Macroscopic friction in the framework of the Frenkel-Kontorova model: application to dynamics of crustal faults

Frenkel-Kontorova 模型框架中的宏观摩擦：在地壳断层动力学中的应用

• 批准号: 1113578
• 负责人: Naum Gershenzon
• 金额: $ 12.91万
• 依托单位: Wright State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-15 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1113578&HistoricalAwards=false
• 关键词: Macroscopic; friction; framework; Frenkel; Kontorova

The economical and technological benefits of controlling friction are enormous. For example, the effects of kinetic friction on energy dissipation and abrasive degradation of materials is ubiquitous in 1) mechanical and material engineering and 2) machine performance and lifetime. In addition friction is a major mechanism controlling the nucleation and development of earthquakes. The latter impacts the lives of millions of people around the globe. A better understanding of conditions responsible for the appearance and dynamics of regular earthquakes and transient fault slip will be one more step toward the long-term goal of prediction of the place and time of large catastrophic earthquakes.The theory of friction is a fundamental problem in physics and geophysics. Macroscopic friction is a highly nonlinear process for which there are no governing equations describing it at either laboratory or crustal-fault scales. However, various models have been used to describe friction in a specific context. Our preliminary studies suggest that the Frenkel-Kontorova (FK) model, which was originally introduced to describe plasticity in crystals, is also an appropriate tool to model friction. In the continuum limit the FK model is described by the sine-Gordon (SG) equation, one of the fully integrable nonlinear equations of mathematical physics. This equation has been intensely investigated due to its exceptional importance and universality in physics. The results obtained and mathematical apparatus developed in various prior applications of both the FK model and the SG equation will be applied in this project to describe friction and compared with the results from laboratory experiments. In addition two specific applications of the model will be considered: (1) Episodic Tremor and Slip (ETS), and (2) triggering of non-volcanic tremor. The recently discovered phenomenon of ETS is a promising tool for monitoring previously unavailable regions of the Earth's crust. An ETS event consists of two parts: non-volcanic tremor and slow slip. These are coupled seismic and geodetic phenomena that are broadly correlated in space and time and strikingly periodic in the northern Cascadia and southwest Japan subduction zones. The latest observations reveal a complicated migration pattern of tremor during an ETS event. How a slip pulse generates tremor remains an open question; however, this question will be considered in this project in the framework of the FK model and the SG equation. Analytical solutions of the latter (allowing a clear analysis of parameter dependencies) will connect slip pulse and tremor parameters. Based on this, the migration pattern of tremor will be analyzed in detail. Also, there is growing evidence of teleseismic and tidal triggering of non-volcanic tremor, but the mechanisms of these phenomena are not clear. We suggest that tides or distant earthquakes may affect tremor production through interaction with slip pulses and this hypothesis will be examined in our model.

控制摩擦的经济和技术效益是巨大的。例如，动摩擦对材料的能量耗散和磨损降解的影响在1）机械和材料工程以及2）机器性能和寿命中普遍存在。此外，摩擦是控制地震孕育和发展的主要机制。后者影响到地球仪各地数百万人的生活。更好地理解规则地震和瞬时断层滑动的出现和动力学条件，将是朝着预测大灾难性地震的地点和时间的长期目标迈出的又一步。摩擦理论是物理学和地球物理学中的一个基本问题。宏观摩擦是一个高度非线性的过程，无论是在实验室尺度还是地壳断层尺度上，都没有描述它的控制方程。然而，各种模型已被用来描述在一个特定的背景下的摩擦。我们的初步研究表明，Frenkel-Kontorova（FK）模型，这是最初介绍的晶体中的塑性，也是一个合适的工具来模拟摩擦。在连续极限下，FK模型由数学物理中完全可积的非线性方程之一sine-Gordon（SG）方程描述。由于该方程在物理学中的特殊重要性和普遍性，人们对它进行了深入的研究。在FK模型和SG方程的各种先前应用中获得的结果和开发的数学装置将在该项目中应用于描述摩擦，并与实验室实验的结果进行比较。此外，将考虑模型的两个具体应用：（1）发作性震颤和滑动（ETS），以及（2）触发非火山震颤。最近发现的ETS现象是一种很有前途的工具，可用于监测以前无法获得的地壳区域。ETS事件包括两个部分：非火山震颤和缓慢滑动。这些是地震和大地测量的耦合现象，在空间和时间上广泛相关，在北方卡斯卡迪亚和日本西南俯冲带具有惊人的周期性。最新的观测结果揭示了在ETS事件期间复杂的震颤迁移模式。滑动脉冲如何产生震颤仍然是一个悬而未决的问题;然而，这个问题将在FK模型和SG方程的框架中被考虑。后者的解析解（允许参数依赖性的清晰分析）将连接滑动脉冲和震颤参数。在此基础上，详细分析了地震动的迁移模式。此外，有越来越多的证据表明，非火山震颤的火山喷发和潮汐触发，但这些现象的机制尚不清楚。我们认为，潮汐或远震可能会影响震颤生产通过相互作用与滑移脉冲，这一假设将在我们的模型进行检查。