The last 25 years have seen significant advances in the modeling and mathematical analysis of fracture. However, the strongest mathematical results have been restricted to variational models that have ...

Wind speed forecasting plays a critical role in ensuring optimal operation and dispatch of power systems, especially with the global expansion of wind energy. However, the inherently nonstationary and ...

Elliptic partial differential equations (PDEs) are a central pillar in the mathematical description of steady-state phenomena across physics, engineering, and applied sciences. Characterised by the ...

We introduce a self-guided, interactive JupyterLab to familiarize undergraduate students with introductory quantum mechanics concepts. In the lab, the linear variational method is applied to a ...

The codebase is currently under development. We are in the process of unifying various parts of the code, including migrating algorithms from the Haiku library to Flax. As a result, some outcomes may ...

This paper examines multiscale theories and numerical methods for interconnect materials in electronic packaging, focusing on the interplay among micro-scale morphology, meso-scale structure, and ...

Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to ...

We overview the main equations of the Rayleigh–Ritz variational method and discuss their connection with the problem of simultaneous diagonalization of two Hermitian matrices.

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A tree-based method for regression is proposed. In a high dimensional feature space, the method has the ability to adapt to the lower intrinsic dimension of data if the data possess such a property so ...