论文标题
对过度阻尼布朗粒子系统的比例依赖性粘弹性的线性响应理论
Linear Response Theory of Scale-Dependent Viscoelasticity for Overdamped Brownian Particle Systems
论文作者
论文摘要
我们显示了用于过度阻尼布朗粒子系统的空间尺度依赖性松弛模量的线性响应理论。我们将欧文 - 柯克伍德应力张量场作为微观应力张量场。我们表明，可以使用Irving-Kirkwood应力张量场的相关函数来表达应力张量张力场对所施加速度梯度场的响应的比例依赖性松弛模量张量。弛豫模量张量的空间傅立叶变换给出了波数依赖的弛豫模量。对于各向同性和均匀的系统，松弛模量张量只有两个独立的组件。横向和纵向变形模式可提供波数依赖性的剪切弛豫模量和波数依赖的散装弛豫模量。作为简单的示例，我们为两个简单模型的弛豫模量提供了显式表达式，即非相互作用的布朗颗粒和谐波哑铃模型。
We show the linear response theory of spatial-scale-dependent relaxation moduli for overdamped Brownian particle systems. We employ the Irving-Kirkwood stress tensor field as the microscopic stress tensor field. We show that the scale-dependent relaxation modulus tensor, which characterizes the response of the stress tensor field to the applied velocity gradient field, can be expressed by using the correlation function of the Irving-Kirkwood stress tensor field. The spatial Fourier transform of the relaxation modulus tensor gives the wavenumber-dependent relaxation modulus. For isotropic and homogeneous systems, the relaxation modulus tensor has only two independent components. The transverse and longitudinal deformation modes give the wavenumber-dependent shear relaxation modulus and the wavenumber-dependent bulk relaxation modulus. As simple examples, we derive the explicit expressions for the relaxation moduli for two simple models the non-interacting Brownian particles and the harmonic dumbbell model.
