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Analysis

This paper addresses a critical challenge in thermal management for advanced semiconductor devices. Conventional finite-element methods (FEM) based on Fourier's law fail to accurately model heat transport in nanoscale hot spots, leading to inaccurate temperature predictions and potentially flawed designs. The authors bridge the gap between computationally expensive molecular dynamics (MD) simulations, which capture non-Fourier effects, and the more practical FEM. They introduce a size-dependent thermal conductivity to improve FEM accuracy and decompose thermal resistance to understand the underlying physics. This work provides a valuable framework for incorporating non-Fourier physics into FEM simulations, enabling more accurate thermal analysis and design of next-generation transistors.
Reference

The introduction of a size-dependent "best" conductivity, $κ_{\mathrm{best}}$, allows FEM to reproduce MD hot-spot temperatures with high fidelity.

Analysis

This paper introduces a new class of flexible intrinsic Gaussian random fields (Whittle-Matérn) to address limitations in existing intrinsic models. It focuses on fast estimation, simulation, and application to kriging and spatial extreme value processes, offering efficient inference in high dimensions. The work's significance lies in its potential to improve spatial modeling, particularly in areas like environmental science and health studies, by providing more flexible and computationally efficient tools.
Reference

The paper introduces the new flexible class of intrinsic Whittle--Matérn Gaussian random fields obtained as the solution to a stochastic partial differential equation (SPDE).