论文标题
非线性流变学的Kramers-Kronig关系：1。一般表达和含义
Kramers-Kronig Relations for Nonlinear Rheology: 1. General Expression and Implications
论文作者
论文摘要
因果关系的原理导致线性kramers-kronig关系（KKR）通过积分变换与复杂模量$ g^{*} $相关的真实和虚构部分。使用非线性流变学的玻尔兹曼叠加原理的多个积分概括，以及因果关系的原理，我们得出了非线性KKR，它与$ n^\ text {th} $ orde confffer comporte复杂模量$ g_ {n}^n}^{*} $的真实和虚构部分相关联。对于$ n $ = 3，我们获得了中等幅度平行叠加（地图）流变的非线性KKR。地图的特殊情况是中等振幅振荡剪切（MAOS）；我们获得了第三谐波Maos模量$ g_ {33}^{*} $的MAOS KKR;但是，对于第一个谐波maos模量$ g_ {31}^{*} $，不存在这样的KKR。我们为单模式Giesekus模型验证了地图和MAOS KKR。当将集成域截断到有限的频率窗口时，我们还探测了MAO KKR的灵敏度。我们发现（i）从$ g_ {\ prime \ prime} $推断$ g_ {33}^{\ prime \ prime} $，比反之亦然，（ii）对特定频率范围上的预测更可靠，（ii）在特定频率范围上进行预测，需要大约超过一个十年的数据范围超出预测范围$ iii $ g___________333333333333333 {{333^{大频率的错误。
The principle of causality leads to linear Kramers-Kronig relations (KKR) that relate the real and imaginary parts of the complex modulus $G^{*}$ through integral transforms. Using the multiple integral generalization of the Boltzmann superposition principle for nonlinear rheology, and the principle of causality, we derived nonlinear KKR, which relate the real and imaginary parts of the $n^\text{th}$ order complex modulus $G_{n}^{*}$. For $n$=3, we obtained nonlinear KKR for medium amplitude parallel superposition (MAPS) rheology. A special case of MAPS is medium amplitude oscillatory shear (MAOS); we obtained MAOS KKR for the third-harmonic MAOS modulus $G_{33}^{*}$; however, no such KKR exists for the first harmonic MAOS modulus $G_{31}^{*}$. We verified MAPS and MAOS KKR for the single mode Giesekus model. We also probed the sensitivity of MAOS KKR when the domain of integration is truncated to a finite frequency window. We found that that (i) inferring $G_{33}^{\prime\prime}$ from $G_{33}^{\prime}$ is more reliable than vice-versa, (ii) predictions over a particular frequency range require approximately an excess of one decade of data beyond the frequency range of prediction, and (iii) $G_{33}^{\prime}$ is particularly susceptible to errors at large frequencies.
