Joint research of secondary ordered optimization problem on diffraction, scattering and magnetic structure analysis【Cancel】

Reference No.	20200010
Type/Category	Grant for General Research-Short-term Joint Research
Title of Research Project	Joint research of secondary ordered optimization problem on diffraction, scattering and magnetic structure analysis【Cancel】
Principal Investigator	Masato Hagihala（Neutron science division, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK)・assistant professor）
Research Period	August 6,2020. - August 8,2020.
Keyword(s) of Research Fields	global optimization, quadratic programming, semidefinite programming, Grobner basis, magnetic structure analysis Landau theory, representation analysis, magnetic space group, neutron diffraction
Abstract for Research Report	【purpose】 We discovered that SemiDefinite Programming (SDP) method is useful for global optimization on magnetic structure analysis and its procedure can be performed in a practical time [1,2]. Magnetic structure analysis, which perform to solve alignment of magnetic moment in the field of solid state physics, is used for study and development of magnet material. For magnetic structure analysis, neutron powder diffraction profiles are needed as experimental data. We can collect those profiles by neutron powder spectroscopes installed at MLF, J-PARC. J-PARC, installed the world class proton accelerator, is joint use facility in Japan. Some of members distribute a package program of crystal and magnetic structure analysis (Z-Code) for general users. We believe that development cooperation of Z-Code project contributes for public benefit. The purpose of this joint study is to create software of magnetic structure analysis based on SDR method. One or two days open meeting is needed to discuss various issue about applying SDP to magnetic structure analysis between experimental physicists and mathematicians. 【expected result】 ・Magnetic structure analysis have mainly performed by experts of solid state physics. Its analysis includes one of mathematic method, called representation analysis. For widely use, especially industry use, reducing users tasks is required. Promoting industry use is important for J-PARC. We think that this study is the first step of the promotion in magnet material region. ・Magnetic structure analysis include various structure models defined mathematically. For example, representation analysis based on Landau theory (i.e. representation of magnetic space group), simulation of reflection position on modulated structure, magnetic quasi-crystal, is used. Those structure models are related to main theme of mathematical crystallography. We think that discussion of those models together with experimental data and observation error can find out new developing demand and new issue. ・SDR method is global optimization method. That is, we can discuss about not only guarantee of the result but also getting all of global optimal solutions (consequently the symmetry of the problem and the solution). How should the mathematically obtained information be provided? Applying SRD to the specific example which is considered its usability is meaningful not only for usage of global optimal method but also for re-examination of discussion of mathematics based on proof. [1] K. Tomiyasu, R. Oishi-Tomiyasu, M. Matsuda, M. Matsuhira, “A new mathematical approach to finding global solutions of the magnetic structure determination problem”, Scientific Reports (2018) 8:16228.? [2] R. Oishi-Tomiyasu, “Application of convex optimization to identification of atomic species from diffraction patterns”, Powder Diffraction Journal, 32(S1) (2017), pp. S179--S185.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Katsuki Fujisawa（Kyushu University・Professor） Toru Ishigaki（Ibaraki University・Professor） Takashi Kamiyama（High Energy Accelerator Research Organization (KEK)・Professor） Taku J Sato（Tohoku University・Professor） Keisuke Tomiyasu（Nissan Arc Ltd.・Chief） Ryoko Tomiyasu（Kyushu University・Associate Professor） Masato Hagihala（High Energy Accelerator Research Organization (KEK)・Assistant Professor）