Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width

A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. The spindle convex body is called a "fat" one, if it contains the centers of its generating balls. The core part of this paper is an extension of Schramm's theorem and its proof on illuminating convex bodies of constant width to the family of "fat" spindle convex bodies.Comment: 17 page

A sampling-based approach for information-theoretic inspection management

A partially supervised approach to Structural Health Monitoring is proposed, to manage the cost associated with expert inspections and maximize the value of monitoring regimes. Unlike conventional data-driven procedures, the monitoring classifier is learnt online while making predictions—negating the requirement for complete data before a system is in operation (which are rarely available). Most critically, periodic inspections are replaced (or enhanced) by an automatic inspection regime, which only queries measurements that appear informative to the evolving model of the damage-sensitive features. The result is a partially supervised Dirichlet process clustering that manages expert inspections online given incremental data. The method is verified on a simulated example and demonstrated on in situ bridge monitoring data

Foundations of population-based SHM, Part I : homogeneous populations and forms

In Structural Health Monitoring (SHM), measured data that correspond to an extensive set of operational and damage conditions (for a given structure) are rarely available. One potential solution considers that information might be transferred, in some sense, between similar systems. A population-based approach to SHM looks to both model and transfer this missing information, by considering data collected from groups of similar structures. Specifically, in this work, a framework is proposed to model a population of nominally-identical systems, such that (complete) datasets are only available from a subset of members. The SHM strategy defines a general model, referred to as the population form, which is used to monitor a homogeneous group of systems. First, the framework is demonstrated through applications to a simulated population, with one experimental (test-rig) member; the form is then adapted and applied to signals recorded from an operational wind farm

A flexible, open, and interactive digital platform to support online and blended experiential learning environments: Thinglink and thin sections

Abstract. This study investigates the potential value of, and provides a method for, the creation of flexible, digital, and asynchronous platforms to create student-centred materials for use in an online and/or blended learning environment. We made use of Thinglink to create a “virtual microscope” resource for geology and associated courses in higher education. This is achieved through the dissemination of a simple learning resource comprising interactive imagery and audio. The visual analysis of rocks under the microscope, termed thin-section petrography, is a fundamental component in geology programmes in higher education, with key skills which are transferable with other fields such as material science, biology, and forensic science. However, learning environments and activities in this field are often dictated by the requirement for access to microscope facilities and supplementary resources which are highly variable in their academic level, availability, design, and scale, ranging from traditional textbooks to online resources. A resource was created which allows individuals to experience some of the aspects of petrographic microscopy in a digital manner. In particular, specific features of the materials observed and how microscopes work were included. The resource was disseminated to a population of learners and educators, who provided responses to a questionnaire. Responses were overwhelmingly positive and indicate considerable interest from learner and teacher alike. Critical areas for improvement include the need for clarity in the user interface and the inclusion of a recorded human voice rather than automated text narration. This study highlights the need for, and benefits of, interactive online learning resources in petrology and associated fields. This type of resource has positive implications for the flexibility, inclusivity, and accessibility of teaching materials. Such resources may prove particularly valuable when distance learning is unavoidable (e.g. the COVID-19 crisis) and/or hybrid, blended learning environments are being deployed. The method and platform used in this study are highly transferable to other subject areas (or other areas of the geosciences)

Similar patterns of leaf temperatures and thermal acclimation to warming in temperate and tropical tree canopies

As the global climate warms, a key question is how increased leaf temperatures will affect tree physiology and the coupling between leaf and air temperatures in forests. To explore the impact of increasing temperatures on plant performance in open air, we warmed leaves in the canopy of two mature evergreen forests, a temperate Eucalyptus woodland and a tropical rainforest. The leaf heaters consistently maintained leaves at a target of 4 °C above ambient leaf temperatures. Ambient leaf temperatures (Tleaf) were mostly coupled to air temperatures (Tair), but at times, leaves could be 8–10 °C warmer than ambient air temperatures, especially in full sun. At both sites, Tleaf was warmer at higher air temperatures (Tair > 25 °C), but was cooler at lower Tair, contrary to the ‘leaf homeothermy hypothesis’. Warmed leaves showed significantly lower stomatal conductance (−0.05 mol m−2 s−1 or −43% across species) and net photosynthesis (−3.91 μmol m−2 s−1 or −39%), with similar rates in leaf respiration rates at a common temperature (no acclimation). Increased canopy leaf temperatures due to future warming could reduce carbon assimilation via reduced photosynthesis in these forests, potentially weakening the land carbon sink in tropical and temperate forests

Mass Loss Due to Sputtering and Thermal Processes in Meteoroid Ablation

Conventional meteoroid theory assumes that the dominant mode of ablation is by evaporation following intense heating during atmospheric flight. In this paper we consider the question of whether sputtering may provide an alternative disintegration process of some importance.For meteoroids in the mass range from 10^-3 to 10^-13 kg and covering a meteor velocity range from 11 to 71 km/s, we numerically modeled both thermal ablation and sputtering ablation during atmospheric flight. We considered three meteoroid models believed to be representative of asteroidal (3300 kg m^-3 mass density), cometary (1000 kg m^-3) and porous cometary (300 kg m^-3) meteoroid structures. Atmospheric profiles which considered the molecular compositions at different heights were used in the sputtering calculations. We find that while in many cases (particularly at low velocities and for relatively large meteoroid masses) sputtering contributes only a small amount of mass loss during atmospheric flight, in some cases sputtering is very important. For example, a 10^-10 kg porous meteoroid at 40 km/s will lose nearly 51% of its mass by sputtering, while a 10^-13 kg asteroidal meteoroid at 60 km/s will lose nearly 83% of its mass by sputtering. We argue that sputtering may explain the light production observed at very great heights in some Leonid meteors. The impact of this work will be most dramatic for very small meteoroids such as those observed with large aperture radars.Comment: in pdf form, 48 pgs incl figures and table

SUSY vertex algebras and supercurves

This article is a continuation of math.QA/0603633 Given a strongly conformal SUSY vertex algebra V and a supercurve X we construct a vector bundle V_X on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle V_X, corresponding to a SUSY vertex algebra, carries the structure of a chiral algebra.Comment: 50 page