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

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

Symmetries and Wavefunctions of Photons Confined in 3D Photonic Band Gap Superlattices

We perform a computational study of confined photonic states that appear in a three-dimensional (3D) superlattice of coupled cavities, resulting from a superstructure of intentional defects. The states are isolated from the vacuum by a 3D photonic band gap, using a diamond-like inverse woodpile crystal structure, and exhibit 'Cartesian' hopping of photons in high-symmetry directions. We investigate the confinement dimensionality to verify which states are fully 3D confined, using a recently developed scaling theory to analyze the influence of the structural parameters of the 3D crystal. We create confinement maps that trace the frequencies of 3D confined bands for select combinations of key structural parameters, namely the pore radii of the underlying regular crystal and of the defect pores. We find that a certain minimum difference between the regular and defect pore radii is necessary for 3D confined bands to appear, and that an increasing difference between the defect pore radii from the regular radii supports more 3D confined bands. In our analysis we find that their symmetries and spatial distributions are more varied than electronic orbitals known from solid state physics. We also discover pairs of degenerate 3D confined bands with p-like orbital shapes and mirror symmetries matching the symmetry of the superlattice. Finally, we investigate the enhancement of the local density of optical states (LDOS) for cavity quantum electrodynamics (cQED) applications. We find that donor-like superlattices, i.e., where the defect pores are smaller than the regular pores, provide greater enhancement in the air region than acceptor-like structures with larger defect pores, and thus offer better prospects for doping with quantum dots and ultimately for 3D networks of single photons steered across strongly-coupled cavities

Dissociative recombination and electron-impact de-excitation in CH photon emission under ITER divertor-relevant plasma conditions

For understanding carbon erosion and redeposition in nuclear fusion devices, it is important to understand the transport and chemical break-up of hydrocarbon molecules in edge plasmas, often diagnosed by emission of the CH A^2\Delta - X^2\Pi Ger\"o band around 430 nm. The CH A-level can be excited either by electron-impact or by dissociative recombination (D.R.) of hydrocarbon ions. These processes were included in the 3D Monte Carlo impurity transport code ERO. A series of methane injection experiments was performed in the high-density, low-temperature linear plasma generator Pilot-PSI, and simulated emission intensity profiles were benchmarked against these experiments. It was confirmed that excitation by D.R. dominates at T_e < 1.5 eV. The results indicate that the fraction of D.R. events that lead to a CH radical in the A-level and consequent photon emission is at least 10%. Additionally, quenching of the excited CH radicals by electron impact de-excitation was included in the modeling. This quenching is shown to be significant: depending on the electron density, it reduces the effective CH emission by a factor of 1.4 at n_e=1.3*10^20 m^-3, to 2.8 at n_e=9.3*10^20 m^-3. Its inclusion significantly improved agreement between experiment and modeling

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

Fluorescence grid analysis for the evaluation of piecemeal surgery in sinonasal inverted papilloma:a proof-of-concept study

PURPOSE: Local recurrence occurs in ~ 19% of sinonasal inverted papilloma (SNIP) surgeries and is strongly associated with incomplete resection. During surgery, it is technically challenging to visualize and resect all SNIP tissue in this anatomically complex area. Proteins that are overexpressed in SNIP, such as vascular endothelial growth factor (VEGF), may serve as a target for fluorescence molecular imaging to guide surgical removal of SNIP. A proof-of-concept study was performed to investigate if the VEGF-targeted near-infrared fluorescent tracer bevacizumab-800CW specifically localizes in SNIP and whether it could be used as a clinical tool to guide SNIP surgery.METHODS: In five patients diagnosed with SNIP, 10 mg of bevacizumab-800CW was intravenously administered 3 days prior to surgery. Fluorescence molecular imaging was performed in vivo during surgery and ex vivo during the processing of the surgical specimen. Fluorescence signals were correlated with final histopathology and VEGF-A immunohistochemistry. We introduced a fluorescence grid analysis to assess the fluorescence signal in individual tissue fragments, due to the nature of the surgical procedure (i.e., piecemeal resection) allowing the detection of small SNIP residues and location of the tracer ex vivo.RESULTS: In all patients, fluorescence signal was detected in vivo during endoscopic SNIP surgery. Using ex vivo fluorescence grid analysis, we were able to correlate bevacizumab-800CW fluorescence of individual tissue fragments with final histopathology. Fluorescence grid analysis showed substantial variability in mean fluorescence intensity (FImean), with SNIP tissue showing a median FImean of 77.54 (IQR 50.47-112.30) compared to 35.99 (IQR 21.48-57.81) in uninvolved tissue (p &lt; 0.0001), although the diagnostic ability was limited with an area under the curve of 0.78.CONCLUSIONS: A fluorescence grid analysis could serve as a valid method to evaluate fluorescence molecular imaging in piecemeal surgeries. As such, although substantial differences were observed in fluorescence intensities, VEGF-A may not be the ideal target for SNIP surgery.TRIAL REGISTRATION: NCT03925285.</p

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