Tengfei Xu | Searcharxiv

arXiv2025

Three-Dimensional Continuous Multi-Walled Carbon Nanotubes Network-Toughened Diamond Composite

Enhancing the fracture toughness of diamond while preserving its hardness is a significant challenge. Traditional toughening strategies have primarily focused on modulating the internal microstructural units of diamonds, including adjustments to stacking sequences, faults, nanotwinning, and the incorporation of amorphous phases, collectively referred to as intrinsic toughening. Here, we introduce an extrinsic toughening strategy to develop an unparalleled tough diamond composite with complex and abundant sp2-sp3 bonding interfaces, by incorporating highly dispersed multi-walled carbon nanotubes (MWCNTs) into the gaps of diamond grains to create a three-dimensional (3D) continuous MWCTNs network-toughen heterogeneous structure. The resultant composite exhibits a hardness of approximately 91.6 GPa and a fracture toughness of roughly 36.4 MPa.m1/2, which is six times higher than that of synthetic diamond and even surpasses that of tungsten alloys, surpassing the benefits achievable through intrinsic toughening alone. The remarkable toughening behavior can be attributed to the formation of numerous mixed sp2-sp3 bonding interactions at the 3D continuous network MWCNTs/diamond interfaces, which facilitate efficient energy dissipation. Our 3D continuous network heterogeneous structure design provides an effective approach for enhancing the fracture toughness of superhard materials, offering a new paradigm for the advanced composite ceramics.

cond-mat.other↗

arXiv2023

Variational operator learning: A unified paradigm marrying training neural operators and solving partial differential equations

Neural operators as novel neural architectures for fast approximating solution operators of partial differential equations (PDEs), have shown considerable promise for future scientific computing. However, the mainstream of training neural operators is still data-driven, which needs an expensive ground-truth dataset from various sources (e.g., solving PDEs' samples with the conventional solvers, real-world experiments) in addition to training stage costs. From a computational perspective, marrying operator learning and specific domain knowledge to solve PDEs is an essential step in reducing dataset costs and label-free learning. We propose a novel paradigm that provides a unified framework of training neural operators and solving PDEs with the variational form, which we refer to as the variational operator learning (VOL). Ritz and Galerkin approach with finite element discretization are developed for VOL to achieve matrix-free approximation of system functional and residual, then direct minimization and iterative update are proposed as two optimization strategies for VOL. Various types of experiments based on reasonable benchmarks about variable heat source, Darcy flow, and variable stiffness elasticity are conducted to demonstrate the effectiveness of VOL. With a label-free training set and a 5-label-only shift set, VOL learns solution operators with its test errors decreasing in a power law with respect to the amount of unlabeled data. To the best of the authors' knowledge, this is the first study that integrates the perspectives of the weak form and efficient iterative methods for solving sparse linear systems into the end-to-end operator learning task.

cs.LG↗