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1. Dirichlet problems in perforated domains

   https://doi.org/10.1080/03605302.2025.2486766  

   Righi, Robert; Shen, Zhongwei (May 2025, Communications in Partial Differential Equations)

   In this paper we establish W1,p estimates for solutions uε to Laplace’s equation with the Dirichlet condition in a bounded and perforated, not necessarily periodically, C1 domain Ωε,η in Rd. The bounding constants depend explicitly on two small parameters ε and η, where ε represents the scale of the minimal distance between holes, and η denotes the ratio between the size of the holes and ε. The proof relies on a large-scale Lp estimate for ∇uε, whose proof is divided into two parts. In the first part, we show that as ε,ηapproach zero, harmonic functions in Ωε,η may be approximated by solutions of an intermediate problem for a Schr¨odinger operator in Ω. In the second part, a real-variable method is employed to establish the large-scale Lp estimate for ∇uε by using the approximation at scales above ε. The results are shown to be sharp except in one particular case d≥3 and p= d or d′. 

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2. Thermal stability and phase transformation of α-, κ(ε)-, and γ-Ga2O3 films under different ambient conditions

   https://doi.org/10.1063/5.0214500  

   Tang, Jingyu; Jiang, Kunyao; Tseng, Po-Sen; Kurchin, Rachel C; Porter, Lisa M; Davis, Robert F (August 2024, Applied Physics Letters)

   Phase transitions in metastable α-, κ(ε)-, and γ-Ga2O3 films to thermodynamically stable β-Ga2O3 during annealing in air, N2, and vacuum have been systematically investigated via in situ high-temperature x-ray diffraction (HT-XRD) and scanning electron microscopy (SEM). These respective polymorphs exhibited thermal stability to ∼471–525 °C, ∼773–825 °C, and ∼490–575 °C before transforming into β-Ga2O3, across all tested ambient conditions. Particular crystallographic orientation relationships were observed before and after the phase transitions, i.e., (0001) α-Ga2O3 → (2¯01) β-Ga2O3, (001) κ(ε)-Ga2O3 → (310) and (2¯01) β-Ga2O3, and (100) γ-Ga2O3 → (100) β-Ga2O3. The phase transition of α-Ga2O3 to β-Ga2O3 resulted in catastrophic damage to the film and upheaval of the surface. The respective primary and possibly secondary causes of this damage are the +8.6% volume expansion and the dual displacive and reconstructive transformations that occur during this transition. The κ(ε)- and γ-Ga2O3 films converted to β-Ga2O3 via singular reconstructive transformations with small changes in volume and unchanged surface microstructures. 

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3. Performance of noisy Nesterov's accelerated method for strongly convex optimization problems

   https://doi.org/10.23919/ACC.2019.8814680  

   Mohammadi, Hesameddin; Razaviyayn, Meisam; Jovanovic, Mihailo R. (July 2019, 2019 American Control Conference (ACC))

   We study the performance of noisy gradient descent and Nesterov's accelerated methods for strongly convex objective functions with Lipschitz continuous gradients. The steady-state second-order moment of the error in the iterates is analyzed when the gradient is perturbed by an additive white noise with zero mean and identity covariance. For any given condition number κ, we derive explicit upper bounds on noise amplification that only depend on κ and the problem size. We use quadratic objective functions to derive lower bounds and to demonstrate that the upper bounds are tight up to a constant factor. The established upper bound for Nesterov's accelerated method is larger than the upper bound for gradient descent by a factor of √κ. This gap identifies a fundamental tradeoff that comes with acceleration in the presence of stochastic uncertainties in the gradient evaluation. 

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4. High‐Pressure Synthesis and Thermal Conductivity of Semimetallic θ‐Tantalum Nitride

   https://doi.org/10.1002/adfm.202212957  

   Lee, Hwijong; Zhou, Yuanyuan; Jung, Sungyeb; Li, Hongze; Cheng, Zhe; He, Jiaming; Chen, Jie; Sokalski, Peter; Dolocan, Andrei; Gearba‐Dolocan, Raluca; et al (February 2023, Advanced Functional Materials)

   Abstract The lattice thermal conductivity (κ_ph) of metals and semimetals is limited by phonon‐phonon scattering at high temperatures and by electron‐phonon scattering at low temperatures or in some systems with weak phonon‐phonon scattering. Following the demonstration of a phonon band engineering approach to achieve an unusually high κ_phin semiconducting cubic‐boron arsenide (c‐BAs), recent theories have predicted ultrahigh κ_phof the semimetal tantalum nitride in the θ‐phase (θ‐TaN) with hexagonal tungsten carbide (WC) structure due to the combination of a small electron density of states near the Fermi level and a large phonon band gap, which suppress electron‐phonon and three‐phonon scattering, respectively. Here, measurements on the thermal and electrical transport properties of polycrystalline θ‐TaN converted from the ε phase via high‐pressure synthesis are reported. The measured thermal conductivity of the θ‐TaN samples shows weak temperature dependence above 200 K and reaches up to 90 Wm⁻¹K⁻¹, one order of magnitude higher than values reported for polycrystalline ε‐TaN and δ‐TaN thin films. These results agree with theoretical calculations that account for phonon scattering by 100 nm‐level grains and suggest κ_phincrease above the 249 Wm⁻¹K⁻¹value predicted for single‐crystal WC when the grain size of θ‐TaN is increased above 400 nm. 

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5. Quantum Linear System Solver Based on Time-optimal Adiabatic Quantum Computing and Quantum Approximate Optimization Algorithm

   https://doi.org/10.1145/3498331  

   An, Dong; Lin, Lin (June 2022, ACM Transactions on Quantum Computing)

   We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with O (κ poly(log (κ ε))) runtime, where κ is the condition number, and ε is the target accuracy. This is near optimal with respect to both κ and ε, and is achieved without relying on complicated amplitude amplification procedures that are difficult to implement. Our method is applicable to general non-Hermitian matrices, and the cost as well as the number of qubits can be reduced when restricted to Hermitian matrices, and further to Hermitian positive definite matrices. The success of the time-optimal AQC implies that the quantum approximate optimization algorithm (QAOA) with an optimal control protocol can also achieve the same complexity in terms of the runtime. Numerical results indicate that QAOA can yield the lowest runtime compared to the time-optimal AQC, vanilla AQC, and the recently proposed randomization method. 

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