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1. The Nitsche phenomenon for weighted Dirichlet energy

   https://doi.org/10.1515/acv-2017-0060  

   Iwaniec, Tadeusz; Onninen, Jani; Radice, Teresa (July 2020, Advances in Calculus of Variations)

   null (Ed.)

   Abstract The present paper arose from recent studies of energy-minimal deformations of planar domains.We are concerned with the Dirichlet energy. In general the minimal mappings need not be homeomorphisms. In fact, a part of the domain near its boundary may collapse into the boundary of the target domain. In mathematical models of nonlinear elasticity this is interpreted as interpenetration of matter . We call such occurrence the Nitsche phenomenon , after Nitsche’s remarkable conjecture (now a theorem) about existence of harmonic homeomorphisms between annuli. Indeed the round annuli proved to be perfect choices to grasp the nuances of the problem. Several papers are devoted to a study of deformations of annuli. Because of rotational symmetry it seems likely that the Dirichlet energy-minimal deformations are radial maps. That is why we confine ourselves to radial minimal mappings. The novelty lies in the presence of a weight in the Dirichlet integral. We observe the Nitsche phenomenon in this case as well, see our main results Theorem 1.4 and Theorem 1.7. However, the arguments require further considerations and new ingredients. One must overcome the inherent difficulties arising from discontinuity of the weight. The Lagrange–Euler equation is unavailable, because the outer variation violates the principle of none interpenetration of matter. Inner variation, on the other hand, leads to an equation that involves the derivative of the weight. But our weight function is only measurable which is the main challenge of the present paper. 

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2. The Dirichlet isospectral problem for trapezoids

   https://doi.org/10.1063/5.0036384  

   Hezari, Hamid; Lu, Z.; Rowlett, J. (May 2021, Journal of Mathematical Physics)

   We show that non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum. This extends our previous result [Hezari et al., Ann. Henri Poincare 18(12), 3759–3792 (2017)], which was only concerned with the Neumann Laplace spectrum. 

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3. Identification of Characteristic Spatial Scales to Improve the Performance of Analytical Spectral Solutions to the Groundwater Flow Equation

   https://doi.org/10.1029/2021WR031044  

   Perez, Gabriel; Gomez‐Velez, Jesus D.; Chen, Xingyuan; Scheibe, T.; Chen, Yunxiang; Bao, Jie (December 2021, Water Resources Research)

   Abstract Analytical solutions for the three‐dimensional groundwater flow equation have been widely used to gain insight about subsurface flow structure and as an alternative to computationally expensive numerical models. Of particular interest are solutions that decompose prescribed hydraulic head boundaries (e.g., Dirichlet boundary condition) into a collection of harmonic functions. Previous studies estimate the frequencies and amplitudes of these harmonics with a least‐square approach where the amplitudes are fitted given a pre‐assigned set of frequencies. In these studies, an ad hoc and structured discretization of the frequency domain is typically used, excluding dominant frequencies while assigning importance to spurious frequencies, with significant consequences for estimating the fluxes and residence times. This study demonstrates the advantages of using a pre‐assigned frequency spectrum that targets the dominant frequencies based on rigorous statistical analysis with predefined significance levels. The new approach is tested for three hydrologic conceptualizations: (a) a synthetic periodic basin, (b) synthetic bedforms, and (c) a natural mountainous watershed. The performance of the frequency spectrum selection is compared with exact analytical or approximate numerical solutions. We found that the new approach better describes the fluxes and residence times for Dirichlet boundaries with well‐defined characteristics spatial scales (e.g., periodic basins and bedforms). For more complex scenarios, such as natural mountainous watersheds, both pre‐assigned frequency spectrums present similar performance. The spectral solutions presented here can play a central role in developing reduced‐complexity models for assessing regional water and solute fluxes within mountain watersheds and hyporheic zones. 

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4. Exact Controllability of the 1-D Wave Equation on Finite Metric Tree Graphs

   https://doi.org/10.1007/s00245-019-09629-3  

   Avdonin, Sergei; Zhao, Yuanyuan (November 2019, Applied Mathematics & Optimization)

   In this paper, we consider initial boundary value problems and control problems for the wave equation on finite metric graphs with Dirichlet boundary controls. We propose new constructive algorithms for solving initial boundary value problems on general graphs and boundary control problems on tree graphs. We demonstrate that the wave equation on a tree is exactly controllable if and only if controls are applied at all or all but one of the boundary vertices. We find the minimal controllability time and prove that our result is optimal in the general case. The proofs for the shape and velocity controllability are purely dynamical, while the proof for the full controllability utilizes both dynamical and moment method approaches. 

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5. Dual-site occupancy induced broadband cyan emission in Ba ₂ CaB ₂ Si ₄ O ₁₄ :Ce ³⁺

   https://doi.org/10.1039/D0TC02625E  

   You, Shihai; Zhuo, Ya; Chen, Qiulin; Brgoch, Jakoah; Xie, Rong-Jun (November 2020, Journal of Materials Chemistry C)

   null (Ed.)

   There is a significant need to identify cyan-emitting phosphors capable of filling the “cyan-gap” (480–520 nm) in full-visible-spectrum phosphor-converted white light-emitting diodes (pc-wLEDs). Here, a new broadband cyan-emitting phosphor that enables addressing of this challenge is reported. The compound, Ba 2 CaB 2 Si 4 O 14 :Ce 3+ , presents a bright cyan emission peaking at 478 nm with a large full width at half maximum of 142 nm (6053 cm −1 ), and minimal thermal quenching. The photoluminescence properties originate from Ce 3+ residing at two different crystallographic sites, a [BaO 9 ] distorted elongated square pyramid and a [CaO 6 ] trigonal prism. This combination results in an efficient, broad emission covering the blue to green region of the visible spectrum. Fabricating a simple dichromatic ultraviolet ( λ ex = 370 nm) pumped pc-wLED using Ba 2 CaB 2 Si 4 O 14 :Ce 3+ along with a commercially available red phosphor demonstrates full-visible-spectrum white light with high color rendering index ( R a > 90) and tunable correlated color temperature, showing the potential of this material for achieving high-quality LED-based lighting. 

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