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In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an essential role in capturing the shape of scalar field data. We present a state‐of‐the‐art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time‐varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.

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We present a state‐of‐the‐art report on time‐dependent flow topology. We survey representative papers in visualization and provide a taxonomy of existing approaches that generalize flow topology from time‐independent to time‐dependent settings. The approaches are classified based upon four categories: tracking of steady topology, reference frame adaption, pathline classification or clustering, and generalization of critical points. Our unique contributions include introducing a set of desirable mathematical properties to interpret physical meaningfulness for time‐dependent flow visualization, inferring mathematical properties associated with selective research papers, and utilizing such properties for classification. The five most important properties identified in the existing literature include coincidence with the steady case, induction of a partition within the domain, Lagrangian invariance, objectivity, and Galilean invariance.

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Capsule robots capable of taking wireless power-transfer systems for diagnosis in the intestine enable the ability to avoid invasive detection, which causes damage to tissue. A targeted therapy capsule robot based on a wireless power-transfer system could move actively in the intestine, implementing diseases detection and drug delivery. Compared with traditional telescope, the capsule robot explores without pain to patients. However, the insufficient power supply has become a big issue for a targeted therapy capsule robot. To address this problem, we proposed a new type of three-dimensional spindle-shaped receiving coil that can couple well with unidirectional magnetic fields and supply sufficient energy even when there is a misalignment in position and angle, owing to which the electromagnetic energy decays quickly. The proposed receiving coil could be embedded on the capsule robot, suitable for the capsule size Φ15 mm × 25 mm. To obtain the maximum energy in three-dimensional space, an optimization model was built. The parameters of the receiving coil were optimized and analyzed. Then, the designed receiving coil was verified with an energy-transfer stability analysis based on both attitude angle and position in a bench test. Furthermore, a curved pipe experiment was conducted using a capsule robot prototype with the proposed three-dimensional spindle-shaped receiving coil. The results demonstrated that stable and sufficient power could be supplied by the proposed receiving coil for the capsule robot at any position and any attitude angle between transmitting and receiving coils.

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