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Turbulent flows, characterized by their chaotic and stochastic nature, have historically presented formidable challenges to predictive computational modeling. Traditional eddy-resolved numerical simulations often require vast computational resources, making them impractical or infeasible for numerous engineering applications. As an alternative, deep learning-based surrogate models have emerged, offering data-drive solutions. However, these are typically constructed within deterministic settings, leading to shortfall in capturing the innate chaotic and stochastic behaviors of turbulent dynamics. In this study, we introduce a novel generative framework grounded in probabilistic diffusion models for versatile generation of spatiotemporal turbulence under various conditions. Our method unifies both unconditional and conditional sampling strategies within a Bayesian framework, which can accommodate diverse conditioning scenarios, including those with a direct differentiable link between specified conditions and generated unsteady flow outcomes, as well as scenarios lacking such explicit correlations. A notable feature of our approach is the method proposed for long-span flow sequence generation, which is based on autoregressive gradient-based conditional sampling, eliminating the need for cumbersome retraining processes. We evaluate and showcase the versatile turbulence generation capability of our framework through a suite of numerical experiments, including: (1) the synthesis of Large Eddy Simulations (LES) simulated instantaneous flow sequences from unsteady Reynolds-Averaged Navier–Stokes (URANS) inputs; (2) holistic generation of inhomogeneous, anisotropic wall-bounded turbulence, whether from given initial conditions, prescribed turbulence statistics, or entirely from scratch; (3) super-resolved generation of high-speed turbulent boundary layer flows from low-resolution data across a range of input resolutions. Collectively, our numerical experiments highlight the merit and transformative potential of the proposed methods, making a significant advance in the field of turbulence generation. 

Metal-boron triple bonds are rare due to the electron deficiency of boron. 

Accurate prediction of dynamical systems in unstructured meshes has recently shown successes in scientific simulations. Many dynamical systems have a nonnegligible level of stochasticity introduced by various factors (e.g. chaoticity), so there is a need for a unified framework that captures both deterministic and stochastic components in the rollouts of these systems. Inspired by regeneration learning, we propose a new model that combines generative and sequential networks to model dynamical systems. Specifically, we use an autoencoder to learn compact representations of full-space physical variables in a low-dimensional space. We then integrate a transformer with a conditional normalizing flow model to model the temporal sequence of latent representations. We evaluate the new model in both deterministic and stochastic systems. The model outperforms several competitive baseline models and makes more accurate predictions of deterministic systems. Its own prediction error is also reflected in its uncertainty estimations. When predicting stochastic systems, the proposed model generates high-quality rollout samples. The mean and variance of these samples well match the statistics of samples computed from expensive numerical simulations. 

Abstract The unusual properties of superconductivity in magic-angle twisted bilayer graphene (MATBG) have sparked considerable research interest^1–13. However, despite the dedication of intensive experimental efforts and the proposal of several possible pairing mechanisms^14–24, the origin of its superconductivity remains elusive. Here, by utilizing angle-resolved photoemission spectroscopy with micrometre spatial resolution, we reveal flat-band replicas in superconducting MATBG, where MATBG is unaligned with its hexagonal boron nitride substrate¹¹. These replicas show uniform energy spacing, approximately 150 ± 15 meV apart, indicative of strong electron–boson coupling. Strikingly, these replicas are absent in non-superconducting twisted bilayer graphene (TBG) systems, either when MATBG is aligned to hexagonal boron nitride or when TBG deviates from the magic angle. Calculations suggest that the formation of these flat-band replicas in superconducting MATBG are attributed to the strong coupling between flat-band electrons and an optical phonon mode at the graphene K point, facilitated by intervalley scattering. These findings, although they do not necessarily put electron–phonon coupling as the main driving force for the superconductivity in MATBG, unravel the electronic structure inherent in superconducting MATBG, thereby providing crucial information for understanding the unusual electronic landscape from which its superconductivity is derived. 

We report a study on the electronic structure and chemical bonding of the BiB molecule using high-resolution photoelectron imaging of cryogenically cooled BiB− anion. By eliminating all the vibrational hot bands, we can resolve the complicated detachment transitions due to the open-shell nature of BiB and the strong spin–orbit coupling. The electron affinity of BiB is measured to be 2.010(1) eV. The ground state of BiB− is determined to be 2Π(3/2) with a σ2π3 valence electron configuration, while the ground state of BiB is found to be 3Σ−(0+) with a σ2π2 electron configuration. Eight low-lying spin–orbit excited states [3Σ−(1), 1Δ(2), 1Σ+(0+), 3Π(2), 3Π(1), 1Π(1)], including two forbidden transitions, [3Π(0−) and 3Π(0+)], are observed for BiB as a result of electron detachment from the σ and π orbitals of BiB−. The angular distribution information from the photoelectron imaging is found to be critical to distinguish detachment transitions from the σ or π orbital for the spectral assignment. This study provides a wealth of information about the low-lying electronic states and spin–orbit coupling of BiB, demonstrating the importance of cryogenic cooling for obtaining well-resolved photoelectron spectra for size-selected clusters produced from a laser vaporization cluster source.