveness of delivering evidence-informed care. Determinants are used to select a set of HSS interventions for further evaluation, where work-packages also theorise selective mechanisms. In the piloting and rolling implementation phase, work-packages pilot the HSS interventions. An iterative process then begins involving evaluation, reflection and adaptation. Throughout this phase, IS determinant frameworks are applied to monitor and identify barriers/enablers to implementation. Selective mechanisms of action are also investigated. Implementation outcomes are evaluated using qualitative and quantitative methods. The psychometric properties of outcome measures including acceptability, appropriateness and feasibility are also evaluated. In a final workshop, work-packages come together, to reflect and explore the utility of the selected IS methods and provide suggestions for future use. Structured templates are used to organise and analyse common and heterogeneous patterns across work-packages. Qualitative data are analysed using thematic analysis and quantitative data are analysed using means and proportions. Conclusions We use a novel combination of IS methods at a programmatic level to facilitate comparisons of determinants and mechanisms that influence the effectiveness of HSS interventions in achieving implementation outcomes across different contexts. The study also contributes conceptual development and clarification at the underdeveloped interface of IS, HSS and global health