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1. Revealing hidden medium-range order in amorphous materials using topological data analysis

   https://doi.org/10.1126/sciadv.abc2320  

   Sørensen, Søren S.; Biscio, Christophe A.; Bauchy, Mathieu; Fajstrup, Lisbeth; Smedskjaer, Morten M. (September 2020, Science Advances)

   null (Ed.)

   Despite the numerous technological applications of amorphous materials, such as glasses, the understanding of their medium-range order (MRO) structure—and particularly the origin of the first sharp diffraction peak (FSDP) in the structure factor—remains elusive. Here, we use persistent homology, an emergent type of topological data analysis, to understand MRO structure in sodium silicate glasses. To enable this analysis, we introduce a self-consistent categorization of rings with rigorous geometrical definitions of the structural entities. Furthermore, we enable quantitative comparison of the persistence diagrams by computing the cumulative sum of all points weighted by their lifetime. On the basis of these analysis methods, we show that the approach can be used to deconvolute the contributions of various MRO features to the FSDP. More generally, the developed methodology can be applied to analyze and categorize molecular dynamics data and understand MRO structure in any class of amorphous solids. 

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2. Nucleation kinetics model for primary crystallization in Al–Y–Fe metallic glass

   https://doi.org/10.1063/5.0135730  

   Duan, Tianrui; Shen, Ye; Imhoff, Seth D.; Yi, Feng; Voyles, Paul M.; Perepezko, John H. (February 2023, The Journal of Chemical Physics)

   The high density of aluminum nanocrystals (>10 21  m −3 ) that develop during the primary crystallization in Al-based metallic glasses indicates a high nucleation rate (∼10 18  m −3  s −1 ). Several studies have been advanced to account for the primary crystallization behavior, but none have been developed to completely describe the reaction kinetics. Recently, structural analysis by fluctuation electron microscopy has demonstrated the presence of the Al-like medium range order (MRO) regions as a spatial heterogeneity in as-spun Al 88 Y 7 Fe 5 metallic glass that is representative for the class of Al-based amorphous alloys that develop Al nanocrystals during primary crystallization. From the structural characterization, an MRO seeded nucleation configuration is established, whereby the Al nanocrystals are catalyzed by the MRO core to decrease the nucleation barrier. The MRO seeded nucleation model and the kinetic data from the delay time ( τ) measurement provide a full accounting of the evolution of the Al nanocrystal density (N v ) during the primary crystallization under isothermal annealing treatments. Moreover, the calculated values of the steady state nucleation rates ( J ss ) predicted by the nucleation model agree with the experimental results. Moreover, the model satisfies constraints on the structural, thermodynamic, and kinetic parameters, such as the critical nucleus size, the interface energy, and the volume-free energy driving force that are essential for a fully self-consistent nucleation kinetics analysis. The nucleation kinetics model can be applied more broadly to materials that are characterized by the presence of spatial heterogeneities. 

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3. Decoupling Simulation Accuracy from Mesh Quality

   Schneider, Teseo; Hu, Yixin; Dumas, Jeremie; Gao, Xifeng; Panozzo, Daniele; Zorin, Denis (December 2018, ACM transactions on graphics)

   For a given PDE problem, three main factors affect the accuracy of FEM solutions: basis order, mesh resolution, and mesh element quality. The first two factors are easy to control, while controlling element shape quality is a challenge, with fundamental limitations on what can be achieved. We propose to use p-refinement (increasing element degree) to decouple the approximation error of the finite element method from the domain mesh quality for elliptic PDEs. Our technique produces an accurate solution even on meshes with badly shaped elements, with a slightly higher running time due to the higher cost of high-order elements. We demonstrate that it is able to automatically adapt the basis to badly shaped elements, ensuring an error consistent with high-quality meshing, without any per-mesh parameter tuning. Our construction reduces to traditional fixed-degree FEM methods on high-quality meshes with identical performance. Our construction decreases the burden on meshing algorithms, reducing the need for often expensive mesh optimization and automatically compensates for badly shaped elements, which are present due to boundary con- straints or limitations of current meshing methods. By tackling mesh gen- eration and finite element simulation jointly, we obtain a pipeline that is both more efficient and more robust than combinations of existing state of the art meshing and FEM algorithms. 

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4. Estimating illumination coherence width from focused-probe intensity profiles

   https://doi.org/10.1017/S1431927621002981  

   Zjajo, Armin; Matzkevich, Itai; Rezikyan, Aram; Du, Hongchu; Dunin-Borkowski, Rafal (August 2021, Microscopy and Microanalysis)

   Fluctuation Electron Microscopy (FEM) examines speckle in images and diffraction patterns that arises from constructive and destructive interferences between the waves scattered by atoms in the thin material. Strong coherence between the scattered waves is necessary if structural correlations between those atoms is to be detected [1]. High spatial coherence in the illumination is crucial. 

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5. Beyond Additive Fusion: Learning Non-Additive Multimodal Interactions

   Wörtwein, Torsten; Sheeber, Lisa; Allen, Nicholas; Cohn, Jeffrey; Morency, Louis-Philippe (January 2022, Findings of the Association for Computational Linguistics: EMNLP 2022)

   Multimodal fusion addresses the problem of analyzing spoken words in the multimodal context, including visual expressions and prosodic cues. Even when multimodal models lead to performance improvements, it is often unclear whether bimodal and trimodal interactions are learned or whether modalities are processed independently of each other. We propose Multimodal Residual Optimization (MRO) to separate unimodal, bimodal, and trimodal interactions in a multimodal model. This improves interpretability as the multimodal interaction can be quantified. Inspired by Occam’s razor, the main intuition of MRO is that (simpler) unimodal contributions should be learned before learning (more complex) bimodal and trimodal interactions. For example, bimodal predictions should learn to correct the mistakes (residuals) of unimodal predictions, thereby letting the bimodal predictions focus on the remaining bimodal interactions. Empirically, we observe that MRO successfully separates unimodal, bimodal, and trimodal interactions while not degrading predictive performance. We complement our empirical results with a human perception study and observe that MRO learns multimodal interactions that align with human judgments. 

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