润滑油膜熔化过程中应力时间序列的多重分形分析
Multifractal analysis of stress time series during ultrathin lubricant film melting
摘要：
本文用粘弹性物质近似的流变学模型研究了两个原子级平面之间的非稳态润滑膜的熔化。考虑到应力、应变和润滑剂温度的附加噪声，建立了对应于滑动、干摩擦和两种$stick-slip$摩擦状态的相图。应力时间序列已获得所有制度的摩擦使用Stratonovich解释。结果表明，当温度噪声强度远大于应变和应力噪声强度时，润滑油熔化过程具有自相似性。这种状态是由均匀分布定义的，在这种状态下，没有特征应力尺度。我们研究应力时间序列获得的所有摩擦制度，使用多重分形去趋势波动分析。已经表明，这些系列的多重分形是由系统中存在的不同相关性以及幂律分布引起的。由于幂律分布与小应力有关，因此这种情况对应于自相似固体状润滑剂。
英文摘要：
Melting of an ultrathin lubricant film confined between two atomically flat surfaces is we studied using the rheological model for viscoelastic matter approximation. Phase diagram with domains, corresponding to sliding, dry, and two types of $stick-slip$ friction regimes has been built taking into account additive noises of stress, strain, and temperature of the lubricant. The stress time series have been obtained for all regimes of friction using the Stratonovich interpretation. It has been shown that self-similar regime of lubricant melting is observed when intensity of temperature noise is much larger than intensities of strain and stress noises. This regime is defined by homogenous distribution, at which characteristic stress scale is absent. We study stress time series obtained for all friction regimes using multifractal detrended fluctuation analysis. It has been shown that multifractality of these series is caused by different correlations that are present in the system and also by a power-law distribution. Since the power-law distribution is related to small stresses, this case corresponds to self-similar solid-like lubricant.
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