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KAKEN_26400147seika.pdf
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:160.2 KB
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:Sep 21, 2017 |
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| Title |
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相分離界面に関連した長距離相関を持つ確率場の研究
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ソウブンリ カイメン ニ カンレンシタ チョウキョリ ソウカン オ モツ カクリツバ ノ ケンキュウ
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Sobunri kaimen ni kanrenshita chokyori sokan o motsu kakuritsuba no kenkyu
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Study on random fields with long range correlations related to phase separating interfaces
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坂川, 博宣
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サカガワ, ヒロノブ
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Sakagawa, Hironobu
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慶應義塾大学・理工学部・准教授
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Research team head
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科研費研究者番号 : 60348810
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2017
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科学研究費補助金研究成果報告書
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2016
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本研究では相分離界面や細胞膜などの数学的な解析を目指し, 関連した長距離相関を持つ確率場の研究を行った。特に確率界面モデルの一つであるΔφモデルに対し以下の結果を得た。(1) 3次元以下の場合に場が常に正となる確率の評価を与え, その挙動が高次元の場合や他の界面モデルと比べて大きく変わることを示した。(2) 2次元以上の場合に場にピンニング効果を加えるとその強さによらず対応する自由エネルギーが常に正となり場が常に局在化することを示した。
In this research, we studied several random fields with long range correlations for mathematical analysis of phase separating interfaces and membranes. In particular, we considered the Δφ interface model and obtained the following results : (1) We give an estimate on the probability that the field stays positive in low dimensions and its behaviors differ greatly from those of the higher dimensional case or other random interface models. (2) We show that in the case of two or more dimensions, once we impose weak pinning potentials the field is always localized in the sense that the corresponding free energy is always positive.
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研究種目 : 基盤研究(C)(一般)
研究期間 : 2014～2016
課題番号 : 26400147
研究分野 : 確率論
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