A New Atomistic-to-Continuum Thermomechanical Model that Enables a Novel Averaging Method for Molecular Dynamics Simulations

提出的研究目标是建立一个新的原子-连续统热力学模型来描述固体中原子（微观）量和连续统（宏观）量之间的关系。该模型允许开发新的多尺度去噪（平均）方法，用于将非平衡分子动力学（MD）模拟获得的动力学量分解为各自的局部热和力学贡献。在本研究中，将通过1)测试高斯近似和温度估计来建立热力学模型，2)开发多尺度时空阈值估计器，3)使用新的多尺度平均方法测试热力学加性模型，4)使用新的平均方法估计连续应力。该研究的成功完成将影响许多学科，包括力学、传热、信号处理和非参数统计。例如，新的多尺度方法耦合MD和有限元方法来模拟非平衡热力学过程，将有可能扩展MD模拟的时间和空间尺度。纳米技术的应用，如激光烧蚀纳米尺度图案化和激光辅助印迹将极大地受益于所提出的研究。扩大学生（包括代表性不足的学生）参与的努力包括：1)组织？纳米技术可视化?为匹兹堡地区的高中生举办研讨会，2)为旧金山的高中生建立一个互动平台，3)引入计算纳米力学的新课程。这些活动将整合本提案的新研究成果和概念。

The objective of the proposed research is to establish a new atomistic-to-continuum thermomechanical model for describing the relation between atomistic (microscopic) quantities and continuum (macroscopic) quantities in solids. The proposed model allows the development of novel multiscale denoising (averaging) method employed to decompose the dynamical quantities obtained from nonequilibrium molecular dynamics (MD) simulations into their respective local thermal and mechanical contributions. In the proposed research, the thermomechanical model will be established by 1) testing the Gaussian approximation and temperature estimation, 2) developing a multiscale spatial-temporal thresholding estimator, 3) testing the thermomechanical additive model with the new multiscale averaging method, and 4) estimating the continuum stress using the new averaging method. The successful completion of the proposed research will impact a number of disciplines that include mechanics, heat transfer, signal processing, and nonparametric statistics. For example, new multiscale method coupling MD and finite element methods for simulating nonequilibrium thermomechanical processes will be made possible to extend the time and spatial scale of MD simulation. Nanotechnology applications such as laser ablation for nanoscale patterning and laser-assisted imprinting will be benefited tremendously from the proposed research. Efforts to broaden the participation of students including the underrepresented ones include 1) organizing ?nanotechnology visualization? workshops for high schools students in the larger Pittsburgh area, 2) building an interaction platform for high school students in San Francisco, and 3) introducing a new course in computational nanomechanics. These activities will integrate new research results and concepts from this proposal.