Theory of ice premelting in porous media

Premelting describes the confluence of phenomena that are responsible for the stable existence of the liquid phase of matter in the solid region of its bulk phase diagram. Here we develop a theoretical description of the premelting of water ice contained in a porous matrix, made of a material with a melting temperature substantially larger than ice itself, to predict the amount of liquid water in the matrix at temperatures below its bulk freezing point. Our theory combines the interfacial premelting of ice in contact with the matrix, grain boundary melting in the ice, and impurity and curvature induced premelting, the latter occurring in regions which force the ice-liquid interface into a high curvature configuration. These regions are typically found at points where the matrix surface is concave, along contact lines of a grain boundary with the matrix, and in liquid veins. Both interfacial premelting and curvature induced premelting depend on the concentration of impurities in the liquid, which, due to the small segregation coefficient of impurities in ice are treated as homogeneously distributed in the premelted liquid. Our principal result is an equation for the fraction of liquid in the porous medium as a function of the undercooling, which embodies the combined effects of interfacial premelting, curvature induced premelting, and impurities. The result is analyzed in detail and applied to a range of experimentally relevant settings.Comment: 14 pages, 10 figures, accepted for publication in Physical Review

Lateral shift of the transmitted light beam through a left-handed slab

It is reported that when a light beam travels through a slab of left-handed medium in the air, the lateral shift of the transmitted beam can be negative as well as positive. The necessary condition for the lateral shift to be positive is given. The validity of the stationary-phase approach is demonstrated by numerical simulations for a Gaussian-shaped beam. A restriction to the slab's thickness is provided that is necessary for the beam to retain its profile in the traveling. It is shown that the lateral shift of the reflected beam is equal to that of the transmitted beam in the symmetric configuration.Comment: 14 pages, 4 figure

Promoting middle school students’ proportional reasoning skills through an ongoing professional development programme for teachers

© 2016, Springer Science+Business Media Dordrecht. Proportional reasoning, the ability to use ratios in situations involving comparison of quantities, is essential for mathematical competence, especially in the middle school years, and is an important determinant of success beyond school. Research shows students find proportional reasoning and its foundational concepts difficult. Proportional reasoning does not always develop naturally, however some research suggests that with targeted teaching, its development can be promoted. This paper reports on a large Australian study involving over 130 teachers and their students. A major goal of the study was to investigate the efficacy of ongoing teacher professional development for promoting middle years students’ proportional reasoning. A series of professional development workshops was designed to enhance the teachers’ understanding of proportional reasoning and to extend their repertoire of teaching strategies to promote their students’ proportional reasoning skills. The workshop design was informed by research literature on proportional reasoning teaching and learning as well as the results of a diagnostic instrument administered to over 2500 middle years students prior to the professional development. Between workshops, the teachers implemented a variety of targeted teaching activities. This paper reports on pre- and post- instrument student data collected at the beginning and end of the first year of the project (i.e., after completion of half of the workshops). The findings suggest that targeted professional development and explicit teaching can make a difference to students’ proportional reasoning

Message passing for vertex covers

Constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints. In this paper, we develop and analyze message passing techniques, namely warning and survey propagation, which serve as efficient heuristic algorithms for solving these computational hard problems. We show also, how previously obtained results on the typical-case behavior of vertex covers of random graphs can be recovered starting from the message passing equations, and how they can be extended.Comment: 25 pages, 9 figures - version accepted for publication in PR

A savings based method for real-life vehicle routing problems

This paper describes a Savings Based algorithm for the Extended Vehicle Routing Problem. This algorithm is compared with a Sequential Insertion algorithm on real-life data. Besides the traditional quality measures such as total distance traveled and total workload, we compare the routing plans of both algorithms according to non-standard quality measures that h

Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an external magnetic field

Using fundamental measure density functional theory we investigate paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thicknesses. An external magnetic field induces uniaxial alignment and acts on the platelets with a strength that is taken to scale with the platelet area. At particle diameter ratio lambda=1.5 the system displays paranematic-nematic coexistence. For lambda=2, demixing into two nematic states with different compositions also occurs, between an upper critical point and a paranematic-nematic-nematic triple point. Increasing the field strength leads to shrinking of the coexistence regions. At high enough field strength a closed loop of immiscibility is induced and phase coexistence vanishes at a double critical point above which the system is homogeneously nematic. For lambda=2.5, besides paranematic-nematic coexistence, there is nematic-nematic coexistence which persists and hence does not end in a critical point. The partial orientational order parameters along the binodals vary strongly with composition and connect smoothly for each species when closed loops of immiscibility are present in the corresponding phase diagram.Comment: 9 pages, to appear in J.Phys:Condensed Matte

A hard-sphere model on generalized Bethe lattices: Statics

We analyze the phase diagram of a model of hard spheres of chemical radius one, which is defined over a generalized Bethe lattice containing short loops. We find a liquid, two different crystalline, a glassy and an unusual crystalline glassy phase. Special attention is also paid to the close-packing limit in the glassy phase. All analytical results are cross-checked by numerical Monte-Carlo simulations.Comment: 24 pages, revised versio

Evaluation and patient experience of wireless noninvasive fetal heart rate monitoring devices

Introduction: In clinical practice, fetal heart rate monitoring is performed intermittently using Doppler ultrasound, typically for 30 minutes. In case of a non-reassuring heart rate pattern, monitoring is usually prolonged. Noninvasive fetal electrocardiography may be more suitable for prolonged monitoring due to improved patient comfort and signal quality. This study evaluates the performance and patient experience of four noninvasive electrocardiography devices to assess candidate devices for prolonged noninvasive fetal heart rate monitoring. Material and methods: Non-critically sick women with a singleton pregnancy from 24 weeks of gestation were eligible for inclusion. Fetal heart rate monitoring was performed during standard care with a Doppler ultrasound device (Philips Avalon-FM30) alone or with this Doppler ultrasound device simultaneously with one of four noninvasive electrocardiography devices (Nemo Fetal Monitoring System, Philips Avalon-Beltless, Demcon Dipha-16 and Dräger Infinity-M300). Performance was evaluated by: success rate, positive percent agreement, bias, 95% limits of agreement, regression line, root mean square error and visual agreement using FIGO guidelines. Patient experience was captured using a self-made questionnaire. Results: A total of 10 women were included per device. For fetal heart rate, Nemo performed best (success rate: 99.4%, positive percent agreement: 94.2%, root mean square error 5.1 BPM, bias: 0.5 BPM, 95% limits of agreement: −9.7 – 10.7 BPM, regression line: y = −0.1x + 11.1) and the cardiotocography tracings obtained simultaneously by Nemo and Avalon-FM30 received the same FIGO classification. Comparable results were found with the Avalon-Beltless from 36 weeks of gestation, whereas the Dipha-16 and Infinity-M300 performed significantly worse. The Avalon-Beltless, Nemo and Infinity-M300 closely matched the performance of the Avalon-FM30 for maternal heart rate, whereas the performance of the Dipha-16 deviated more. Patient experience scores were higher for the noninvasive electrocardiography devices. Conclusions: Both Nemo and Avalon-Beltless are suitable devices for (prolonged) noninvasive fetal heart rate monitoring, taking their intended use into account. But outside its intended use limit of 36 weeks’ gestation, the Avalon-Beltless performs less well, comparable to the Dipha-16 and Infinity-M300, making them currently unsuitable for (prolonged) noninvasive fetal heart rate monitoring. Noninvasive electrocardiography devices appear to be preferred due to greater comfort and mobility.</p