Stochastic Constitutive Models for Nano-Scale Heat Transport

纳米级热传输的随机本构模型

• 批准号: 1819011
• 负责人: Xiantao Li
• 金额: $ 20万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1819011&HistoricalAwards=false
• 关键词: Stochastic; Constitutive; Models; Nano; Scale

At the nano-mechanical scale, heat conduction processes exhibit a wide variety of phenomena that are different from macroscopic observations. Conventional models, such as the Fourier's law, are inadequate. In addition, there are overwhelming observations that suggest that heat conduction properties depend critically on the system size and geometry, creating a unique challenge for the portability of the mathematical models. This project aims to bridge the modeling gap by developing a first-principle based approach that leads to a hierarchy of generalized models. The new models have the potential capabilities to describe various important behavior of heat conduction processes, including the wave propagation characteristic, fluctuation, delay, and more. The proposed approach will derive new constitutive models from first-principle, and mathematically, the models are obtained from a microscopic many-particle description with three levels of reductions: A spatial reduction that eliminates atomic-level details and singles out the dynamics of the average energy, a temporal reduction that removes the nonlocality in time, and a statistical reduction that efficiently samples scale-dependent, statistical noises. Such a first-principle based approach derives its benefit from its combination of mathematical transparency, robustness, and amenability to error estimates. Unlike conventional theories, the current approach yields a stochastic constitutive model. Combined with energy balance, the constitutive models lead to stochastic partial differential equations, for which there is a wealth of interesting mathematical and computational issues.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在纳米力学尺度下，热传导过程表现出与宏观观察不同的各种现象。 传统的模型，如傅立叶定律，是不够的。此外，有压倒性的观察结果表明，热传导特性严重依赖于系统的大小和几何形状，这对数学模型的可移植性提出了独特的挑战。该项目旨在通过开发一种基于第一原理的方法来弥合建模差距，该方法导致了广义模型的层次结构。新模型具有描述热传导过程的各种重要行为的潜在能力，包括波的传播特性，波动，延迟等。所提出的方法将从第一原理推导出新的本构模型，并且在数学上，这些模型是从具有三个级别的减少的微观多粒子描述中获得的：消除原子级细节并挑出平均能量的动态的空间减少，消除时间上的非局部性的时间减少，以及有效地对尺度相关的统计噪声进行采样的统计减少。这种基于第一原理的方法得益于其数学透明性、鲁棒性和对误差估计的顺从性的组合。与传统的理论，目前的方法产生一个随机本构模型。与能量平衡相结合，本构模型导致随机偏微分方程，其中有大量有趣的数学和计算问题。该奖项反映了NSF的法定使命，并已被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

Reduced-Order Modeling Approach for Electron Transport in Molecular Junctions

分子结中电子传输的降阶建模方法

• DOI: 10.1021/acs.jctc.9b01090
• 发表时间: 2020
• 期刊: Journal of Chemical Theory and Computation
• 影响因子: 5.5
• 作者: Chu, Weiqi;Li, Xiantao
• 通讯作者: Li, Xiantao

The computation of local stress in ab initio molecular simulations

• DOI: 10.1088/1361-651x/ab2b8a
• 发表时间: 2018-12
• 期刊: Modelling and Simulation in Materials Science and Engineering
• 影响因子: 1.8
• 作者: Xiantao Li

Nonlinear Constitutive Models for Nano-Scale Heat Conduction

纳米级热传导的非线性本构模型

• DOI: 10.1137/19m1257664
• 发表时间: 2021
• 期刊: Multiscale Modeling & Simulation
• 影响因子: 1.6
• 作者: Chu, Weiqi;Li, Xiantao
• 通讯作者: Li, Xiantao

Absorbing boundary conditions for time-dependent Schrödinger equations: A density-matrix formulation

瞬态薛定谔方程的吸收边界条件：密度矩阵公式

• DOI: 10.1063/1.5079326
• 发表时间: 2019
• 期刊: The Journal of Chemical Physics
• 作者: Li, Xiantao

The Mori–Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics

• DOI: 10.4310/cms.2019.v17.n2.a10
• 发表时间: 2017-08
• 期刊: Communications in Mathematical Sciences
• 影响因子: 1
• 作者: Weiqi Chu;Xiantao Li