Some examples of rank one convex functions in dimension two

We study the rank one convexity of some functions f(ξ) where ξ is a 2 × 2 matrix. Examples such as |ξ|2α + h(detξ) and | ξ |2α (| ξ |2 − γdet ξ) are investigated. Numerical computations are done on the example of Dacorogna and Marcellini, indicating that this function is quasiconve

Multimodal discrimination of immune cells using a combination of Raman spectroscopy and digital holographic microscopy

This work was supported by the UK Engineering and Physical Sciences Research Council under grant EP/J01771X/1, A European Union FAMOS project (FP7 ICT, 317744), and the ’BRAINS’ 600th anniversary appeal, and Dr. E. Killick. We would also like to thank The RS Macdonald Charitable Trust for funding support. KD acknowledges support of a Royal Society Leverhulme Trust Senior Fellowship. This work was also supported by the PreDiCT-TB consortium [IMI Joint undertaking grant agreement number 115337, resources of which are composed of financial contribution from the European Union’s Seventh Framework Programme (FP7/2007-2013) and EFPIA companies’ in kind contribution (www.imi.europa.eu)]The ability to identify and characterise individual cells of the immune system under label-free conditions would be a significant advantage in biomedical and clinical studies where untouched and unmodified cells are required. We present a multi-modal system capable of simultaneously acquiring both single point Raman spectra and digital holographic images of single cells. We use this combined approach to identify and discriminate between immune cell populations CD4+ T cells, B cells and monocytes. We investigate several approaches to interpret the phase images including signal intensity histograms and texture analysis. Both modalities are independently able to discriminate between cell subsets and dual-modality may therefore be used a means for validation. We demonstrate here sensitivities achieved in the range of 86.8% to 100%, and specificities in the range of 85.4% to 100%. Additionally each modality provides information not available from the other providing both a molecular and a morphological signature of each cell.Publisher PDFPeer reviewe

Relationship between solidification microstructure and hot cracking susceptibility for continuous casting of low-carbon and high-strength low-alloyed steels: A phase-field study

© The Minerals, Metals & Materials Society and ASM International 2013Hot cracking is one of the major defects in continuous casting of steels, frequently limiting the productivity. To understand the factors leading to this defect, microstructure formation is simulated for a low-carbon and two high-strength low-alloyed steels. 2D simulation of the initial stage of solidification is performed in a moving slice of the slab using proprietary multiphase-field software and taking into account all elements which are expected to have a relevant effect on the mechanical properties and structure formation during solidification. To account for the correct thermodynamic and kinetic properties of the multicomponent alloy grades, the simulation software is online coupled to commercial thermodynamic and mobility databases. A moving-frame boundary condition allows traveling through the entire solidification history starting from the slab surface, and tracking the morphology changes during growth of the shell. From the simulation results, significant microstructure differences between the steel grades are quantitatively evaluated and correlated with their hot cracking behavior according to the Rappaz-Drezet-Gremaud (RDG) hot cracking criterion. The possible role of the microalloying elements in hot cracking, in particular of traces of Ti, is analyzed. With the assumption that TiN precipitates trigger coalescence of the primary dendrites, quantitative evaluation of the critical strain rates leads to a full agreement with the observed hot cracking behavior. © 2013 The Minerals, Metals & Materials Society and ASM International

Analysis of vaginal microbicide film hydration kinetics by quantitative imaging refractometry

We have developed a quantitative imaging refractometry technique, based on holographic phase microscopy, as a tool for investigating microscopic structural changes in water-soluble polymeric materials. Here we apply the approach to analyze the structural degradation of vaginal topical microbicide films due to water uptake. We implemented transmission imaging of 1-mm diameter film samples loaded into a flow chamber with a 1.5×2 mm field of view. After water was flooded into the chamber, interference images were captured and analyzed to obtain high resolution maps of the local refractive index and subsequently the volume fraction and mass density of film material at each spatial location. Here, we compare the hydration dynamics of a panel of films with varying thicknesses and polymer compositions, demonstrating that quantitative imaging refractometry can be an effective tool for evaluating and characterizing the performance of candidate microbicide film designs for anti-HIV drug delivery. © 2014 Rinehart et al

Some examples of rank one convex functions in dimension two

SynopsisWe study the rank one convexity of some functionsf(ξ) where ξ is a 2 × 2 matrix. Examples such as |ξ|2α+h(detξ) and | ξ |2α(| ξ |2− γdet ξ) are investigated. Numerical computations are done on the example of Dacorogna and Marcellini,indicating that this function is quasiconvex.</jats:p

A 3D Granular Model Of Equiaxed-Granular Solidification

The solidification of an aluminum-copper alloy has been simulated in 3D using a granular model. Compared to previous similar 2D approaches for where only one phase is continuous, the extension to 3D allows for concurrent continuity of the solid and liquid phases. This concurrent continuity is a key factor in the formation of the solidification defect known as hot tearing. In this 3D model, grains are modeled as polyhedrons based on a Voronoi tessellation of a pseudo-random set of nucleation centers. Solidification within each polyhedron is calculated using a back-diffusion model. By performing a series of simulations over a range of grain sizes and cooling rates, the percolation of the solid grains is determined. The results, which indicate that the grain size and cooling rates play an important role in hot tear formation, constitute a basis on which feeding and deformation calculations will be carried out further

Morphology and Growth Kinetic Advantage of Quenched Twinned Dendrites in Al-Zn Alloys

Twinned dendrites appearing in an Al-26 wt pct Zn alloy have been quenched during growth using a specifically designed setup that is positioned on top of a directional solidification experiment. X-ray tomography performed at the Swiss Light Source (SLS-beamline TOMCAT) allowed us to reconstruct the 3D morphology of these structures and to confirm previous observations performed on single 2D sections (Henry et al., Metall Mater Trans A 35A:2495-2501, 2004; Salgado-Ordorica and Rappaz, Acta Mater 56:5708-5718, 2008). Further characterization of these quenched specimens led to a better description of the mechanisms involved in the in-plane and lateral growth propagation of twinned dendrites. These were then put into relation with the competition mechanisms taking place during simultaneous solidification of twinned and regular dendrites. DOI: 10.1007/s11661-012-1539-0 (C) The Minerals, Metals & Materials Society and ASM International 201

Synchrotron radiography studies of shear-induced dilation in semi-solid Al alloys and steels

An improved understanding of the response of solidifying microstructures to load is required to further minimize casting defects and optimize casting processes. This article overviews synchrotron radiography studies that directly measure the micromechanics of semisolid alloy deformation in a thin sample direct-shear cell. It is shown that shear-induced dilation (also known as Reynolds’ dilatancy) occurs in semisolid alloys with morphologies ranging from equiaxed-dendritic to globular, at solid fractions from the dendrite coherency point to ~90% solid, and it occurs in both Al alloys and carbon steels. Discrete-element method simulations that treat solidifying microstructures as granular materials are then used to explore the origins of dilatancy in semisolid alloys

Prediction of Hot Tear Formation in Vertical DC Casting of Aluminum Billets Using a Granular Approach

A coupled hydromechanical granular model aimed at predicting hot tear formation and stress-strain behavior in metallic alloys during solidification is applied to the semicontinuous direct chill casting of aluminum alloy round billets. This granular model consists of four separate three-dimensional (3D) modules: (I) a solidification module that is used for generating the solid-liquid geometry at a given solid fraction, (II) a fluid flow module that is used to calculate the solidification shrinkage and deformation-induced pressure drop within the intergranular liquid, (III) a semisolid deformation module that is based on a combined finite element/discrete element method and simulates the rheological behavior of the granular structure, and (IV) a failure module that simulates crack initiation and propagation. To investigate hot tearing, the granular model has been applied to a representative volume within the direct chill cast billet that is located at the bottom of the liquid sump, and it reveals that semisolid deformations imposed on the mushy zone open the liquid channels due to localization of the deformation at grains boundaries. At a low casting speed, only individual pores are able to form in the widest channels because liquid feeding remains efficient. However, as the casting speed increases, the flow of liquid required to compensate for solidification shrinkage also increases and as a result the pores propagate and coalesce to form a centerline crack

High-throughput, nonperturbing quantification of lipid droplets with digital holographic microscopy.

In vitro differentiating adipocytes are sensitive to liquid manipulations and have the tendency to float. Assessing adipocyte differentiation using current microscopy techniques involves cell staining and washing, while using flow cytometry involves cell retrieval in suspension. These methods induce biases, are difficult to reproduce, and involve tedious optimizations. In this study, we present digital holographic microscopy (DHM) as a label-free, nonperturbing means to quantify lipid droplets in differentiating adipocytes in a robust medium- to high-throughput manner. Taking advantage of the high refractive index of lipid droplets, DHM can assess the production of intracellular lipid droplets by differences in phase shift in a quantitative manner. Adipocytic differentiation, combined with other morphological features including cell confluence and cell death, was tracked over 6 days in live OP9 mesenchymal stromal cells. We compared DHM with other currently available methods of lipid droplet quantification and demonstrated its robustness with modulators of adipocytic differentiation in a dose-responsive manner. This study suggests DHM as a novel marker-free nonperturbing method to study lipid droplet accumulation and may be envisioned for drug screens and mechanistic studies on adipocytic differentiation