Computational model of twisted elastic ribbons

We develop an irregular lattice mass-spring model to simulate and study the deformation modes of a thin elastic ribbon as a function of applied end-to-end twist and tension. Our simulations reproduce all reported experimentally observed modes, including transitions from helicoids to longitudinal wrinkles, creased helicoids and loops with self-contact, and transverse wrinkles to accordion self-folds. Our simulations also show that the twist angles at which the primary longitudinal and transverse wrinkles appear are well described by various analyses of the Föppl-von Kármán equations, but the characteristic wavelength of the longitudinal wrinkles has a more complex relationship to applied tension than previously estimated. The clamped edges are shown to suppress longitudinal wrinkling over a distance set by the applied tension and the ribbon width, but otherwise have no apparent effect on measured wavelength. Further, by analyzing the stress profile, we find that longitudinal wrinkling does not completely alleviate compression, but caps the magnitude of the compression. Nonetheless, the width over which wrinkles form is observed to be wider than the near-threshold analysis predictions: the width is more consistent with the predictions of far-from-threshold analysis. However, the end-to-end contraction of the ribbon as a function of twist is found to more closely follow the corresponding near-threshold prediction as tension in the ribbon is increased, in contrast to the expectations of far-from-threshold analysis. These results point to the need for further theoretical analysis of this rich thin elastic system, guided by our physically robust and intuitive simulation model.

Machine-Learning Spectral Indicators of Topology

Topological materials discovery has emerged as an important frontier in condensed matter physics. While theoretical classification frameworks have been used to identify thousands of candidate topological materials, experimental determination of materials' topology often poses significant technical challenges. X-ray absorption spectroscopy (XAS) is a widely used materials characterization technique sensitive to atoms' local symmetry and chemical bonding, which are intimately linked to band topology by the theory of topological quantum chemistry (TQC). Moreover, as a local structural probe, XAS is known to have high quantitative agreement between experiment and calculation, suggesting that insights from computational spectra can effectively inform experiments. In this work, computed X-ray absorption near-edge structure (XANES) spectra of more than 10 000 inorganic materials to train a neural network (NN) classifier that predicts topological class directly from XANES signatures, achieving F₁ scores of 89% and 93% for topological and trivial classes, respectively is leveraged. Given the simplicity of the XAS setup and its compatibility with multimodal sample environments, the proposed machine-learning-augmented XAS topological indicator has the potential to discover broader categories of topological materials, such as non-cleavable compounds and amorphous materials, and may further inform field-driven phenomena in situ, such as magnetic field-driven topological phase transitions.

Author Correction: A model for the fragmentation kinetics of crumpled thin sheets

A Correction to this paper has been published: https://doi.org/10.1038/s41467-021-22791-z

A model for the fragmentation kinetics of crumpled thin sheets

As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility. Experiments have shown that the total crease length accrues logarithmically when repeatedly compacting and unfolding a sheet of paper. Here, we offer insight to this unexpected result by exploring the correspondence between crumpling and fragmentation processes. We identify a physical model for the evolution of facet area and ridge length distributions of crumpled sheets, and propose a mechanism for re-fragmentation driven by geometric frustration. This mechanism establishes a feedback loop in which the facet size distribution informs the subsequent rate of fragmentation under repeated confinement, thereby producing a new size distribution. We then demonstrate the capacity of this model to reproduce the characteristic logarithmic scaling of total crease length, thereby supplying a missing physical basis for the observed phenomenon.

Machine learning in a data-limited regime: Augmenting experiments with synthetic data uncovers order in crumpled sheets

Machine learning has gained widespread attention as a powerful tool to identify structure in complex, high-dimensional data. However, these techniques are ostensibly inapplicable for experimental systems where data are scarce or expensive to obtain. Here, we introduce a strategy to resolve this impasse by augmenting the experimental dataset with synthetically generated data of a much simpler sister system. Specifically, we study spontaneously emerging local order in crease networks of crumpled thin sheets, a paradigmatic example of spatial complexity, and show that machine learning techniques can be effective even in a data-limited regime. This is achieved by augmenting the scarce experimental dataset with inexhaustible amounts of simulated data of rigid flat-folded sheets, which are simple to simulate and share common statistical properties. This considerably improves the predictive power in a test problem of pattern completion and demonstrates the usefulness of machine learning in bench-top experiments where data are good but scarce.

Simple Molecular Reactive Force Field for Metal-Organic Synthesis

For colloidal quantum dots to transition from research laboratories to deployment as optical and electronic products, there will be a need to scale-up their production to large-scale manufacturing processes. This demand increases the need to understand their formation via a molecular representation of the nucleation of lead sulfide (PbS) quantum dot systems passivated by lead oleate complexes. We demonstrate the effectiveness of a new type of reactive potential, custom-made for this system, that is drawn from simple Morse, Lennard-Jones, and Coulombic components, which can reproduce reactions across a broad range of PbS quantum dot sizes with good accuracy. We validate the capability of this model to capture reactive systems by comparison to ab initio calculations for a reaction between two dots.