AI 中文总结
介绍粗糙表面接触的佩尔松随机过程模型，讨论其纯法向弹性接触理论，包括用偏微分方程求解相关概率密度，还提及在其他摩擦学领域的应用及未来研究建议，助力该理论发展。
AI 中文摘要
粗糙表面接触的随机过程模型，即广为人知的佩尔松接触理论，是具有代表性的多尺度模型，已在摩擦学各领域广泛应用。本章简要介绍佩尔松接触理论的发展背景，深入讨论纯法向弹性接触理论，特别关注用偏微分方程求解接触压力和界面间隙的概率密度。还考察了这些基本结果在解决摩擦学其他领域更复杂界面特性方面的后续应用。最后提出了关于佩尔松理论未来研究的若干建议。这篇综述文章有望帮助研究人员快速熟悉佩尔松理论的当前技术水平，并吸引摩擦学家和固体力学家更多关注，从而推动佩尔松接触理论的发展与应用。
英文摘要
The stochastic process model of rough surface contact, widely known as Persson's theory of contact, serves as a representative multi-scale model that has been extensively applied across various fields of tribology. In this chapter, we briefly introduce the background of the development of Persson's theory of contact. We thoroughly discuss Persson's theory for purely normal elastic contact, with a special focus on solving the probability density of the contact pressure and the interfacial gap using partial differential equations. Subsequent applications of these fundamental results in addressing more complex interfacial properties in other fields of tribology are also examined. Finally, several recommendations regarding future studies of Persson's theory are proposed. This review article is expected to assist researchers in quickly familiarizing themselves with the current state of the art of Persson's theory and to attract more attention from tribologists and solid mechanicians, thereby contributing to the development and application of Persson's theory of contact.
