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A crossover emerges as a result of the interference from similarity parameters of the higher class of the self-similarity. This framework was verified for the dynamical impact of solid sphere onto a viscoelastic board. All the physical factors including the size of spheres and the impact of velocity are successfully summarized using primal dimensionless numbers which construct a self-similar solution of the second kind, which represents the balance between dynamical elements involved in the problem. The self-similar solution gives two different scaling laws by the perturbation method describing the crossover. These theoretical predictions are compared with experimental results to show good agreement. It was suggested that a hierarchical structure of similarity plays a fundamental role on crossover, which offers a fundamental insight to self-similarity in general."}]},{"notation":[{"@value":"21 pages, 6 Figures and 9 Supplemental Figures"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1380865815688726658","@type":"Researcher","foaf:name":[{"@value":"Hirokazu Maruoka"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"12928941"},{"@type":"EISSN","@value":"1292895X"}],"prism:publicationName":[{"@value":"The European Physical Journal E"}],"dc:publisher":[{"@value":"Springer Science and Business Media LLC"}],"prism:publicationDate":"2023-05","prism:volume":"46","prism:number":"5"},"reviewed":"false","dcterms:accessRights":"http://purl.org/coar/access_right/c_abf2","dc:rights":["https://www.springernature.com/gp/researchers/text-and-data-mining","https://www.springernature.com/gp/researchers/text-and-data-mining"],"url":[{"@id":"https://link.springer.com/content/pdf/10.1140/epje/s10189-023-00292-9.pdf"},{"@id":"https://link.springer.com/article/10.1140/epje/s10189-023-00292-9/fulltext.html"}],"createdAt":"2023-05-24","modifiedAt":"2024-03-20","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=Soft%20Condensed%20Matter%20(cond-mat.soft)","dc:title":"Soft Condensed Matter (cond-mat.soft)"},{"@id":"https://cir.nii.ac.jp/all?q=FOS:%20Physical%20sciences","dc:title":"FOS: Physical sciences"},{"@id":"https://cir.nii.ac.jp/all?q=Condensed%20Matter%20-%20Soft%20Condensed%20Matter","dc:title":"Condensed Matter - 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