TIME-DOMAIN METHODS FOR DIFFUSIVE TRANSPORT IN SOFT MATTER.
TIME-DOMAIN METHODS FOR DIFFUSIVE TRANSPORT IN SOFT MATTER.
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DOI：
10.1137/070695186
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发表时间：
2009
影响因子：
1.9
通讯作者：
Gregory Forest AM
中科院分区：
文献类型：
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作者：
Fricks J;Yao L;Elston TC;Gregory Forest AM
被动微流变学利用噪声、熵波动（即，扩散特性）来推断体积频率相关损耗和储能模量。在这里，我们只关心布朗粒子在粘弹性介质中的扩散，梅森-韦茨理论-实验协议是理想的，更具有挑战性的推断散装粘弹性模量解耦。扩散理论从广义朗之万方程（GLE）开始，该方程具有由核指定的记忆阻力定律。我们开始与离散制定的GLE作为一个自回归随机过程管理微珠路径测量颗粒跟踪。对于逆问题（从实验数据中恢复记忆核），我们直接将时间序列分析（通过卡尔曼滤波器的最大似然估计）应用于珠位置数据，这是基于频率空间中均方位移统计的公式的替代方案。对于直接建模，我们提出了统计上精确的GLE算法的单个粒子的路径，以及位移和速度的统计相关性。我们的时域方法依赖于一个推广的知名结果为一个单模指数内核的任意M-模式的指数系列，GLE被转换为一个向量Ornstein-Uhlenbeck过程。
Passive microrheology utilizes measurements of noisy, entropic fluctuations (i.e., diffusive properties) of micron-scale spheres in soft matter to infer bulk frequency-dependent loss and storage moduli. Here, we are concerned exclusively with diffusion of Brownian particles in viscoelastic media, for which the Mason-Weitz theoretical-experimental protocol is ideal, and the more challenging inference of bulk viscoelastic moduli is decoupled. The diffusive theory begins with a generalized Langevin equation (GLE) with a memory drag law specified by a kernel. We start with a discrete formulation of the GLE as an autoregressive stochastic process governing microbead paths measured by particle tracking. For the inverse problem (recovery of the memory kernel from experimental data) we apply time series analysis (maximum likelihood estimators via the Kalman filter) directly to bead position data, an alternative to formulas based on mean-squared displacement statistics in frequency space. For direct modeling, we present statistically exact GLE algorithms for individual particle paths as well as statistical correlations for displacement and velocity. Our time-domain methods rest upon a generalization of well-known results for a single-mode exponential kernel to an arbitrary M-mode exponential series, for which the GLE is transformed to a vector Ornstein-Uhlenbeck process.