Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements

An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method is that the tangential or normal trace of the exact solution is not well-defined on the mesh faces of the computational mesh. We overcome this difficulty by two steps. First, we employ a lifting operator to replace the integrals of the tangential/normal traces on mesh faces by volume integrals. Second, optimal convergence rates are proven by using smoothed interpolations that are well-defined for merely integrable functions. As a byproduct of our analysis, an explicit and easily computable stabilization parameter is given

"Cartesian light": unconventional propagation of light in a 3D superlattice of coupled cavities within a 3D photonic band gap

We explore the unconventional propagation of light in a three-dimensional (3D) superlattice of coupled resonant cavities in a 3D photonic band gap crystal. Such a 3D cavity superlattice is the photonic analogue of the Anderson model for spins and electrons in the limit of zero disorder. Using the plane-wave expansion method, we calculate the dispersion relations of the 3D cavity superlattice with the cubic inverse woodpile structure that reveal five coupled-cavity bands, typical of quadrupole-like resonances. For three out of five bands, we observe that the dispersion bandwidth is significantly larger in the $(k_x, k_z)$-diagonal directions than in other directions. To explain the directionality of the dispersion bandwidth, we employ the tight-binding method from which we derive coupling coefficients in 3D. For all converged coupled-cavity bands, we find that light hops predominantly in a few high-symmetry directions including the Cartesian $(x, y, z)$ directions, therefore we propose the name "Cartesian light". Such 3D Cartesian hopping of light in a band gap yields propagation as superlattice Bloch modes that differ fundamentally from the conventional 3D spatially-extended Bloch wave propagation in crystals, from light tunneling through a band gap, from coupled-resonator optical waveguiding, and also from light diffusing at the edge of a gap

An investigation of data-driven player positional roles within the Australian Football League Women's competition using technical skill match-play data

Understanding player positional roles are important for match-play tactics, player recruitment, talent identification, and development by providing a greater understanding of what each positional role constitutes. Currently, no analysis of competition technical skill data exists by player position in the Australian Football League Women's (AFLW) competition. The primary aim of the research was to use data-driven techniques to observe what positions and roles characterise AFLW match-play using detailed technical skill action data of players. A secondary aim was to comment on the application of clustering methods to achieve more interpretable, reflective positional clustering. A two-stage, unsupervised clustering approach was applied to meet these aims. Data cleaning resulted in 165 variables across 1296 player seasons in the 2019–2022 AFLW seasons which was used for clustering. First-stage clustering found four positions following a common convention (forwards, midfielders, defenders, and rucks). Second-stage clustering found roles within positions, resulting in a further 13 clusters with three forwards, three midfielders, four defenders, and three ruck positional roles. Key variables across all positions and roles included the field location of actions, number of contested possessions, clearances, interceptions, hitouts, inside 50s, and rebound 50s. Unsupervised clustering allowed the discovery of new roles rather than being constrained to pre-defined existing classifications of previous literature. This research assists coaches and practitioners by identifying key game actions players need to perform in match-play by position, which can assist in player recruitment, player development, and identifying appropriate match-play styles and tactics, while also defining new roles and suggestions of how to best use available data

Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures

We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate cluster validity indices as a means to find the correct number of confinement dimensionalities to be used as an input to the clustering algorithms. Subsequently, we analyze the performance of the two clustering algorithms when compared to the direct application of the scaling method without clustering. We find that the clustering approach provides more physically meaningful results, but may struggle with identifying the correct set of confinement dimensionalities. We conclude that the most accurate outcome is obtained by first applying the direct scaling to find the correct set of confinement dimensionalities and subsequently employing clustering to refine the results. Moreover, our model-based algorithm outperforms the standard k-means++ clustering.Comment: 24 pages, 11 figure

Події революції 1905-1907 рр. та діяльність партії соціалістів-революціонерів на Чернігівщині

В запропонованій статті автор намагається розглянути взаємовплив народного та есерівського рухів на Лівобережній Україні в зазначений період. Метою дослідження є спроба аналізу тактики, методів, напрямків та динаміки діяльності партії соціалістів – революціонерів у Чернігівській губернії

Nothing moves a surface: vacancy mediated surface diffusion

We report scanning tunneling microscopy observations, which imply that all atoms in a close-packed copper surface move frequently, even at room temperature. Using a low density of embedded indium `tracer' atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to make concerted, long jumps. Responsible for this motion is an ultra-low density of surface vacancies, diffusing rapidly within the surface. This interpretation is supported by a detailed analysis of the displacement distribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusion mechanism that we propose.Comment: 4 pages; for associated movie, see http://www-lion.leidenuniv.nl/sections/cm/groups/interface/projects/therm

Imaging in Primary Sjogren's Syndrome

Primary Sjögren's syndrome (pSS) is a systemic autoimmune disease characterized by dysfunction and lymphocytic infiltration of the salivary and lacrimal glands. Besides the characteristic sicca complaints, pSS patients can present a spectrum of signs and symptoms, which challenges the diagnostic process. Various imaging techniques can be used to assist in the diagnostic work-up and follow-up of pSS patients. Developments in imaging techniques provide new opportunities and perspectives. In this descriptive review, we discuss imaging techniques that are used in pSS with a focus on the salivary glands. The emphasis is on the contribution of these techniques to the diagnosis of pSS, their potential in assessing disease activity and disease progression in pSS, and their contribution to diagnosing and staging of pSS-associated lymphomas. Imaging findings of the salivary glands will be linked to histopathological changes in the salivary glands of pSS patients