Topological analysis of flow (phenomena that can be regarded as such)
Social Infrastructure (Saitama University Research Seed Collection 2025-27 p.3)
Keywords: Flow, Topology, Data Analysis, Dynamical Systems, Streamline Topology Analysis, TFDA, Stability
This is a study that builds a framework to express flow without ambiguity and analyzes phenomena that can be regarded as flow. This is a theory created by my collaborators and me, and it has been applied in various fields such as engineering, medicine, oceanography, and meteorology. As for specific research content, for example, it provides tools to distinguish between two states that appear similar but have significantly different characteristics. Furthermore, it can identify the governing regions of vortices in the sense of topology without ambiguity, thereby making insights that could not be explicitly expressed explicit through the use of topology. In particular, we have implemented a theory for extracting the topology of flow on a computer and are conducting topological data analysis of flow. On the other hand, regarding the implementation of the theory for extracting the topology of flow on a computer, there are parts of the theory that have been implemented and parts that are still under implementation, so we are developing the portions that are still in progress.
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Tomoo Yokoyama, Professor Graduate School of Science and Technology, Department of Mathematical and Electronic Information, Mathematical Area 【Recent Research Themes】 ● The shape and distance structure of flow spaces ● Limits of flows ● Mechanisms of non-existence of averages ● A framework for extracting finite structures from the connections between flow, shape, and space ● General structures of "incompressible" oriented fields (e.g., liquid crystals, patterns on lines)
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【Appeal Points to the Industry】 ● It is a theory developed in collaboration with co-researchers and has novelty (established about 10 years ago). ● Three granted domestic patents, one domestic patent application, and a PCT application (some have been granted in the USA, Europe, India, China, etc.). ● Received the 2020 Paper Award from the Japan Society for Industrial and Applied Mathematics for a paper on streamline topology analysis. ● Implementation of patent licensing to companies. 【Examples of Practical Use, Applications, and Utilization】 ● Improvement of industrial machinery (press release issued). ● Application to cardiovascular blood flow. ● Application to meteorology and oceanography.
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All flows and their changes that generally occur with two or fewer vortices.
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The Saitama University Open Innovation Center is a center that functions as a liaison office for industry-academia-government collaboration. It consists of three departments: the Industry-Academia-Government Collaboration Department, the Intellectual Property Department, and the Startup Support Department, each staffed with coordinators well-versed in various fields. The center's activities include solving technical challenges in companies, supporting the implementation of joint research, and conducting technology transfer aimed at introducing and utilizing Saitama University's intellectual property.
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