Comprehensive research on minimum energy structures by design theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800082
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyushu Institute of Technology
• Principal Investigator: Tagami Makoto 九州工業大学, 大学院情報工学研究院, 准教授 (50380671)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: デザイン / エネルギー最小化構造 / 調和指数デザイン / ハミングスキーム

Outline of Final Research Achievements

From the viewpoint of design theory in algebraic combinatorics, we carried out a search for minimum energy structures. Under the assumption of having the fixed moment, we constructed a computer program to make a search for distributions of finite points in Euclidean space which minimizes the energy for many kinds of potential functions. Using the program, we observed a pattern for the minimum energy structures on the plane.
We considered the finite version for spherical designs of harmonic index t in the space, which is called Hamming scheme and studied well in coding theory. In particular, we gave the constructions and the classifications for designs of harmonic index t in Hamming scheme.

Free Research Field

代数的組合せ論