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Coherent structures are ubiquitous in unsteady flows. They can be regarded as certain kinds of spatial-temporal patterns that interact with the neighboring field. Although they play a key role in convection and mixing, there is no consensus on how to define them, and their dynamics are complicated. In the past decades, many methods are developed to identify coherent structures based on instantaneous velocity fields (e.g., vortex identification) or long-time statistics (e.g., proper orthogonal decomposition), but the evolution process of individual structures is not well considered in the identification. In this paper, we propose a new method to classify coherent motions according to their evolution dynamics. Specifically, the evolutions are represented by trajectories in the phase space. We define a distance between two trajectories and use it to construct a network that characterizes all evolution patterns. Using spectrum clustering, we categorize these patterns into various groups. This method is applied to a low Reynolds number wake flow downstream of two cylinders-in-tandem, where one of the cylinders oscillates in the transverse direction. The flow is quasi-periodic, and four types of recurrent spatial-temporal patterns can be identified. It is a useful tool to investigate low Reynolds number unsteady flows. 

Magnetic particle tracking is a recently developed technology that can measure the translation and rotation of a particle in an opaque environment like a turbidity flow and fluidized-bed flow. The trajectory reconstruction usually relies on numerical optimization or filtering, which involve artificial parameters or thresholds. Existing analytical reconstruction algorithms have certain limitations and usually depend on the gradient of the magnetic field, which is not easy to measure accurately in many applications. This paper discusses a new semi-analytical solution and the related reconstruction algorithm. The new method can be used for an arbitrary sensor arrangement. To reduce the measurement uncertainty in practical applications, deep neural network (DNN)-based models are developed to denoise the reconstructed trajectory. Compared to traditional approaches such as wavelet-based filtering, the DNN-based denoisers are more accurate in the position reconstruction. However, they often over-smooth the velocity signal, and a hybrid method that combines the wavelet and DNN model provides a more accurate velocity reconstruction. All the DNN-based and wavelet methods perform well in the orientation reconstruction.