Theoretical Studies on the Structures and the Physical Properties of Triply Periodic Minimal Surfaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400431
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Biological physics/Chemical physics/Soft matter physics
• Research Institution: Kinki University
• Principal Investigator: DOTERA Tomonari 近畿大学, 理工学部, 教授 (30217616)
• Co-Investigator(Renkei-kenkyūsha): MATSUZAWA Junichi 奈良女子大学, 自然科学系, 教授 (00212217)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: ソフトマター / 3重周期極小曲面 / ジャイロイド / タイリング / アルダー転移 / 空間群

Outline of Final Research Achievements

On a flat surface the hexagonal arrangement is a ubiquitous regular arrangement arising from dense packing, space division, or interactions between particles. What is regular arrangement when a surface is curved? On a sphere, this question was firstly raised by J. J. Thomson for electrons constituting atoms, Goldberg elucidated regular polyhedra, and for biological icosahedral viruses Caspar and Klug found a construction principle of regular arrangements on a sphere. In contrast, regular arrangements of particles on saddle-shaped periodic surfaces with negative curvatures have not been pursued. In this project, we have shown numerous regular arrangements of spheres on the Schwarz P- and D-surfaces obtained through the Alder transition, where magic numbers have been obtained in analogy with icosahedral viruses. These unprecedented arrangements are analyzed in terms of space groups, and polygonal & hyperbolic tilings.

Free Research Field

ソフトマター物理学