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1. Phonon scattering and vibrational localization in 2D embedded nanoparticle composites

   https://doi.org/10.1063/5.0089340  

   Chowdhury, Ongira; Feser, Joseph P. (May 2022, Journal of Applied Physics)

   The frequency domain perfectly matched layer (FDPML) approach is used to study phonon transport in a series of large 2D domains with randomly embedded nanoparticles over a wide range of nanoparticle loadings and wavelengths. The effect of nanoparticle packing density on the mean free path and localization length is characterized. We observe that, in the Mie scattering regime, the independent scattering approximation is valid up to volume fractions exceeding 10% and often higher depending on scattering parameter, indicating that the mean free path can usually be calculated much less expensively using the number density and the scattering cross section of a single scatterer. We also study localization lengths and their dependence on particle loading. For heavy nanoparticles embedded in a lighter material, using the FDPML approach, we only observe localization at volume fractions [Formula: see text] and only for short wavelength modes where vibrational frequencies exceed those available in the embedded nanoparticles. Using modal analysis, we show that localization in nanoparticle laden materials is primarily due to energetic confinement rather than Anderson localization. We then show that, by using light particles in a heavy matrix, the fraction of confined modes can be substantially increased. 

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2. Stochastic Localization Methods for Convex Discrete Optimization via Simulation

   https://doi.org/10.1287/opre.2022.0030  

   Zhang, Haixiang; Zheng, Zeyu; Lavaei, Javad (March 2025, Operations Research)

   Solving Convex Discrete Optimization via Simulation via Stochastic Localization Algorithms Many decision-making problems in operations research and management science require the optimization of large-scale complex stochastic systems. For a number of applications, the objective function exhibits convexity in the discrete decision variables or the problem can be transformed into a convex one. In “Stochastic Localization Methods for Convex Discrete Optimization via Simulation,” Zhang, Zheng, and Lavaei propose provably efficient simulation-optimization algorithms for general large-scale convex discrete optimization via simulation problems. By utilizing the convex structure and the idea of localization and cutting-plane methods, the developed stochastic localization algorithms demonstrate a polynomial dependence on the dimension and scale of the decision space. In addition, the simulation cost is upper bounded by a value that is independent of the objective function. The stochastic localization methods also exhibit a superior numerical performance compared with existing algorithms. 

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3. Asymptotics of sample tail autocorrelations for tail-dependent time series: phase transition and visualization

   https://doi.org/10.1093/biomet/asab038  

   Zhang, Ting (July 2021, Biometrika)

   Summary In this article we develop an asymptotic theory for sample tail autocorrelations of time series data that can exhibit serial dependence in both tail and non-tail regions. Unlike with the traditional autocorrelation function, the study of tail autocorrelations requires a double asymptotic scheme to capture the tail phenomena, and our results do not impose any restrictions on the dependence structure in non-tail regions and allow processes that are not necessarily strongly mixing. The newly developed asymptotic theory reveals a previously undiscovered phase transition phenomenon, where the asymptotic behaviour of sample tail autocorrelations, including their convergence rate, can transition from one phase to another as the lag index moves past the point beyond which serial tail dependence vanishes. The phase transition discovery fills a gap in existing research on tail autocorrelations and can be used to construct the lines of significance, in analogy to the traditional autocorrelation plot, when visualizing sample tail autocorrelations to assess the existence of serial tail dependence or to identify the maximal lag of tail dependence. 

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4. Sprain energy consequences for damage localization and fracture mechanics

   https://doi.org/10.1073/pnas.2410668121  

   Xu, Houlin; Nguyen, Anh Tay; Bažant, Zdeněk P (October 2024, Proceedings of the National Academy of Sciences)

   The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( $C_0$) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals. 

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5. Photoluminescence Study of Carrier Localization and Recombination in Nearly Strain‐Balanced Nonpolar InGaN/AlGaN Quantum Wells

   https://doi.org/10.1002/pssb.202100569  

   Cao, Yang; Dzuba, Brandon; Magill, Brenden A.; Senichev, Alexander; Nguyen, Trang; Diaz, Rosa E.; Manfra, Michael J.; McGill, Stephen; Garcia, Carlos; Khodaparast, Giti A.; et al (April 2022, physica status solidi (b))

   Temperature-dependent continuous-excitation and time-resolved photoluminescence are studied to probe carrier localization and recombination in nearly strain-balanced m-plane In0.09Ga0.91N/Al0.19Ga0.81N multi-quantum wells grown by plasma-assisted molecular-beam epitaxy. An average localization depth of 21 meV is estimated for the undoped sample. This depth is much smaller than the reported values in polar structures and m-plane InGaN quantum wells. As part of this study, temperature and magnetic field dependence of time-resolved photoluminescence is performed. At 2 K, an initial fast decay time of 0.3 ns is measured for both undoped and doped structures. The undoped sample also exhibits a slow decay component with a time scale of 2.2 ns. The existence of two relaxation paths in the undoped structure can be attributed to different localization centers. The fast relaxation decays are relatively insensitive to external magnetic fields, while the slower relaxation time constant decreases significantly with increasing magnetic fields. The fast decay time scale in the undoped sample is likely due to indium fluctuations in the quantum well. The slow decay time may be related to carrier localization in the barriers. The addition of doping leads to a single fast decay time likely due to stronger exciton localization in the InGaN quantum wells. 

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