Titlebook: A Mathematical Approach to Research Problems of Science and Technology; Theoretical Basis an Ryuei Nishii,Shin-ichiro Ei,Tomoyuki Shirai Bo

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Mathematical Analysis for Pattern Formation Problems978-3-322-83650-2

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Models and Applications of Organism Transportation978-3-322-94629-4

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The Renormalization Group Method for Ordinary Differential Equations978-3-322-94512-9

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https://doi.org/10.1057/9780230114623We explain our theoretical treatment of various kinds of patterns appearing in nature in this paper. We introduce one of our typical approaches to focus on the pattern boundaries and to derive a curvature flow equation for the motion of these boundaries. This approach is based on the idea that patterns are defined by their boundaries.

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Studies in Contemporary HistoryWe consider a phase field model for crack propagation in an elastic body. The model is derived as an irreversible gradient flow of the Francfort-Marigo energy with the Ambrosio-Tortorelli regularization and is consistent to the classical Griffith theory. Some numerical examples computed by adaptive mesh finite element method are presented.

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https://doi.org/10.1007/978-4-431-55060-0Applications for Industry; Big Data Visualization; Mathematical Modelling; Public-key Encryption; Symbol

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978-4-431-56393-8The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Japan KK