␌⏱␔␝⏚ྰ‫ܤ‬μ‫ܖ‬ỉ˳ኒ҄ểᴾἋἰὊἚἂἼἕἛ‫ܤ‬μࣱồỉᢘဇᴾ

ᴾ

Ӽോ૎ဏ

MUKAIDONO Masao৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈи৑ᧈ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ‫ܤ‬μ‫ܖ‬Ღ߻‫ܖ‬Ҧٟȷଢ඙‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ɧᄩ‫ܭ‬ƳǷǹȆȠƷȢȇȪȳǰƓǑƼᚐௌᄂᆮಒᙲ

Modeling Group䝅䝇䝔䝮䛾Ᏻ඲ᛶ☜ಖ䛿䚸ᢏ⾡ⓗഃ㠃(౛䛘䜀䚸≀⌮䚸໬Ꮫ䚸ᩘ⌮䚸ᕤᏛⓗഃ㠃➼)䛰䛡䛷䛿ᐇ⌧䛷䛝䛺䛔䚹䝅䝇䝔䝮䜢タィ䚸㐠⏝䚸⟶⌮䛩䜛ே䛻㛵䛩䜛ே㛫ⓗഃ㠃(౛䛘䜀䚸ே㛫ᕤᏛ䚸ㄆ▱⛉Ꮫ䚸ᚰ⌮Ꮫ䚸㘒ㄗ䚸Ᏻ඲ព㆑ⓗഃ㠃➼)䚸ཬ䜃䚸䝅䝇䝔䝮䛾タィ䚸㐠⏝䚸⟶⌮䚸ಖᏲ➼䛻㛵䛩䜛䝹䞊䝹䜔ᇶ‽䛺䛹䛾⤌⧊ⓗഃ㠃(౛䛘䛿Ᏻ඲ᇶ‽䚸⟶⌮యไ䚸ἲᚊ䚸ᶆ‽䚸♫఍ไᗘ➼䛾௙⤌䜏)䛾୕ഃ㠃䛜䚸᭦䛻䚸䛭䛾ୖ䛻Ᏻ඲䛾⌮ᛕⓗഃ㠃(౛䛘䜀䚸Ᏻ඲ဴᏛ䚸Ᏻ඲ᛮ᝿䚸Ᏻ඲ᩥ໬)䜢⨨䛝䚸䛭䛾ୗ䛻⤫୍ⓗ䛻䚸ᩚྜⓗ䛻䚸⥲ྜⓗ䛻㐺⏝䛥䜜䛺䛡䜜䜀䛺䜙䛺䛔䚹䛣䛾䜘䛖䛺᪂䛧䛔Ꮫၥ䛿䚸⮬↛⛉Ꮫ䚸ேᩥ⛉Ꮫ䚸♫఍⛉Ꮫ䜢ໟྵ䛧䛯㡿ᇦᶓ᩿ⓗ䛺䜒䛾䛷䛒䜚䚸➹⪅䛿䛣䜜䜢䛂Ᏻ඲Ꮫ䛃䛸ྡ௜䛡䛶䚸䛭䛾య⣔໬䛻ྲྀ䜚⤌䜣䛷䛔䜛䚹䛣䛣䛷䛾㔜せ䛺せᅉ䛿䚸Ᏻ඲䛸䛔䛖ᐈほᛶ䛾ᇶ䛵䛟⛉Ꮫⓗ஦ᐇ䛸䚸䛭䜜䜢ཷ䛡ධ䜜䜛౯್ほ䛻ᇶ䛵䛟ே㛫䛾୺ほⓗ䛺Ᏻᚰ䛸䛾㛵ಀ䛷䛒䜚䚸䝅䝇䝔䝮䛻䛚䛡䜛୙☜ᐃᛶ䛿䚸䝅䝇䝔䝮䛸ே㛫䛸䛾䛿䛦䜎䛻኱䛝䛟ᶓ䛯䜟䛳䛶䛔䜛䚹㻌 ᮏᖺᗘ䛿䚸Ᏻ඲Ꮫࡢయ⣔໬࡜ࡑࡢ᭱ୖ఩࡟఩⨨௜ࡅࡉࢀࡿᏳ඲ᛮ᝿࡟ࡘ࠸࡚⪃ᐹࡋࠊࡑࡢ⪃࠼᪉ࢆࠊᑗ᮶ࠊᾘ㈝⪅࡜࢖ࣥࣇࣛࢫࢺࣛࢡࢳࣕࢆໟྵࡍࡿࢩࢫࢸ࣒࡟Ⓨᒎࡍࡿࡇ࡜ࡀ☜ᐇどࡉࢀ࡚࠸ࡿࢫ࣐࣮ࢺࢢࣜࢵࢻࡢᏳ඲ᛶ࡜ࢭ࢟ࣗࣜࢸ࢕࡟ᑐࡋ࡚㐺⏝ࡍࡿࡇ࡜ࢆヨࡳࡓࠋཧ⪃ᩥ⊩(1) ྥẊᨻ⏨䚸Ᏻ඲Ꮫ䛾య⣔໬䛻䛴䛔䛶䡚Ᏻ඲᭭ⲷ⨶䜢䝧䞊䝇䛻⪃䛘䜛䡚䚸᪥ᮏᏳ඲Ꮫᩍ⫱◊✲఍ㄅ䚸Vol.4, pp.47-53, ᪥ᮏᏳ඲Ꮫᩍ⫱◊✲఍, 2011-8(2) ྥẊᨻ⏨䚸Ᏻ඲タィ䛾ᛮ᝿䚸⚟ᓥ➨୍ཎᏊຊⓎ㟁ᡤ஦ᨾᚋ䛾㟁Ẽ䜶䝛䝹䜼䞊䛾෇⁥䛺౪⤥䛻ྥ䛡䛶䚸pp.7-10, EAJ Information, No.150,᪥ᮏᕤᏛ䜰䜹䝕䝭䞊, 2011-12(3) Amy Poh Ai Ling , Masao Mukaidono, Selection of Model in Developing Information Security
Criteria on Smart Grid Security System, Journal of Convergence, Vol.2, No.1, pp.39-46, 2011-6(4) Amy Poh Ai Ling and Masao Mukaidono, Grid Information Security Functional Requirement
Fulfilling Information Security of a Smart Grid System, International Journal of Grid Computing &Applications, Vol. 2, No. 2, pp. 1–19, 2011-6(5) Amy Poh Ai Ling and Masao Mukaidono, Smart Grid Information Security (IS) Functional
Requirement, International Journal of Emerging Sciences, Vol.1, No.3, pp. 371-386, 2011-9

Ḙᴾ ‫ ׎‬ͺ ̖ ఍ Ὁᅈ ͺ ̖ ఍ Ў ௌᴾ Ḙ␌⏱␔␝⏚ྰ

А‫ދ‬നଯ

ᴾ᣿ᗡἼἋἁἰ἟ἊἳὅἚỉ᭗ࡇ҄ ᴾ

KARIYA Takeaki৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹᲦǰȭȸȐȫȷȓ Ǹȍǹᄂᆮᅹ૙੉ ɟ೛‫ܖٻ‬Ӹᛎ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ᣿ᗡ߻‫ܖ‬Ღ2J&ȷȟȍǽǿ‫ܖٻ‬Ღྸ‫ܖ‬Ҧٟȷʋ߸‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ᣿ᗡƷȢȇȪȳǰƓǑƼᚐௌ㻌 䠎䠌䠌䠒ᖺ䠕᭶䛛䜙䠎䠌䠍䠌ᖺ䠔᭶䜎䛷䛾᪥ᮏᅜമ౯᱁䝕䞊䝍䛸⡿ᅜᅜമ౯᱁䝕䞊䝍䛻ᇶ䛵䛔䛶䚸ྛ᭶ᮎ᫬䛾䜽䝻䝇䝉䜽䝅䝵䞁䡿䢚䡬䡼䛻䜘䜚䚸౯᱁䝰䝕䝹䜢᥎ᐃ䛧䚸౯᱁䛻ᑐ䛧䛶䚸ᖐ↓௬ㄝ H0䠖ᒓᛶຠᯝ䛺䛧䚸㻌䛻ᑐ䛧䛶䚸ᑐ❧௬ㄝ H1䠖‶ᮇ㑅ዲ䛾ᒓᛶ䛒䜚䚸H2:䜽䞊䝫䞁㑅ዲ䛾ᒓᛶ䛒䜚䚸H3:‶ᮇ㑅ዲ䞉䡴䡬䢊䢛䢙ᒓᛶ䛒䜚䚸䜢᳨ᐃ䛧䛯䚹䛭䛾⤖ᯝ䚸䛩䜉䛶䛾᫬Ⅼ䛻䛚䛔䛶䚸䛩䜉䛶䛾ᑐ❧௬ㄝ䛻ᑐ䛧䛶ᖐ↓௬ㄝ䜢Რ༷䛩䜛䛜䚸䛭䛾ព࿡䛿䚸ᩘ⌮䝣䜯䜲䝘䞁䝇䛾↓⿢ᐃ⌮ㄽ䛾䝟䝷䝎䜲䝮䜢ྰᐃ䛩䜛䛸䛔䛖ព࿡䛷㔜せ䛷䛒䜛䚹㻌 䛣䛾஦ᐇ䛻ᇶ䛵䛔䛶䚸♫മ౯᱁䛾ᇶ♏ศᯒ䜢⾜䛳䛯䚹䠎䠌䠍䠌ᖺ䠔᭶ᮎ䛷䛾♫മ౯᱁䛻ᑐ䛧䛶䚸ᴗ✀䛸᱁௜䛾᝟ሗ䜢⏝䛔䛺䛜䜙䚸ᅜമ౯᱁䛻ᑐ䛧䛶♫മ౯᱁䝇䝥䝺䝑䝗䜢⟬ฟ䛩䜛䚹䛭䛾ሙྜ䚸ୖ䛷䛾௬ㄝ᳨ᐃ䛾⤖ᯝ䛻䜘䜚䚸♫മ䛾‶ᮇ䛸䜽䞊䝫䞁䜢⪃៖䛧䛯䛂↓䝸䝇䜽♫മ౯᱁䛃䠄ᅜമ⌮ㄽ౯᱁䠅䜢᥎ᐃ䛧䚸ᕷሙ♫മ౯᱁䛛䜙䛣䛾↓䝸䝇䜽౯᱁䜢ᕪ䛧ᘬ䛝䚸䝇䝥䝺䝑䝗䜢ศᯒ䛧䛯䚹䛣䛾⤖ᯝ䚸᱁௜䛡఍♫䛾᱁௜䛡䛜ᴗ✀ෆ䛷䛺䛟ᴗ✀ᅗ䠍㻌 ౯᱁䝇䝥䝺䝑䝗䛾ᇶ♏ศᯒ䠄䠎䠌䠍䠌䠊䠔䠅㛫䛻ᑐ䛧䛶ᩚྜⓗ䛷䛺䛔䛸ุ᩿䛥䜜䜛䛾䛷䚸⌧ᅾ䝇䝥䝺䝑䝗䛻ᇶ䛵䛔䛶⤫ィⓗ䛺᱁௜䛡䜢⾜䛖᪉ἲ䜢⪃ᐹ䛧䛶䛔䜛䚹ᅗ䠍ཧ↷䚹㻌 䛥䜙䛻䚸Kariya(2012)䛾ᥦ᱌䛩䜛♫മ౯᱁䝰䝕䝹䛾䜒䛸䛷䚸ᴗ✀䛸᱁௜䛡䛾᝟ሗ䛾䜒䛸䛻䝕䜱䝣䜷䝹䝖☜⋡䛾ᮇ㛫ᵓ㐀䜢ᑟฟ䛩䜛◊✲䜢䛧䛶䛔䜛䚹௨ୗ䛾ᅗ䠎䛿䛭䛾୍㒊䠄㟁ຊ䛾䜏䠅䛷䛒䜛䚹
䛣䛾◊✲䛿䚸สᒇ䞉ᒣᮧ䞉஝䞉⋤䛾ඹྠ◊✲䚹ᅗ䠎㻌 䝕䜱䝣䜷䝹䝖☜⋡䛾ᮇ㛫ᵓ㐀䠄䠎䠌䠍䠌䠊䠔䠅㻌㻌 ᅇ཰⋡䠙䠌㻌 㻹䠌䠉㻹㻟 䛿௬ㄝ 㻴㻜㻙㻴㻟 䛻ᑐᛂ㻌

Kariya, T.(2012) A CB (corporate bond) pricing model for deriving default probabilities and recovery rates,
To appear from Contributions to Probability and statistics in honor of Morris L. Eaton, Institute ofMathematical Statistics

Modeling Groupᄂᆮಒᙲ␌⏱␔␝⏚ྰἋἰὊἚἂἼἕἛỆấẬỦᴾ
ỶὅἘἼἊỹὅἚʖยὉஇᢘ҄ỉᄂᆮᴾ

ౕգʂ

MORI Hiroyuki৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ჷᏡऴ‫ܖإ‬Ღ߻‫ܖ‬Ҧٟȷଔᆖဋ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ǤȳȆȪǸǧȳȈǷǹȆȠƷȢȇȪȳǰƓǑƼᚐௌᄂᆮಒᙲ

Modeling Group䠎䠌䠍䠍ᖺᗘ䛾䛂䝇䝬䞊䝖䜾䝸䝑䝗䛻䛚䛡䜛䜲䞁䝔䝸䝆䜵䞁䝖ண䞉᭱㐺໬䛾◊✲䛃䛸䛧䛶䚸䜎䛪䚸኱つᶍኴ㝧ගⓎ㟁ᡤ䛷䛒䜛䝯䜺䝋䞊䝷䛜タ⨨䛥䜜䛯㏦㟁䝛䝑䝖䝽䞊䜽䛻䛚䛔䛶㟁ຊไᚚᶵჾ䛷䛒䜛䠢䠝䠟T䠯
䠄Flexible AC Transmission System䠅䛾᭱㐺㓄⨨䛻䛴䛔䛶◊✲䛧䛯䚹䠢䠝䠟䠰䠯䛾୍䛴䛷䛒䜛䠱䠬䠢C 䜢᭱㐺㓄⨨䛩䜛䛯䜑䛻䛿䚸䛭䛾タ⨨ሙᡤ䛷䛒䜛䝜䞊䝗␒ྕ䛸䛭䛾ฟຊ䛷䛒䜛᭷ຠ㟁ຊ䛸↓ຠ㟁ຊ䜢Ỵᐃ䛩䜛ᚲせ䛜䛒䜛䚹㓄⨨ሙᡤ䛿䚸㞳ᩓᩘ䛷䛒䜚䚸ฟຊ䛿㐃⥆ᩘ䛷䛒䜛䛯䜑䚸ΰྜᩚᩘィ⏬ၥ㢟䜢ゎ䛟䛣䛸䛻䛺䜛䚹㟁ຊ⮬⏤໬䛜⾜䜟䜜䛶䛔䜛㏦㟁䝛䝑䝖䝽䞊䜽䛷䛿䚸䛒䜛」ᩘ䛾Ⓨ㟁఍♫䛛䜙䛒䜛」ᩘ䛾㓄㟁఍♫䛻㟁ຊ䜢䛷䛝䜛䛰䛡ከ䛟㏦㟁䛩䜛䛣䛸䛜㔜せ䛷䛒䜛䚹䛧䛛䛧䚸䝯䜺䝋䞊䝷䛜タ⨨䛥䜜䛶䛔䜛㏦
㟁䝛䝑䝖䝽䞊䜽䛷䛿䚸䛭䛾ฟຊ䛜☜⋡ⓗ䛻ኚື䛩䜛䛯䜑䚸䠢䠝䠟䠰䠯䛾᭱㐺㓄⨨䛾☜⋡ⓗホ౯䛜ᚲせ䛸䛺䜛䚹䛭䛣䛷䚸☜⋡ⓗ䛻ฟຊኚື䛩䜛」ᩘ䛾䝯䜺䝋䞊䝷䛜Ꮡᅾ䛩䜛㏦㟁䝛䝑䝖䝽䞊䜽䛻䛚䛔䛶」ᩘ䛾䠱䠬䠢C 䜢タ⨨䛩䜛ၥ㢟䜢㐍໬ⓗィ⟬ἲ䛷䛒䜛䠡䠬䠯䠫䠄Evolutionary Particle Swarm Optimization䠅䜢౑⏝䛧䛶ゎ䛟䛣䛸䛻䛴䛔䛶◊✲䛧䛯䚹ලయⓗ䛻䛿䚸ΰྜᩚᩘィ⏬ၥ㢟䜢ゎ䛯䜑䛻䚸䠎ẁ㝵䛾䠡䠬䠯O
䜢⪃᱌䛧䛯䚹䛣䛣䛷䚸䠎ẁ㝵䛾䠡䠬䠯O 䛸䛿䚸䠍ẁ㝵┠䛷䠱䠬䠢C 䛾タ⨨ሙᡤೃ⿵䜢㑅ᐃ䛧䚸䠎ẁ㝵┠䛷ྛタ⨨䛷䠱䠬䠢C 䛾ฟຊ䜢᭱㐺໬䛧䚸䛭䛾୰䛷᭱Ⰻ䛾ゎ䜢㑅䜃䚸䛭䛾ゎ䜢ึᮇ್䛻䛧䛶཯᚟ィ⟬䜢⾜䛖䚹䠍ẁ㝵┠䛷䠎㐍䝁䞊䝗䜢⏝䛔䛯㞳ᩓᆺ䠡䠬䠯O䠈䠍䠌㐍䝁䞊䝗䜢⏝䛔䛯䠎ẁ㝵┠䛷㐃⥆ᆺ䠡䠬䠯O 䜢౑⏝䛧䛯䚹䛥䜙䛻䚸ィ⟬᫬㛫䜢㧗㏿໬䛩䜛䛯䜑䚸䠎㐍䝁䞊䝗䛸䠍䠌㐍䝁䞊䝗䜢ే⏝䛧䛯䝝䜲䝤䝸䝑䝗䝁䞊䝗䜢ᥦ᱌䛧䚸Ⰻዲ䛺⤖ᯝ䜢ᚓ䛯䚹㻌 ḟ䛻䚸㏦㟁䝛䝑䝖䝽䞊䜽䛻䛚䛡䜛☜⋡౪⤥ಙ㢗ᗘ䜢ồ䜑䜛䛯䜑䛾ከ┠ⓗ᭱㐺໬ᡭἲ䛻䛴䛔䛶◊✲䛧䛯䚹䝇䝬䞊䝖䜾䝸䝑䝗䛻䛚䛔䛶Ⓨ㟁ฟຊ䛜㢧ⴭ䛻ኚື䛩䜛෌⏕ྍ⬟䜶䝛䝹䜼䞊䛜ᑟධ䛥䜜䜛䛸䚸୙☜ᐃᛶ䛜ቑ኱䛩䜛䛯䜑䚸౪⤥㟁ຊ䛾☜ಖ䜢┠ᣦ䛩䛣䛸㔜せど䛥䜜䛶䛔䜛䚹䛭䛾䜘䛖䛺⎔ቃୗ䛷䛿䚸☜⋡ⓗ䛺౪⤥ಙ㢗ᗘ䛾◊✲䛜ᛴົ䛸䛺䛳䛶䛔䜛䚹䛣䛾◊✲䛷䛿䚸┠ⓗ㛵ᩘ䛸䛧䛶㏦㟁䝛䝑䝖䝽䞊䜽䛷Ⓨ⏕☜⋡䛾᭱኱໬䚸䛛䛴౪⤥ᨭ㞀㟁ຊ䛾᭱኱໬䜢‶㊊䛩䜛⣔⤫≧ែ䜢䝟䝺䞊䝖ゎ㞟ྜ䛸䛧䛶ồ䜑䜛䛯䜑䛻䚸☜⋡ⓗ䝅䝭䝳䝺䞊䝅䝵䞁ἲ䛷䛒䜛䝰䞁䝔䜹䝹䝻䝅䝭䝳䝺䞊䝅䝵䞁䛷䛿䛺䛟䛶ከ┠ⓗ䝯䝍䝠䝳䞊䝸䝇䝔䜱䜽䝇䛷ホ౯䛩䜛ᡭἲ䜢ᥦ᱌䛧䛯䚹ᥦ᱌ἲ䛻䛚䛔䛶ලయⓗ䛻䝟䝺䞊䝖ゎ䜢ồ䜑䜛ᡭἲ䛿ከ┠ⓗ䝯䝍䝠䝳䞊䝸䝇䝔䜱䜽䝇䛷䛒䜛䠯䠬䠡䠝䠎(Strength Pareto Evolution Algorithm 2)䛻䛚䛔䛶ゎ䛾ከᵝᛶ䛻䛴䛔䛶ຠ⋡䛾䜘䛔ᡓ␎䜢ᑟධ䛧䛯䛯䜑䚸㠀ᖖ䛻Ⰻዲ䛺⤖ᯝ䛜ᚓ䜙䜜䛯䚹䛣䛣䛷䚸䠯䠬䠡䠝䠎䛿䠣䠝䜢ᇶ䛻䛧䛶⪃᱌䛥䜜䛯ከ┠ⓗ䝯䝍䝠䝳䞊䝸䝇䝔䜱䜽䝇䛷䛒䜛䛜䚸ゎ᥈⣴䛾೵⁫䛜ሗ࿌䛥䜜䛶䛔䜛ㄢ㢟䛜䛒䛳䛯䚹䛭䛣䛷䚸ᥦ᱌䛧䛯ᡓ␎䛸䛿䚸䝅䜵䜰䝸䞁䜾㛵ᩘ䛻ไ⣙᮲௳䜢ㄢ䛩᪉ἲ䛷ゎ䛾ከᵝᛶ䜢ᐇ⌧䛧䚸ゎ᥈⣴䜢ຠᯝⓗ䛩䜛䛣䛸䛷䛒䜛䚹

KOBAYASHI Ryo

ᴾ

‫ݱ‬௎ʰ

␌⏱␔␝⏚ྰ

ѣཋỉᢃѣểСࣂỉૠྸႎᄂᆮиȪȸȀȸ৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ࠼޽‫ܖٻܖٻ‬ᨈྸ‫ܖ‬ᄂᆮᅹ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ྵᝋૠྸ‫ܖ‬ᲦҦٟ ૠྸᅹ‫ ܖ‬ȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ဃཋƷನᡯ࢟঺ȷᢃѣȷऴ‫إ‬ϼྸƷૠྸႎᄂᆮ
ᄂᆮಒᙲ୰ࢆືࡁᅇࢀࡿࣟ࣎ࢵࢺࢆసࡿࡇ࡜ࢆ┠ᣦࡋ࡚ࠊ⏕≀Ꮫ⪅࣭ᩘᏛ⪅࣭ᕤᏛ⪅࠿ࡽ࡞ࡿࢳ࣮࣒࡛
◊✲ࢆ⾜࡞ࡗ࡚࠸ࡿࠋ࣮࢟࡜࡞ࡿࡢࡣࠊ⮬ᚊศᩓไᚚ࡜⮬ᕫ⤌⧊໬࡟ࡼࡿࣟࢥ࣮ࣔࢩࣙࣥ⏕ᡂ࡛࠶ࡿࠋᡃࠎࡣࠊ⢓⳦ࡢ㐠ືࡢᩘ⌮ࣔࢹࣝ࠿ࡽࠕ㱈㱒㛵ᩘࠖ࡜࠸࠺ᴫᛕࢆᢳฟࡋࠊࡑࢀࢆ⏝࠸ࡓ⮬ᚊศᩓไᚚ᪉⟇ࢆᥦ᱌ࡋࡓࠋࡑࡋ࡚ࠊࡑࢀࢆ࢔࣓࣮ࣂᵝࣟ࣎ࢵࢺ࣭࣊ࣅᆺࣟ࣎ࢵࢺ࣭ࢡࣔ
ࣄࢺࢹᆺࣟ࣎ࢵࢺ࣭㸲⬮Ṍ⾜ࣟ࣎ࢵࢺ࡞࡝࡟㐺⏝ࡋࠊࡑࡢ᭷ຠᛶࢆ♧ࡋ࡚ࡁࡓࠋ
䠆㏺⾜ຊᏛ䛾୍⯡໬䝰䝕䝹䛸䛭䛾ᐇ㦂ⓗ᳨ド࣑࣑ࢬࡸ࢝ࢱࢶ࣒ࣜࡢࡼ࠺࡞⏕≀ࡀ⾜࡞ࡗ࡚࠸ࡿ⽸ືⓗ㏺⾜ࡢࣔࢹࣝࡀࠊᣑᩓ᪉⛬ᘧ࡟ᖐ╔ࡉࢀࡿࡇ࡜ࢆ♧ࡋࡓࠋᦤືἲࢆ⏝࠸ࡓ⌮ㄽゎᯒ࡜ࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ⾜࠸ࠊຊᏛⓗᶵᵓࢆ᫂ࡽ࠿࡟ࡋࡓࠋ
ࡉࡽ࡟ࠊ࣒࢝ࢹࡸࣖࢫࢹ࡞࡝ࡢከ㊊㢮ࡢ⬮Ṍ⾜ࡀࠊ⽸ືⓗ㏺⾜ࡢຊᏛⓗཎ⌮ࢆὶ⏝ࡋ࡚࠸ࡿࡇ࡜ࢆ
♧ࡋࠊ⎔ᙧື≀࠿ࡽከ㊊㢮࡬ࡢ㐍໬࡟࠾࠸࡚ࠊ㐠ືᵝᘧࡀ㐃⥆ⓗ࡟⥅ᢎࡉࢀࡓࡇ࡜ࢆ♧ࡋࡓࠋ⌧ᅾࠊࡇࡢ⌮ㄽࡢᐇ㦂ⓗ᳨ドࢆᵝࠎ࡞ື≀࡛⾜࡞ࡗ࡚࠸ࡿࠋ

㸨┿ṇ⢓⳦ኚᙧయ䛜♧䛩⮬Ⓨⓗ䛺䜰䝖䝷䜽䝍㑄⛣䛾Ⓨ⌧ᶵᗎゎ᫂䛸䝻䝪䝑䝖䜈䛾ᐇ⿦
ཎᙧ㉁㔞ಖᏑ๎䜢⪃៖䛧䛯⤖ྜ᣺ືᏊ⣔䛸㱈㱒㛵ᩘ䛻ᇶ䛵䛟ᒁᡤⓗ䛺䝉䞁䝃䝣䜱䞊䝗䝞䝑䜽䛛䜙䠈⢓⳦䛻ぢ䜙䜜䜛䜘䛖䛺⮬Ⓨⓗ䛺䜰䝖䝷䜽䝍㑄⛣䛜⏕䜏ฟ䛥䜜䜛䛣䛸䜢♧䛧䛯䚹䜎䛯䚸⢓⳦᣺ືᏊ䝻䝪䝑䝖䛻䜘䜛ᐇᶵ᳨ド䜢⾜䛳䛯䚹䠆㠀ᵓ㐀⎔ቃୗ䛷䛾䝦䝡䛾䝻䝁䝰䞊䝅䝵䞁䛻ෆᅾ䛩䜛⮬ᚊศᩓไᚚ๎䛾⌮ㄽⓗ⪃ᐹ䝦䝡䛾௦⾲ⓗ䛺㐠ື䝰䞊䝗䛷䛒䜛 Lateral undulation 䛻䛚䛔䛶䛿䚸ഃ᪉䛛䜙䛾㝣Ꮫⓗᨭᣢ䛜ᮏ㉁ⓗ䛻㔜せ䛷䚸ഃ᪉䜈䛾༑ศ䛺ᦶ᧿䛜ぢ㎸䜑䛺䛔≧ἣ䛻䛚䛔䛶䛿䚸䝦䝡䛿ఱ䜙䛛䛾䛂䛸䛳䛛䛛䜚䛃䜢฼⏝䛩䜛䚹῝㒊యᛶឤぬ᝟ሗ䛻ᇶ䛵䛟᭤⋡ᚤศไᚚ䛸䠈యቨ䛾⾲ᅾឤぬ᝟ሗ䛻ᇶ䛵䛔䛯཯ᑕ䝯䜹䝙䝈䝮䛾⤌䜏ྜ䜟䛫䛷䚸䛸䛳䛛䛛䜚䜢฼⏝䛧䛯⮬ᚊศᩓⓗ䛺䝻䝁䝰䞊䝅䝵䞁䛜ຠᯝⓗ䛻ᐇ⌧䛥䜜䜛䛣䛸䜢⌮ㄽⓗ䛻♧䛧䛯䚹

Modeling Groupື≀࡟Ꮫࡪࡇ࡜࡟ࡼࡾࠊື≀୪ࡳ࡟ࡋ࡞ࡸ࠿࡟ࣟࣂࢫࢺ࡟ࠊ」㞧࡛୙☜ᐃ࡞⌧ᐇࡢ⎔ቃࡢ␌⏱␔␝⏚ྰʴể᧙ỪỦᙻᙾὉᎮᙾऴ‫إ‬ϼྸᒰ߷ᕣ

ARAKAWA Kaoruᴾ৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ဒ΂ȷ᪦٣̮ӭϼྸᲦ߻‫ܖ‬Ҧٟȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ჷᙾǷǹȆȠƷȢȇȪȳǰƓǑƼᚐௌᄂᆮಒᙲ

Modeling Groupே䛸㛵䜟䜛どぬ䞉⫈ぬ᝟ሗฎ⌮䛸䛧䛶䠈௨ୗ䛾◊✲䜢⾜䛳䛯䚹䠄䠍䠅䝇䝬䞊䝖䝣䜷䞁䜰䝥䝸䛻䜘䜛ᐇ⿦䛾䛯䜑䛾ᑐヰᆺ㢦⏬ീ⨾ほ໬ฎ⌮䛾᧯సᛶᨵၿ
䠄䠎䠅୰ᅜே䛜Ⓨኌ䛧䛯᪥ᮏㄒ㡢ኌ䛾≉ᚩゎᯒ䛸䛭䛾⮬ືㄆ㆑䛾䛯䜑䛾᪉ᘧ䛾ᥦ᱌䠄䠍䠅䛷䛿䠈ᮏ◊✲⪅䛜ඛ䛻ᥦ᱌䛧䛯㠀⥺ᙧ䝕䜱䝆䝍䝹䝣䜱䝹䝍䝞䞁䜽䜢⏝䛔䛯ᑐヰᆺ㢦⏬ീ⨾ほ໬䝅䝇䝔䝮䜢䝇䝬䞊䝖䝣䜷䞁䛺䛹䛾ᑠᆺ᝟ሗ➃ᮎ䛷ᐇ⿦䛩䜛䛯䛣䛸䜢┠ⓗ䛸䛧䛶䠈ᑡ䛺䛔ೃ⿵㢦⏬ീ䛾⾲♧䛸ᑡ䛺䛔⧞䜚㏉䛧ᅇᩘ䛷䠈฼⏝⪅䛜༑ศ‶㊊䛷䛝䜛㢦⏬ീ䜢ᚓ䜙䜜䜛䛯䜑䛻䠈㑇ఏⓗ䜰䝹䝂䝸䝈
䝮(GA)䛾ᨵⰋ䜢⾜䛳䛯䚹䛣䛾䝅䝇䝔䝮䛿䠣䠝䛻ᇶ䛵䛟ᑐヰᆺ㐍໬ィ⟬䛻䜘䜚䠈㢦⏬ീ⨾ほ໬䝣䜱䝹䝍䝅䝇䝔䝮䛾」ᩘ䛾䝟䝷䝯䞊䝍䜢୺ほⓗ䛻᭱㐺タィ䛩䜛䜒䛾䛷䛒䜛䚹ᥦ♧䛥䜜䜛 10 ᯛ⛬ᗘ䛾⨾ほ໬ೃ⿵㢦⏬ീ䛛䜙฼⏝⪅䛜ྛ⮬䛾୺ほ䛻ᇶ䛵䛔䛶ᮃ䜎䛧䛔䛸ᛮ䛖㢦⏬ീ䜢ఱᯛ䛛㑅䜆䛸䛔䛖᧯స䜢」ᩘ
ᅇ⧞䜚㏉䛧䛶㢦⏬ീ䛾⨾ほ໬䜢⾜䛖䜒䛾䛷䛒䜛䛜䠈ᑠᆺ᝟ሗ➃ᮎ䛷䛿䠈⾲♧䛷䛝䜛ೃ⿵㢦⏬ീ䛾ᩘ䛜ไ㝈䛥䜜䜛䚹䜎䛯䠈䛣䛾ሙྜ䠈༑ศ‶㊊䛷䛝䜛㢦⏬ീ䛜ᚓ䜙䜜䜛䜎䛷䠈ከ䛟䛾⧞䜚㏉䛧ᅇᩘ䜢せ䛧䠈᧯సᛶ䛜పୗ䛩䜛䚹䛭䛣䛷䠈㐣ཤ䛻ᚓ䜙䜜䛯᭱㐺䝟䝷䝯䞊䝍䝕䞊䝍㞟ᅋ䜢⏝䛔䛯ึᮇタᐃἲ䛸䠈㑅ᢥ䛥䜜䛯ೃ⿵㢦⏬ീ䛾ෆศ䛸እศ䜢ྲྀ䜚ධ䜜䛯ୡ௦஺௦䜢⏝䛔䛯㐍໬ィ⟬ἲ䜢᪂䛯䛻ᥦ᱌䛧䛯䚹ᐇ㝿䛻」ᩘ䛾฼⏝⪅䛻ᮏ䝅䝇䝔䝮䛸ᚑ᮶䝅䝇䝔䝮䜢౑⏝䛧䛶䜒䜙䛔䠈ᮏ䝅䝇䝔䝮䛷䛿 6 ᯛ䛾ೃ⿵㢦⏬ീ䛾⾲♧䛷䠈ᚑ᮶䜘䜚ᑡ䛺䛔⧞䜚㏉䛧ᅇᩘ䛷䠈༑ศ‶㊊䛷䛝䜛⨾ほ໬㢦⏬ീ䛜ᚓ䜙䜜䜛䛣䛸䛜♧䛥䜜䛯䚹฼⏝⪅䛻䜘䜛䜰䞁䜿䞊䝖⤖ᯝ䛷䜒䠈ᮏ䝅䝇䝔䝮䛾᪉䛜䠈᧯సᛶ䛜㧗䛟䠈䜎䛯䠈᭱⤊ⓗ䛻ᚓ䜙䜜䛯㢦⏬ീ䜒ᚑ᮶ἲ䜘䜚୺ほⓗ䛻㧗䛟ホ౯䛥䜜䜛䛸䛔䛖䛣䛸䛜♧䛥䜜䛯䚹䠄䠎䠅䛷䛿䠈୰ᅜே䛜Ⓨኌ䛧䛯᪥ᮏㄒ㡢ኌ䛾≉ᛶゎᯒ䜢⾜䛔䠈䜘䜚⢭ᗘⰋ䛟㡢ኌㄆ㆑䜢⾜䛖䛯䜑䛾᪉ᘧ䜢ᥦ᱌䛧䛯䚹୰ᅜே䛜Ⓨኌ䛧䛯᪥ᮏㄒ㡢ኌ䛻ᑐ䛧䛶᪥ᮏㄒ㡢ኌㄆ㆑䝅䝇䝔䝮䜢㐺⏝䛧䛯ሙྜ䠈䛭䛾ㄆ㆑⋡䛿᪥ᮏே䛾㡢ኌ䛻ᑐ䛩䜛䜒䛾䜘䜚ప䛔䚹㡢ኌ䛾≉ᚩゎᯒ䜢䛧䛯䛸䛣䜝䠈୰ᅜே䛿᪥ᮏே䜘䜚䠈ẕ㡢䜢㛗䛟ఙ䜀䛩ഴྥ䛜䛒䜛䛣䛸䛜♧䛥䜜䛯䚹䛣䛾䛣䛸䛿䠈୰ᅜே䛾᪥ᮏㄒ㡢ኌ䛻ᑐ䛩䜛ㄆ㆑⋡䛾పୗ䛻䛴䛺䛜䛳䛶䛔䜛䚹䛭䛣䛷䠈୰ᅜே䛾᪥ᮏㄒ㡢ኌ䛻ᑐ䛧䛶䠈ẕ㡢䛾㛗䛥䜢▷⦰䛩䜛䛣䛸䛻䜘䜚䠈᪥ᮏㄒ㡢ኌㄆ㆑䝅䝇䝔䝮䛻ᑐ䛩䜛ㄆ㆑⋡䜢ྥୖ䛥䛫䜛᪉ᘧ䜢ᥦ᱌䛧䛯䚹33 ே䛾୰ᅜே䛾᪥ᮏㄒ㡢ኌ䝕
䞊䝍 115 ಶ䛻ᑐ䛧䛶㐺⏝䛧䛯⤖ᯝ䠈ᮏᥦ᱌ᡭἲ䜢⏝䛔䛺䛔ሙྜ䛾ṇ⟅⋡䛜 68.5䠂䛷䛒䛳䛯䛾䛻ᑐ䛧䠈ᮏᥦ᱌ᡭἲ㐺⏝ᚋ䛾ṇ⟅⋡䛿 80.2%䛸䛺䛳䛯䚹䛣䛾௚䠈⤒ᖺຎ໬䛻䜘䜚യ䛜⏕䛨䛯ᫎ⏬䝣䜱䝹䝮䛾⏬㉁ᨵၿ䜢⾜䛖⏬ീฎ⌮ἲ䠈Ⓩ㘓㢦⏬ീ䛛䜙ຍ㱋䛻䜘䜚㢦ᙧ≧䛜ኚ໬䛧䛯ே≀䛾ಶேㄆドἲ䛻㛵䛩䜛◊✲䜢⾜䛳䛯䚹␌⏱␔␝⏚ྰỡỤẫᙲእᨼ‫ׇ‬ỉᴾἒỶἜἱἁἋểೞᏡỉᚐଢᴾ
NISHIMORI Hirakuᴾᙱౕਏ৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ࠼޽‫ܖٻܖٻ‬ᨈྸ‫ܖ‬ᄂᆮᅹ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ᩼࠯ᘖཋྸ‫ܖ‬Ღྸ‫ܖ‬Ҧٟȷிʮ߻ಅ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ңӷྵᝋƷȢȇȪȳǰƓǑƼᚐௌᡃࠎࢆྲྀࡾᅖࡴ⮬↛ࡢ୰࡟ࡣᵝࠎ࡞ࢱ࢖ࣉࡢせ⣲㞟ᅋࡀ࠶ࡿࠋ㨶࣭㫽ࡢ⩌ࢀ, ᪻⹸ࡢ⩌ࢀ࡞
࡝ࡀ㌟㏆࡞౛࡛࠶ࡿࠋࡲࡓ, ㌴ࡢ⩌ࢀ, Ṍ⾜⪅ࡢ⩌ࢀ࡞࡝࡟ࡘ࠸࡚ࡣ, ὶࢀࢆ㐽᩿ࡍࡿᅉᏊࡢ
≉ᐃࡀ♫఍඲యࡢ⏕⏘ᛶ࡟኱ࡁࡃ㛵㐃ࡋ࡚ࡃࡿࠋᚑ᮶ࡢ⩌ࢀ㐠ືࡢ⌮ㄽᶍᆺࡢከࡃࡣ, ྛᵓᡂせ⣲ࡢ㐠ືࢆ༢⣧࡞࣮࡛ࣝࣝ⾲ࡋࠊ⩌ࢀ඲య࡜ࡋ࡚ほᐹࡉࢀࡿ」㞧࡞㐠ື࡜ẚ㍑ࡋࠊ⩌ࢀ㐠ືࡢᇶᮏᶵᵓࢆ᥈ࡗ࡚᮶ࡓࠋ୍᪉࡛, ⌧ᐇࡢࢩࢫࢸ࣒࡟࠾࠸࡚ࡣ, ᵓᡂせ⣲⮬㌟ࡢᣢࡘ」㞧࡞ෆ㒊⮬⏤ᗘࡀ, ⩌ࢀ඲యࡢ㐠ື࡟Ỵᐃⓗ࡞ᙳ㡪ࢆ୚࠼ࡿྍ⬟ᛶࡶ᤼㝖࡛ࡁ࡞࠸ࠋࡑࡇ࡛ࠊ2011ᖺᗘࡢᡃࠎࡢ◊✲┠ᶆࡢ୍ࡘ࡜ࡋ࡚ࠊ࠸ࡃࡘ࠿ࡢ⩌ࢀ㐠ື࡟࠾࠸࡚ࠊᐇ㦂ⓗほ ࡜⌮ㄽᶍᆺసᡂࢆ୪⾜ࡋ࡚㐍ࡵࡿࡇ࡜࡛ࠊ⌧ᐇ࡟༶ᛂࡋࡓ⩌ࢀ㐠ືࡢᶵᵓࡢ⌮ゎࢆࡵࡊࡋࡓࠋලయⓗ࡟ࡣࠊ
1. ࢔ࣜࡢ㞟ᅋ᥇㣵⾜ື࡟࠾ࡅࡿ, ໬Ꮫ᝟ሗ࡜どぬ᝟ሗࡢ฼⏝ࡢඃඛ㡰఩Ỵᐃᶵᵓࡢゎ᫂
2. ෇⎔≧Ỉ㊰ෆࡢᶋ⬻⯪㞟ᅋࡢ஺㏻ὶ࡜῰⁫ࡢᐇ㦂࡜ᩘ⌮ᶍᆺ࡟ࡼࡿゎᯒࢆ⾜ࡗࡓࠋ1 ࡟㛵ࡋ࡚ࡣ, ๓ᖺᗘࡲ࡛ࡢ◊✲࡟ᘬࡁ⥆ࡁࠊ᥇㣵Ṍ⾜୰ࡢ࢔ࣜ(ࢺࣅ࢖ࣟࢣ࢔ࣜ)ࡢᖐᕢ⤒㊰ᵓ⠏ࡢᐇ㦂ࢆ⾜࠸ࠊ࢔ࣜࡀࣇ࢙ࣟࣔࣥ࡟ࡼࡿ໬Ꮫ᝟ሗࡔࡅ࡛࡞ࡃ, ᥇㣵㏵ୖ࡟࠾ࡅ
ࡿࣛࣥࢻ࣐࣮ࢡ࡞࡝ࡢどぬ᝟ሗࡶ฼⏝ࡋ࡞ࡀࡽ᫬ࠎ้ࠎࡢ⮬ศࡢ఩⨨ࢆᢕᥱࡋࠊ᥇㣵⤒㊰ࢆᵓ⠏ࡋ࡚࠸ࡿࡇ࡜ࢆᐃ㔞ⓗ࡟♧ࡋࡓࠋ2 ࡟㛵ࡋ࡚ࡶࠊ๓ᖺᗘࡲ࡛࡟ᘬࡁ⥆ࡁࠊ᫂἞኱Ꮫ≉௵ㅮᖌ
(GCOE ◊✲༠ຊ⪅)ࡢᮎᯇಙᙪẶࡸ㸪ᗈᓥ኱Ꮫ GCOE ◊✲ဨཧ⣡ᘪᙪẶࡽ࡜ඹྠࡋ, ⾲㠃ᙇຊᕪ࡛⮬ᕫ㥑ືࡍࡿ๓ᚋᑐ⛠࠾ࡼࡧ๓ᚋ㠀ᑐ⛠࡞ᶋ⬻⯪ࡢ㞟ᅋࢆ෇⎔≧Ỉ㊰࡟୪࡭,ᚑ᮶▱ࡽࢀ࡚࠸࡞࠸᪂ࡓ࡞ᙧࡢ㞟ᅋ㐠ື࣮ࣔࢻ=ࢡࣛࢫࢱ࣮≧ែࢆⓎぢࡋ, ࡑࡢᶵᵓࡢࣔࢹࣝ໬࡜⌮ㄽⓗ࡞ゎ᫂ࢆ⾜ࡗࡓࠋ ୖࡢ⩌ࢀ㐠ືࡢ◊✲࡜ࡣ⊂❧ࡋ࡚ࠊ㠀⥺ᙧࢲ࢖ࢼ࣑ࢡࢫ࡟࠾ࡅࡿࡺࡽࡂ࡜ᶵ⬟ࡢ㛵ಀࢆ▱ࡿࡓࡵ࡟ࠊ
3. ☜⋡ඹ㬆ࢆ㉳ࡇࡍ⣲Ꮚ㞟ᅋ࡟࠾ࡅࡿࡺࡽࡂࡢ㠀୍ᵝᛶ࡜, ☜⋡ඹ㬆ຠ⋡ࡢ㛵ಀࢆ FitzHugh-Nagumo ⣲Ꮚ⣔࡟ࡘ࠸࡚ㄪ࡭ࠊࡉࡽ࡟ேᕤෆ⪥⿦⨨ࡢ㧗ᛶ⬟໬࡟࠾ࡅࡿ☜⋡ඹ㬆ࡢ฼⏝࡟㛵ࡋ࡚ࡶࠊ୺࡟⌮ㄽⓗ࡟⪃ᐹࢆ⾜ࡗࡓࠋ௨ୖࡢᡂᯝࡣࠊᏛ⾡㞧ㄅ࡞࡝࡛ฟ∧ࡉࢀࠊᅜ㝿఍㆟࡟࠾࠸࡚ࡶⓎ⾲ࡉࢀࡓࠋ

Modeling Groupᄂᆮಒᙲ␌⏱␔␝⏚ྰኺฎཋྸ‫‒↺↷↚ܖ‬᣿ᗡүೞ↝ѣщ‫↝ܖ‬ᚐଢ‒ᴾ᭗‫ܤ‬ᅵ೔ TAKAYASU Hideki৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻ‬ᄂᆮȷჷᝠ৆ဦೞನܲՃ૙੉ ǽȋȸǳȳȔȥȸǿǵǤǨȳǹᄂᆮ৑ȷǷȋǢȪǵȸȁȣȸ‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ᩼ዴ࢟ཋྸ‫ܖ‬Ღྸ‫ܖ‬ҦٟȷӸӞ‫ܖٻދ‬ᄂ ᆮ ϋ ܾᲴ ኺฎཋྸ‫ܖ‬ƷؕᄽƔǒࣖဇǇưModeling Groupᄂᆮಒᙲ㻌 䝤䝷䝑䜽䝬䞁䝕䞊䠄䠍䠕䠔䠓ᖺ䠅䚸䜰䝆䜰㏻㈌༴ᶵ䠄䠍䠕䠕䠓ᖺ䠅䚸䝸䞊䝬䞁䝅䝵䝑䜽䠄䠎䠌䠌䠔ᖺ䠅䚸䞉䞉䞉䚸ୡ⏺䛾㔠⼥ᕷሙ䛿䚸䜋䜌䠍䠌ᖺ䛤䛸䛻኱䛝䛺༴ᶵ䜢㏄䛘䛶䛔䜛䚹䛣䜜䜙䛾⌧㇟䛻㛵䛧䛶䛿䚸䛣䜜䜎䛷䜒ᵝ䚻䛺ศᯒ䛜䛺䛥䜜䛶䛔䜛䛜䚸⚾䛿䚸≀⌮Ꮫ䛾どⅬ䛛䜙⤒῭⌧㇟䜢ゎ᫂䛩䜛䛣䛸䛷䚸㔠⼥༴ᶵ䛿䛺䛬㉳䛣䜚䚸䛹䛾䜘䛖䛻Ⓨᒎ䛩䜛䛾䛛䛻㛵䛩䜛᪂䛧䛔▱ぢ䜢ᚓ䜛䛣䛸䛜䛷䛝䚸ḟ䛾㔠⼥༴ᶵ䛾Ⓨ⏕䜢ᅇ㑊䛩䜛ᡭ᥃䛛䜚䛜ᚓ䜙䜜䜛䜒䛾䛸⪃䛘䛶䛔䜛䚹䝅䝇䝔䝮䛸䛧䛶ぢ䛯᫬䚸⌧ᅾ䛾㔠⼥ᕷሙ䛿䚸≀㉁䛷ゝ䛘䜀䚸䜺䝷䝇䛾䜘䛖䛺⬤ᙅᛶ䜢ෆᅾ䛧䛶䛔䜛䛣䛸䛜䜟䛛䛳䛶䛝䛯䚹㻌 㔠⼥ᕷሙ䜢ᵓᡂ䛩䜛䛭䜜䛮䜜䛾㔠⼥ᶵ㛵䛿㔠⼥ᶵ㛵ྠኈ䛷䛚㔠䛾㈚䛧೉䜚䜢䛧䛶䛔䜛䚹ὀ┠䛩䜉䛝䛿䚸୍ᗘ䛷䜒㏉῭䛾⣙᮰䜢◚䜛䛸䚸䛭䛾㔠⼥ᶵ㛵䛿௚䛾඲䛶䛾㔠⼥ᶵ㛵䛸䛾ྲྀᘬ䛜೵Ṇ䛥䜜䚸ಽ⏘䛧䛯䜒䛾䛸䜏䛺䛥䜜䜛䛣䛸䛜ୡ⏺ⓗ䛺㔠⼥ᶵ㛵䛾䝹䞊䝹䛻䛺䛳䛶䛔䜛䛣䛸䛷䛒䜛䚹೺඲䛻ぢ䛘䜛㔠⼥ᶵ㛵䛷䜒䛚㔠䛾䜔䜚䛟䜚䛻ኻᩋ䛩䜛䛸✺↛ಽ⏘䛩䜛䛣䛸䛿䚸䜺䝷䝇䛾䜘䛖䛺⬤ᛶ≀㉁䛻ṍ䜢ຍ䛘䛯䛸䛝䚸䛒䜛䝺䝧䝹䛻䜎䛷㐩䛩䜛䛸✺↛◚ቯ䛩䜛䛣䛸䛸㓞ఝ䛧䛶䛚䜚䚸䛹䛱䜙䛾⌧㇟䜒䚸䛧䛝䛔್ືຊᏛ䛷䝰䝕䝹໬䛩䜛䛣䛸䛜䛷䛝䜛䚹㻌 䜎䛯䚸䜂䛸䛴䛾㔠⼥ᶵ㛵䛜䛚㔠䛾䜔䜚䛟䜚䛻ኻᩋ䛧䛶ಽ⏘䛩䜛䛸䚸䛭䛾㔠⼥ᶵ㛵䛻䛚㔠䜢㈚䛧䛶䛔䛯㔠⼥ᶵ㛵䛿䛒䛶䛻䛧䛶䛔䛯䛚㔠䛜ධ䜙䛺䛟䛺䜚䚸䛚㔠䛾䜔䜚䛟䜚䛜ᅔ㞴䛻䛺䜚䚸㐃㙐ⓗ䛻ಽ⏘䛩䜛ྍ⬟ᛶ䛜㧗䛟䛺䜛䚹䛣䛾䛣䛸䛿䚸⬤ᛶ◚ቯ䛻䛚䛔䛶୍䛛ᡤ䛷◚ቯ䛜㉳䛣䜛䛸䚸䛭䛣䛷ᨭ䛘䛶䛔䛯ṍ䛜࿘ᅖ䛻ศ㓄䛥䜜䚸㐃㙐ⓗ䛻◚ቯ䛜⥆䛟䛣䛸䛸ᑐᛂ䛜䛴䛟䚹䛭䛾䜘䛖䛺≧ἣ䛻䛺䜛䛸䚸㔠⼥ᶵ㛵ྠኈ䛷䛔䛴┦ᡭ㔠⼥ᶵ㛵䛜ಽ⏘䛩䜛䛛␲ᚰᬯ㨣䛻䛺䜚䚸᪂䛯䛺䛚㔠䛾㈚䛧೉䜚䛜⾜䜟䜜䛻䛟䛟䛺䜚䚸㈨㔠⧞䜚䛿୍ᒙᅔ㞴䛻䛺䜛䚹䠍䠌䠌ᖺ௨ୖ䛾Ṕྐ䛜䛒䛳䛯ୡ⏺ⓗ䛺㔠⼥ᶵ㛵䝸䞊䝬䞁䝤䝷䝄䞊䝈♫䛜ಽ⏘䛧䛯┤ᚋ䛻䛿䚸䜎䛥䛻䚸䛣䛾䜘䛖䛺≧ἣ䛻䛺䜚䚸䜒䛧䜒ྛᅜᨻᗓ䛜⥭ᛴ䛻↓ไ㝈䛷䛭䜜䛮䜜䛾ᅜ䛾㔠⼥ᶵ㛵䛻䛚㔠䜢㈚䛧ฟ䛩Ỵ᩿䜢䛧䛺䛛䛳䛯䛺䜙䜀䚸ୡ⏺୰䛻㔠⼥ᶵ㛵䛾㐃㙐ⓗಽ⏘䛜Ἴཬ䛧䛶䛔䛯ྍ⬟ᛶ䛜㧗䛔䚹㻌 ≀㉁䛾ሙྜ䛻䛿䚸ረᛶኚᙧ䛩䜛䜘䛖䛺≀㉁䛿⬤ᛶ◚ቯ䜢㉳䛣䛥䛺䛔䚹䛣䛾䜰䝘䝻䝆䞊䛻ᇶ䛵䛔䛶⪃䛘䜜䜀䚸㔠⼥䝅䝇䝔䝮䛻Ḟዴ䛧䛶䛔䜛䛾䛿䚸ṍ䛻ᑐ䛧䛶ረᛶኚᙧ䛩䜛䜘䛖䛺ຠᯝ䛷䛒䜚䚸⚾䛿䚸஦๓䛻㔠฼䜢Ỵ䜑䛶䛚䛟䛾䛷䛿䛺䛟䚸⤖ᯝ䛻ᛂ䛨䛶㏉῭㢠䛜ኚ䜟䜛䜘䛖䛺௙⤌䜏䜢ᑟධ䛩䜛䛣䛸䛻䜘䛳䛶ᐇ⌧䛷䛝䜛䜒䛾䛸ᮇᚅ䛧䛶䛔䜛䚹ཧ⪃ᩥ⊩䠖㧗Ᏻ⚽ᶞ ”㔠⼥ᕷሙ࡟࠾ࡅࡿࣜࢫࢡ࡜≉ᛶ㸫」㞧⣔ࢩࢫࢸ࣒ࡢ≀⌮ᏛࡢどⅬ࠿ࡽ”ࠊ㔠⼥༴ᶵ࡜࣐ࢡࣟ⤒῭Ꮫ㸫㈨⏘ᕷሙࡢኚື࡜㔠⼥ᨻ⟇࣭つไ㸦ᒾ஭ඞே࣭℩ྂ⨾႐࣭⩝ⓒྜ⦅ࠊᮾி኱Ꮫฟ∧఍ࠊ2011 ᖺࠊ➨ 7 ❶ࠊ163㸫187ࠋ

SHIBATA Tatsuoᴾ௷ဋᢋ‫پ‬

␌⏱␔␝⏚ྰ

ἧỵἊỽἽἢỶỼἿἊὊ

ᄂᆮಒᙲ
ィ

ᢏ⾡ࡢⓎ㐩࡛ࠊⓎ⏕ࡸ෌⏕࡟㛵ࢃࡿ⣽⬊ࡸ⤌⧊ࡢᵓ㐀ᙧᡂࡸ᝟ሗฎ⌮࡞࡝ࡢᶵ⬟Ⓨ⌧ࡢࢲ࢖ࢼ࣑ࢵࢡ࡞ࣉࣟࢭࢫࡀぢ࠼࡚ࡁࡲࡋࡓࠋ⏕ࡁࡓ⣽⬊ࡸ⣽⬊ࡢ㞟ᅋࡀ♧ࡍࠊ┿࡟⏕≀ࡽࡋ࠸ࢲ࢖ࢼ࣑ࢵࢡ࡞⌧㇟ࡣࠊศᏊࡸ㑇ఏᏊ࡞࡝ࡢከࡃࡢせ⣲ࡀ༠ຊࡋ࡚ാࡃࡇ࡜࡛⏕ࡳฟࡉࢀ࡚
࠸ࡲࡍࠋࡑࡢࡼ࠺࡞ࠊከࡃࡢせ⣲ࡀ༠ຊࡋ࡚⏕ࡳฟࡍࠊ⏕≀ࡢ」㞧࡞⌧㇟ࡢືసཎ⌮ࡸタィཎ⌮ࡢ⌮ゎࢆ┠ᣦࡍࠊ⤫ྜⓗ࡛ࢩࢫࢸ࣒ㄽⓗ࡞◊✲ࡢᚲせᛶࡀ㧗ࡲࡗ࡚࠸ࡲࡍࠋࡑࡢࡓࡵ࡟ࡣࠊ
㧗ᗘ࡞ィ ᢏ⾡࡜㐃ືࡍࡿᩘ⌮ⓗ࡞᪉ἲㄽࡢⓎᒎࡀᚲせ࡛ࡍࠋࡇ࠺ࡋࡓ᪂ࡋ࠸⏕࿨⛉Ꮫࡢㄢ㢟࡟ࠊ≀⌮Ꮫࡸᩘ⌮⛉Ꮫ࡞࡝ࡢᩘ⌮ⓗ࡞Ⓨ᝿ࡸ᪉ἲㄽࢆ⏝࠸࡚ゎ᫂ࡍࡿࡇ࡜ࢆ┠ᣦࡋ࡚࠸ࡲࡍࠋ
㏆ᖺ㸪⣽⬊ෆ㒊࡟࠾࠸࡚཯ᛂᣑᩓ⣔ⓗ࡞௙⤌ࡳ࡟ࡼࡗ࡚᫬㛫–✵㛫ⓗᵓ㐀ᙧᡂࡢ㉳ࡇࡿࡇ࡜ࡀከᩘሗ࿌ࡉࢀ࡚࠸ࡲࡍࠋࡑࢀࡽ࡟ࡣ᫬㛫ⓗ᣺ື㸪✵㛫ࣃࢱࣥ㸪ከᏳᐃᛶ࡞࡝ࡀྵࡲࢀ㸪ࡑࢀࡒࢀࡢᩥ⬦࡛㔜せ࡞ᶵ⬟ࢆᢸࡗ࡚࠸ࡲࡍࠋ⣽⬊ࡢࢫࢣ࣮࡛ࣝࡣ཯ᛂࡢ☜⋡ⓗᛶ᱁ࡣ㢧ⴭࡔ࠿ࡽ㸪ࡑࢀࡽࡢᵓ㐀ᙧᡂࡢ௙⤌ࡳࡣ☜⋡ⓗ࡞ࣀ࢖ࢬ࡟ᑐࡋ࡚㡹ᙉ࡛࠶ࡿᚲせࡀ࠶ࡾࡲࡍࠋ୍᪉࡛ᵓ㐀ᙧᡂࡢ௙⤌ࡳࡣ㸪⣲㐣⛬ࡢ☜⋡ᛶࢆᕧどⓗࢫࢣ࣮ࣝ࡟ቑᖜࡋ⣽⬊ࡢ᣺ࡿ⯙࠸࡟ከᵝᛶࢆࡶࡓࡽ
ࡍ㸪୍ぢ┦཯ࡍࡿᛶ㉁ࢆවࡡഛ࠼࡚࠸ࡲࡍࠋࡇࢀࡽࡀ࡝ࡢࡼ࠺࡟ࡋ࡚ྍ⬟࡟࡞ࡿ࠿ࢆᐇ㝿ࡢ㸯⣽⬊⺯ග࢖࣓࣮ࢪࢹ࣮ࢱࡢゎᯒࡸᩘ⌮ࣔࢹࣝࡢᵓ⠏࣭ゎᯒࢆ㏻ࡌ࡚◊✲ࢆ㐍ࡵ࡚࠸ࡲࡍࠋ
ࡲࡓ㸪Ⓨ⏕ࡣ⣽⬊ෆࡢ཯ᛂࣉࣟࢢ࣒ࣛࢆṇ☜࡟సືࡉࡏ࡚㸪㸯⣽⬊࠿ࡽᵝࠎ࡞✀㢮࠿ࡽ࡞ࡿ⣽⬊ࢆ⏕ᡂࡋ✵㛫ⓗ࡟ㄪ࿴ࡢ࡜ࢀࡓᵓ㐀ࢆᙧᡂࡍࡿ㐣⛬࡛࠶ࡾࡲࡍࠋ⤌⧊ࡢᵓ㐀ᙧᡂ࡟ࡣ⣽⬊ࢆᇶᮏ༢఩࡜ࡍࡿ⢓ᙎᛶయࡢࡼ࠺࡞ຊᏛ㐣⛬ࡀ㛵୚ࡋ࡚࠾ࡾࠊࡑࢀࡀࡉࡽ࡟㑇ఏᏊࡸࢩࢢࢼ
ࣝ࡞࡝ࡢ཯ᛂᣑᩓ㐣⛬࡜┦஫࡟స⏝ࡋ࠶ࡗ࡚࠸ࡲࡍࠋ⣽⬊ࡸ⤌⧊ࡢᐇ㝿ࡢᙧែᙧᡂ࡛ࡣࠊึᮇ
᮲௳ࡸቃ⏺᮲௳ࡀࡋࡤࡋࡤᮏ㉁ⓗ࡟㔜せ࡞ᙺ๭ࢆᯝࡓࡍࡇ࡜ࡀ࠶ࡾࡲࡍࠋࡑࡋ࡚ࠊࡑࢀࡽࡢึ
ᮇ᮲௳ࡸቃ⏺᮲௳ࡶࡲࡓ௚ࡢ⏕࿨㐣⛬࡟ࡼࡗ࡚సࡽࢀ࡚࠸ࡲࡍࠋ඲యࡢ⌧㇟ࡢ࠺ࡕࠊ࡝ࡢ㒊ศࢆࣔࢹࣝ࡜ࡋ࡚ษࡾฟࡋ࡚ࠊࡲࡓ࡝ࡢ㒊ศࢆึᮇ᮲௳ࡸቃ⏺᮲௳࡜ࡋ࡚グ㏙ࡍࡿࡢ࠿ࡣ⯆࿡῝࠸ၥ㢟࡛ࡍࠋࡇࢀࡽࡢၥ㢟ࢆⓎ⏕෌⏕⥲ྜ⛉Ꮫ◊✲ࢭࣥࢱ࣮ࡸᗈᓥ኱Ꮫࡢࢢ࣮ࣝࣉ࡜༠ຊࡋ࡚ࠊ
ᩘ⌮ⓗࠊᐃ㔞ⓗ࡞ᡭἲࢆ⏝࠸࡚⌮ゎࡍࡿྲྀࡾ⤌ࡳࢆࡋ࡚࠸ࡲࡍࠋ
Modeling Group৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻ‬ᄂᆮȷჷᝠ৆ဦೞನܲՃϱ૙੉ Ტ཯Უྸ҄‫ܖ‬ᄂᆮ৑ ႆဃȷϐဃᅹ‫ܖ‬ዮӳᄂᆮǻȳǿȸȦᲴ ȋȃȈȪȸȀȸᲦ‫ܖٻܖٻ᧵ٻ‬ᨈဃԡೞᏡᄂᆮᅹਔǁƍᲴ ૙੉Ღ࠼޽‫ܖٻܖٻ‬ᨈྸ‫ܖ‬ᄂᆮᅹܲՃ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ ȕǣǸǫȫȐǤǪȭǸȸᲦҦٟ ‫ܖ‬ᘐ ȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾ ኬᏘƓǑƼႆဃƷྸᛯႎȷ᬴ܱႎᄂᆮ

␌⏱␔␝⏚ྰResearches on Biological Evolution:
Theory and Applications

ᴾ

ᒉ᣼Ӑɟᢹ

WAKANO Joe Yuichiro৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹཎ˓ϱ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ૠྸဃཋ‫ܖ‬ᲦҦٟ ྸ‫ ܖ‬ȷʮᣃ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ Ȟǯȭဃཋኒȷဃ७ኒƷȢȇȪȳǰƓǑƼᚐௌ

Modeling Groupᄂᆮಒᙲ
I have continued researches on biological evolution using mathematical models. Currently, I am
involved in the following two major projects:

Theoretical research: JST PRESTO, "Unified understanding of two major theories of biologicalevolution"
Applied research: JSPS Grand-in-Aid for scientific research on innovative areas, "Replacement of
Neanderthals by modern humans: Testing evolutionary models of learning"
In the theoretical research (which is a single-researcher type project), the ultimate goal is to obtain theunified understanding of inclusive fitness theory (IFT) and adaptive dynamics theory (ADT). The
project lies between biology and mathematics, with more focus on mathematics.

This year I havemainly worked on ADT, to provide a mathematical framework to clarify convergence stability,
evolutionary stability, and evolutionary branching.

Despite its history, we have found thatconvergence stability might be more natural concept when we consider individual-based theoreticalmodels based on population genetics. I want to understand evolutionary stability and evolutionary
branching more in depth in the following years.
In the applied research, I am involved in a large project on the evolution of human. Focusing on thereplacement of Neanderthals by Homo sapeins that was estimated to have occurred 50,000 years ago,
this large-scale multidisciplinary project is participated by researchers from a wide range of academic
fields.

The research group consists of physical anthropologists studying fossil human bones,archaeologists researching sites, brain scientists studying the learning ability unique to modern human,paleoclimateologists calculating the ancient environment, cultural anthropologists studying modern
hunter-gatherers, and theoretical biologists analyzing mathematical models. We have found that theschedule of learning (individual or social learning when young or mature) is a very important factor toconsider cultural evolution in human.

ჿဋМɟ

SUNADA Toshikazu

ૠྸᚐௌྰTopological CrystallographyૠྸᚐௌྰȪȸȀȸ৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ᩉ૝࠹˴ᚐௌ‫ܖ‬Ღྸ‫ܖ‬Ҧٟȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ȍȃȈȯȸǯǷǹȆȠƷᚐௌThe primarily purpose of this project was to provide a mathematical insight into the modern
crystallography, a typical practical science that originated in the classification of the observed shapes ofcrystals. The tools we employed are adopted from algebraic topology, a field in pure mathematics
cultivated during the first half of the last century. More specifically the elementary theory of covering
spaces and homology is effectively used in the study of 3D networks associated with crystals. Further
we formulate a minimum principle for crystals in the framework of discrete geometric analysis, which
provides us with the concept of standard realizations, a canonical way to place a given crystal structurein space so as to produce the most symmetric microscopic shape. In spite of its pure-mathematicalnature, this concept combined with homology theory turns out to fit with a systematic design andenumeration of crystal structures, an area of considerable scientific interest for many years. Meanwhile,
standard realizations show up in asymptotic behaviors of random walks on topological crystals, theabstraction of crystal structures, and are closely related to a discrete analogue of Abel-Jacobi maps inalgebraic geometry.
The outcome of this project was published in the paper “Lecture on topological crystallography”,
Japanese Journal of Mathematics, 7 (2012), 1-39. A full account will be given in the forthcoming book
“Topological Crystallography” published from Springer.

Mathematical Analysis Groupᄂᆮಒᙲૠྸᚐௌྰ

ဃཋ≏҄‫ܖ‬ኒ↚ྵ↻↺‒ᐯࠁኵጢ҄⇷⇥∞∙↝∈⇭∑ૅੲᚐௌɤ஭ଡ඲ MIMURA Masayasu ȪȸȀȸᲢᄂᆮወਙᲣ
৑‫ޓ‬ȷࢫᎰ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑ᧈ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹ૙੉
‫ᧉݦ‬ȷ‫ܖ‬ˮ Ჴ ྵᝋૠྸ‫ܖ‬Ღ߻‫ܖ‬Ҧٟȷʮᣃ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ᩼ዴ࢟᩼࠯ᘖྵᝋƷૠྸᚐௌ

Mathematical Analysis Groupᄂᆮಒᙲ㻌 ⏕࿨䚸⏕≀⌧㇟䜢䛿䛨䜑䛸䛩䜛⮬↛⏺䛾䛥䜎䛦䜎䛺Ⴀ䜏䜢⌮ゎ䛩䜛䛖䛘䛷䛾䜻䞊䝽䞊䝗䛿㠀⥺ᙧ䞉㠀ᖹ⾮䛷䛒䜛䚹≉䛻䠈⮬ᕫ⤌⧊ⓗ䛻ᙧᡂ䛥䜜䜛䝟䝍䞊䞁䜔ᙧែ䠈⇿Ⓨ䞉จ⦰䛸䛔䛳䛯≉␗ᛶ䛺䛹䛾ฟ⌧䛜䛭䛾୺ᙺ䛷䛒䜛䚹䛣䜜䜙⌧㇟䛾⫼ᚋ䛻䛿㠀⥺ᙧᛶ䛜₯䜣䛷䛚䜚䠈䛭䛾ゎ᫂䛺䛟䛧䛶⌧㇟䜢⌮ゎ䛩䜛䛣䛸䛿䛷䛝䛺䛔䚹䈊䛂㠀⥺ᙧ䛃䛸䛔䛖ゝⴥ䛿≀⌮Ꮫ䠈໬Ꮫ䠈⏕≀Ꮫ䛺䛹䛾⮬↛⛉Ꮫ䜔ᕤᏛ䛾ศ㔝䛻⌧䜜䛶䛚䜚䚸ᩘᏛ䛾ศ㔝䛻䛚䛔䛶䜒䛂㠀⥺ᙧ䛾ᩘ⌮䛃䛸䛔䛖ゝⴥ䛜Ⰻ䛟⏝䛔䜙䜜䛶䛔䜛䚹䛧䛛䛧䛺䛜䜙䚸䛂㠀ᖹ⾮⣔䛾ᩘ⌮䛃䛸䛔䛖どⅬ䛛䜙䛾◊✲䛿䛔䜎䛰☜❧䛥䜜䛶䛔䛺䛔䚹᭱㏆䛷䛿䠈௚ศ㔝䛸䛾㐃ᦠ䠈䝁䞁䝢䝳䞊䝍䛾ᛴ㏿䛺Ⓨᒎ䛻䜘䜚䚸䝰䝕䝸䞁䜾䚸ᩘ್ⓗ◊✲䛭䛧䛶⣧ᩘᏛⓗ⌮ㄽ◊✲䛜┦⿵ⓗ䛻㐙⾜䛷䛝䜛䜘䛖䛻䛺䛳䛯䛣䛸䛛䜙⌧㇟ᩘ⌮Ꮫ䛸䜘䜀䜜䜛ᩘ⌮⛉Ꮫⓗ᪉ἲㄽ䛜☜❧䛥䜜䛶᮶䛯䚹ᮏᖺᗘ䛿䚸㠀⥺ᙧ㠀ᖹ⾮⌧㇟䜢グ㏙䛩䜛䝰䝕䝹䛸䛧䛶䛾཯ᛂᣑᩓ⣔䛻ᑐ䛧䛶䚸䛾⣧ᩘᏛⓗ⌮ㄽ◊✲䛾どⅬ䛛䜙䚸䛂≉␗ᴟ㝈ゎᯒἲ䛃䛾㛤Ⓨ䛻ຊ䜢ධ䜜䛯䚹䛭䛾ᛂ⏝䛸䛧䛶䚸ᩘ⌮⏕ែᏛ䛻⌧䜜䜛➇தᣑᩓ⣔䛻ᑐ䛧䛶䛔䛟䛴䛛䛾ᡂᯝ䜢䛒䛢䛯䠄[p2], [s2], [s3]䠅䚹
䠎䠌䠍䠍ᖺᗘⓎ⾲ㄽᩥ䠄ᰝㄞ௜䛝䠅[p1] M. Henry, D. Hilhorst and M. Mimura: A reaction-diffusion approximation to an area preserving
mean curvature flow coupled with a bulk equation, Discrete and Continuous Dynamical Systems –Series S, 4 no.1, 125-154 (2011)[p2] J. Y. Wakano, K. Ikeda, T. Miki and M. Mimura : 䈊Effective dispersal rate is a function of habitat
size and corridor shape: mechanistic formulation of a two-patch compartment model for spatiallycontinuous systems, 䈊Oikos, 120, 1712-1720 (2011)௚䠎⦅䠎䠌䠍䠍ᖺᗘᅜ㝿఍㆟䛷䛾ᣍᚅㅮ₇[s1] Dynamics of soliton-like dynamics in excitable reaction-diffusion systems, International
Conference on Perspective in Mathematics and Life Sciences, June 8, 2011, Granada, Spain[s2] Competitive exclusion and competitor-mediated coexistence, Fronts and Nonlinear PDEs, June 21,
2011, Ecole Normale Superier, Paris, France[s3] Competitor-mediated coexistence, Mathematical Frontiers in the life Sciences, July 5, 2011,
Limerick, Ireland௚䠐௳ྚஙʁ‫پ‬ૠྸᚐௌྰ‫ܭ׍‬ἣἻἳὊἑỴἽἆἼἌἲỉᴾ
ؕᄽểࣖဇᴾTAMAKI Hisaoᄂᆮಒᙲィ⟬ᅔ㞴࡞ၥ㢟࡟ᑐࡍࡿ࢔ࣉ࣮ࣟࢳࡢࡦ࡜ࡘ࡟ᅛᐃࣃ࣓࣮ࣛࢱ࢔ࣝࢦࣜࢬ࣒ࡀ࠶ࡿࠋࡇࢀ
ࡣࠊၥ㢟ࡢ኱ࡁࡉ n ࡟ຍ࠼࡚ၥ㢟ᅛ᭷ࡢࣃ࣓࣮ࣛࢱ k ࢆ⪃࠼ࠊィ⟬᫬㛫ࡢ k ࡬ࡢ౫Ꮡᗘࡣ㧗࠸ࡀ n ࡬ࡢ౫Ꮡᗘࡣప࠸ࡼ࠺࡞࢔ࣝࢦࣜࢬ࣒ࢆ㛤Ⓨࡋࡼ࠺࡜࠸࠺ࡶࡢ࡛࠶ࡿࠋࡼࡾලయⓗ࡟ࡣࠊf ࢆ n ࡟౫Ꮡࡋ࡞࠸㛵ᩘ࡜ࡋ࡚ࠊィ⟬᫬㛫ࡀ݂ሺ݇ሻ݊୓ሺଵሻ ࡛࠶ࡿࡼ࠺࡞࢔ࣝࢦࣜࢬ࣒ࢆ┠ᣦࡍࠋࡇࡢࡼ࠺࡞࢔ࣝࢦࣜࢬ࣒ࡀᏑᅾࡍࡿ࡜ࡁࠊࡑࡢၥ㢟ࡣ㸦ࡑࡇ࡛㑅ࡤࢀࡓࣃ࣓࣮ࣛࢱ࡟㛵ࡋ࡚㸧ᅛᐃࣃ࣓࣮ࣛࢱࢺࣛࢡࢱࣈ࡛ࣝ࠶ࡿ࡜࠸ࢃࢀࡿࠋලయⓗ࡞ၥ㢟࡜ࡋ࡚ࠊ㸰㒊ࢢࣛࣇࡢ㸰ᒙᥥ⏬࡟࠾ࡅࡿ㎶஺ᕪᩘ᭱ᑠ໬ࢆ࡜ࡾ࠶ࡆࡓࠋ㸰ᒙᥥ⏬࡛ࡣ㸰㒊ࢢࣛࣇࡢ∦᪉ࡢ㡬Ⅼ㞟ྜࢆ୍ᮏࡢ┤⥺ୖ࡟ࠊࡶ࠺୍᪉ࡢ㡬Ⅼ㞟ྜࢆ➨୍ࡢ┤⥺࡜୪⾜࡞┤⥺ୖ࡟⨨ࡁࠊ㎶ࡣࡇࢀࡽࡢ஧ࡘࡢ┤⥺ࢆ⤖ࡪ┤⥺ศ࡟ࡼࡗ࡚⾲ࡍࠋ∦ഃ᭱㐺໬ၥ㢟࡛ࡣࠊ୍᪉ࡢᒙࡢ㡬Ⅼ㡰ࡀ୚࠼ࡽࢀࠊࡶ࠺ࡦ࡜ࡘࡢᒙ
ࡢ㡬Ⅼ㡰ࢆ㑅ࢇ࡛஺ᕪࡍࡿ㎶ࡢᑐࡢಶᩘࢆ᭱ᑠ໬ࡍࡿࠋ᭱㐺ࡢ஺ᕪᩘࢆ kࠊࢢࣛࣇࡢ㡬Ⅼᩘࢆn ࡜ࡍࡿ࡜ࡁࠊʹ୓൫ξ௞ ୪୭୥ ௞൯ ݊୓ሺଵሻ ᫬㛫ࡢᅛᐃࣃ࣓࣮ࣛࢱ࢔ࣝࢦࣜࢬ࣒ࡀ▱ࡽࢀ࡚࠸ࡓࠋᡃࠎࡣࠊ
ࡇࡢィ⟬᫬㛫ࢆᨵⰋࡋࠊ ቀ͵ξଶ௞ ൅ ݊ቁ᫬㛫ࡢ࢔ࣝࢦࣜࢬ࣒ࢆ㛤Ⓨࡋࡓࠋᣦᩘ㒊ξʹ݇ࡣࠊࡼࡃ⏝࠸ࡽࢀࡿィ⟬㔞ⓗ௬ᐃ࡛࠶ࡿᣦᩘ᫬㛫௬ㄝ㸦㹃㹒㹆㸧ࡢࡶ࡜࡛ࡣ₞㏆ⓗ࡟᭱㐺࡛࠶ࡿࠋࡲࡓࠊn ࡟㛵ࡋ࡚⥺ᙧ᫬㛫࡛࠶ࡿࡇ࡜ࡶ኱ࡁ࡞≉㛗࡛࠶ࡿࠋࡉࡽ࡟ࠊ࢔ࣝࢦࣜࢬ࣒⮬యࡣࡇࢀࡲ࡛࡟
▱ࡽࢀ࡚࠸ࡓᅛᐃࣃ࣓࣮ࣛࢱ࢔ࣝࢦࣜࢬ࣒ࡼࡾࡶ༢⣧࡛࠶ࡾࠊᐜ᫆࡟ᐇ⿦࡛ࡁࡿ࡜࠸࠺฼Ⅼࢆᣢࡗ࡚࠸ࡿࠋࡇࡢ⤖ᯝࡣ The 20th European Symposium on Algorithms ࡟᥇㘓ࡉࢀ㸰㸮㸯㸰ᖺࡢ㸷᭶࡟Ⓨ⾲ணᐃ࡛࠶ࡿࠋࡇࡢ◊✲ࡣࠊᮏ◊✲ᐊᡤᒓࡢᑠᯘ㟹᫂ຓᡭ࡜ࡢඹྠ◊✲࡛࠶ࡿࠋࡲࡓࠊᅛᐃࣃ࣓࣮ࣛࢱ࢔ࣝࢦࣜࢬ࣒ࡢᇶ♏࡜ࡋ࡚㔜せ࡞ࠊ᭷ྥࣃࢫᖜࢆồࡵࡿ࢔ࣝࢦࣜࢬ
࣒࡟ࡘ࠸࡚ࠊ๓ᖺᗘࡢᡂᯝࢆᅜ㝿఍㆟ The 37th International Workshop on Graph Theoretic
Concepts in Computer Science ࡛Ⓨ⾲ࡋࡓࠋMathematical Analysis Group৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ᚘምƷྸᛯᲦ2J&ȷȈȭȳȈ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ᚘምƱǢȫǴȪǺȠྸᛯૠྸᚐௌྰ

Dynamics observed ina reaction-diffusion system withtriple degeneracy‫߷ݱ‬ჷʂ

OGAWA Toshiyuki৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ щ‫ܖ‬ኒྸᛯᲦҦٟ ྸ‫ ܖ‬ȷ࠼޽‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ଺ᆰȑǿȸȳƷᚐௌȷЎ‫ޟ‬ᚐௌMathematical Analysis Groupᄂᆮಒᙲ
There has been a lot of studies about spatiotemporal patterns and their dynamics to systems ofreaction-diffusion equations. Let us consider variations of bifurcations from a stationary solution.
Suppose this stationary solution is spatially uniform. Then we linearize the equation about thisequilibrium and we know a bifurcation occurs only if the linearized problem has zero- or purely
imaginary eigenvalues which we call critical eigenvalues. Moreover if this critical eigenvalue is 0 withspatially non-trivial eigenfunction, a stationary bifurcation to non-uniform steady state occurs. One of
the typical examples for this is the well-known Turing instability. On the contrary, if the criticaleigenvalues are a pair of purely imaginary numbers with spatially non-trivial eigenfunctions, spatiallynon-trivial oscillations may occur. The so-called wave instability corresponds to this.
Now what can we say about the bifurcations from a spatially non-uniform steady state? Since thelinearization about non-uniform steady states is not easy in general, we need to restrict ourselves tosome special cases. One of the possibility where we can calculate the bifurcations of non-uniform
steady state is to consider about the degenerate instability points.
We focus our attention to the case where the system has the triple degeneracy with 0, 1 and 2 modes(0:1:2-mode interaction). We can, in fact, show that this type of triple degeneracy really occurs in
3-component RD system. And we found the case where the 1-mode stationary solution may become
unstable with a pair ofpurely imaginary criticaleigenvalues. Moreover weobtained the complete
condition for the Hopf
bifurcationfromthe
1-modestationary
solutions. Thus we canconclude that oscillatory
solutions may bifurcatefrom a non-uniform steadystate in 3 component RD
systems.
This is the joint workwithTakashiOkuda(Takashi Sakamoto) in
Fig. caption:Periodic motion around 1-mode stationary solution in a RD system.
Meterological college.

ʚܷ࠼ԧ

ૠྸᚐௌྰ

ἣἑὊὅᚐỉನ঺ểẸỉೞᏡࣖဇ
NINOMIYA Hirokazu৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹϱ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ᩼ዴ࢟͞ࣇЎ૾ᆉࡸᲦҦٟ ྸ‫ ܖ‬ȷʮᣃ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ਘ૝ȷˡછྵᝋǍȑǿȸȳನᡯƷૠྸ ࣃࢱ࣮ࣥࢆࡶࡘ཯ᛂᣑᩓ⣔ࡢゎࡢᵓᡂࢆ⾜ࡗ࡚࠸ࡿࠋ཯ᛂᣑᩓ⣔ࡢᏙ❧ゎࡢᵓᡂࡸ⮬⏤ቃ⏺
ၥ㢟ࡢࢫࣃ࢖ࣛࣝἼࡢᵓᡂࠊ཯ᛂᣑᩓ㏆ఝ࡟ࡼࡿ᪂ࡋ࠸⮬⏤ቃ⏺ၥ㢟ࡢᑟฟࢆ⾜ࡗࡓࠋࡲࡓࠊ
ᚰᐊ⣽ືࡣࠊάື㟁఩ࡢࢫࣃ࢖ࣛࣝἼࡢⓎ⏕ࡀ୍ࡘࡢཎᅉ࡜⪃࠼ࡽࢀ࡚࠸ࡿࠋࢫࣃ࢖ࣛࣝἼࡢ
⮬ⓎⓗⓎ⏕࣓࢝ࢽࢬ࣒ࢆㄪ࡭࡚࠸ࡿࠋ    (a) ⮬⏤ቃ⏺ၥ㢟࠿ࡽ⾲ࢀࡿࢫࣃ࢖ࣛࣝἼ   (b) ཯ᛂᣑᩓ㏆ఝ࡟ぢࡽࢀࡿࢫࣃ࢖ࣛࣝἼ

ᴗ⦼1.

H. Murakawa and H. Ninomiya: Fast reaction limit of a three-component reaction-diffusion
system, Journal of Mathematical Analysis and Applications, 379 (2011), No. 1,

2.

150-170

M. Iida, R. Lui, and H. Ninomiya: Stacked Fronts for Cooperative Systems with Equal Diffusion
Coefficients, SIAM J. Math. Anal. 43, (2011) No. 3, 1369-1389

Mathematical Analysis Groupᄂᆮಒᙲ⏡␉␏␖␢⏡␑␝ྰ‫ܬܢ‬ἩἻἌἰྵᝋỉἉἱἷἾὊἉἹὅểᴾ‫ٽ‬ᨗἧἾỴỉʖยᄂᆮᒬ᣼‫ܦ‬ʍ

KUSANO Kanya ǷȟȥȬȸǷȧȳྰȪȸȀȸ৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻ‬ᄂᆮȷჷᝠ৆ဦೞನܲՃ૙੉ ӸӞ‫ٽܖٻދ‬ᨗ‫ྶע‬࿢‫ؾ‬ᄂᆮ৑૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ǷȟȥȬȸǷȧȳᅹ‫ܖ‬Ღྸ‫ܖ‬Ҧٟȷ࠼޽‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ‫ᙹٻ‬೉᨞‫ޖ‬ኒƷȢȇȪȳǰƓǑƼǷȟȥȬȸǷȧȳ

ᴾ
Simulation Groupᄂᆮಒᙲ㻌 䝥䝷䝈䝬䛿Ᏹᐂ䛻䛚䛡䜛ᬑ㐢ⓗ䛺≀㉁䛾ᙧែ䛷䛒䜚䚸䛭䛣䛷⏕䛪䜛ᵝ䚻䛺⌧㇟䛿㠀⥺ᙧ㐣⛬䛾ᐆᗜ䛷䜒䛒䜛䚹ᡃ䚻䛿ᵝ䚻䛺Ᏹᐂ䝥䝷䝈䝬㠀⥺ᙧ⌧㇟䛾䝯䜹䝙䝈䝮䜢䝅䝭䝳䝺䞊䝅䝵䞁䜢ᇶ䛻ゎ᫂䛩䜛◊✲䜢⾜䛳䛶䛔䜛䚹㻌 ≉䛻䚸ᮏᖺᗘ䛿ኴ㝧䝣䝺䜰⇿Ⓨ䛾䝖䝸䜺ᶵᵓ䛾ゎ᫂䛸䛭䛾ண ྍ⬟ᛶ䛾◊✲䛻㛵䛧䛶ᡂᯝ䜢ᚓ䛯䚹ኴ㝧䝣䝺䜰䛿ኴ㝧㯮Ⅼ䛾㏆ഐ䛷Ⓨ⏕䛩䜛ᕧ኱䛺⇿Ⓨ⌧㇟䛷䛒䜚䚸䛭䛾ᙳ㡪䛿ᆅ⌫ୖ䛾ᵝ䚻䛺䜲䞁䝣䝷䜔Ᏹᐂ㣕⾜ኈ䞉⯟✵ᶵ஌ဨ஌ᐈ䛾೺ᗣ⿕ᐖ䛻䜒ཬ䜆䛣䛸䛜ᣦ᦬䛥䜜䛶䛔䜛䚹ኴ㝧䝣䝺䜰䛿㯮Ⅼ☢ሙ䛾୍㒊䛜䝥䝷䝈䝬䛾⇕䛸㐠ື䜶䝛䝹䜼䞊䛻⇿Ⓨⓗ䛻ゎᨺ䛥䜜䜛⌧㇟䛷䛒䜛䛜䚸䛭䛾Ⓨ⏕ᶵᵓ䛿ᮍゎ᫂䛷䛒䜛䚹䛭䛾䛯䜑䚸䛔䛴䚸䛹䛣䛷䚸䛹䜜⛬䛾つᶍ䛾䝣䝺䜰䛜Ⓨ⏕䛩䜛䛛䜢ṇ☜䛻ண 䛩䜛䛣䛸䛿ᮍ䛰䛻ᅔ㞴䛷䛒䜛䚹㻌 ᡃ䚻䛿ኴ㝧䝣䝺䜰䛜ኴ㝧⾲㠃䛻䛚䛡䜛䛂኱つᶍ䛺☢ሙ䛾᤬䛨䜜䛃䛸䛂ᑠつᶍ䛺☢ሙ䛾ኚ໬䛃䛾┦஫స⏝䜢㏻䛧䛶Ⓨ⏕䛩䜛䛸䛔䛖௬ㄝ䛻ᇶ䛵䛝䚸ኴ㝧⾲㠃☢ሙ䛸䝣䝺䜰Ⓨ⏕䛾㛵ಀ䜢䛣䜜䜎䛷䛻↓䛔ヲ⣽䛺ィ⟬ᶵ䝅䝭䝳䝺䞊䝅䝵䞁䛻䜘䛳䛶ㄪᰝ䛧䛯䚹䝇䞊䝟䞊䝁䞁䝢䝳䞊䝍䜢⏝䛔䛶 100 ㏻䜚௨ୖ䛾␗䛺䜛☢
ሙᵓ㐀䛻㛵䛧䛶䛭䜜䛮䜜䝣䝺䜰Ⓨ⏕䛾᭷↓䜢ㄪ䜉䜛ᩘ್ᐇ㦂䠄㟁☢ὶయຊᏛ䝅䝭䝳䝺䞊䝅䝵䞁䠅䜢⾜䛖䛣䛸䛷䠄ᅗ䠅䚸᤬䛨䜜䛯☢ሙ୰䛻䛂཯ᴟᛶ(OP)ᆺ䛃䜎䛯䛿䛂㏫䝅䜰(RS)ᆺ䛃䛸࿧䜀䜜䜛 2 ✀㢮䛾≉Ṧ䛺ᵓ㐀䜢ᣢ䛴ᑠつᶍ䛺☢ሙ䛜Ꮡᅾ䛧䛯䛸䛝䛻䝣䝺䜰䛜Ⓨ⏕䛩䜛䛣䛸䜢ゎ᫂䛧䛯䚹䛥䜙䛻䚸䛣䛾ண 䜢᳨ド䛩䜛Ⅽ䚸2006 ᖺ 12 ᭶ 13 ᪥ཬ䜃 2011 ᖺ 2 ᭶ 13 ᪥䛻Ⓨ⏕䛧䛯኱つᶍ䝣䝺䜰䜢䚸ኴ㝧ほ ⾨ᫍ䛂䜂䛾䛷䛃䛜ほ 䛧䛯䝕䞊䝍䛻ᇶ䛵䛔䛶ヲ⣽䛻ゎᯒ䛧䛯䚹䛭䛾⤖ᯝ䚸䝅䝭䝳䝺䞊䝅䝵䞁䛜ண 䛧䛯 2 ✀㢮䛾☢ሙᵓ㐀䛜䛭䜜䛮䜜ኴ㝧⾲㠃䛻⌧䜜䛯ᩘ᫬㛫ᚋ䛻䚸䛣䜜䜙䠎䛴䛾䝣䝺䜰䛜䛭䛾㡿ᇦ䛷Ⓨ⏕䛧䛯䛣䛸䛜☜ㄆ䛥䜜䛯䚹䜎䛯䚸㐣ཤ䛻ほ 䛥䜜䛯」ᩘ䛾䝣䝺䜰䜒䝅䝭䝳䝺䞊䝅䝵䞁䛾ண 䛻୍⮴䛩䜛☢ሙᵓ㐀䜢క䛳䛶䛔䛯䛣䛸䜢✺䛝Ṇ䜑䛯䚹ᮏ◊✲䛿ኴ㝧䝣䝺䜰䛾Ⓨ⏕ᶵᵓ䛾⌮ゎ䛻኱䛝䛟㈉⊩䛩䜛䛸ඹ䛻䚸⢭ᐦ䛺☢ሙほ 䛸䝅䝭䝳䝺䞊䝅䝵䞁䛾㐃ᦠ䛻䜘䛳䛶ᆅ⌫つᶍ䛾䜲䞁䝣䝷䛻῝้䛺ᙳ㡪䜢ཬ䜌䛩ᕧ኱䝣䝺䜰䛾ண 䛜ྍ⬟䛷䛒䜛䛣䛸䜢ព࿡䛧䛶䛔䜛䛣䛸䛛䜙䚸ᏱᐂኳẼணሗ䛾ᐇ⌧䛾䛯䜑䛻䜒㔜せ䛺㈉⊩䜢䛩䜛䜒䛾䛷䛒䜛䚹னҾҽӴ

SUGIHARA Kokichi⏡␉␏␖␢⏡␑␝ྰဒ΂ჷᙾỉọẵỚểᛍ‫࠼ٻ‬ԓỉүᨖࣱ৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈи৑ᧈ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹཎ˓૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ࠹˴ૠྸ߻‫ܖ‬Ღ߻‫ܖ‬Ҧٟȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ཋྸྵᝋᲦဃ˳ྵᝋᲦᅈ˟ྵᝋƷᚘምૠྸ

ᴾ ⏬ീ࠿ࡽዟ⾜ࡁࢆ▱ぬࡍࡿ㐣⛬ࡢᩘ⌮ࣔࢹࣝࢆసࡾࠊࡑࢀ࡟ᇶ࡙࠸࡚෗┿ࢆ౑ࡗ࡚ᐇ㝿࡜ࡣ␗࡞ࡿ༳㇟ࢆ୚࠼ࡿࡇ࡜ࡢ࡛ࡁࡿᢏ⾡ࢆ᫂ࡽ࠿࡟ࡋࡓࠋ
㸱ḟඖࡢୡ⏺ࢆ┤᥋ぢ࡚▱ぬࡍࡿ⾜Ⅽ࡜ࠊ㸱ḟඖୡ⏺ࢆ㸰ḟඖᖹ㠃࡟ᢞᙳࡋࡓ⏬ീࢆぢ࡚ඖࡢ㸱ḟඖᵓ㐀ࢆ▱ぬࡋࡼ࠺࡜ࡍࡿ⾜Ⅽࡣ኱ࡁࡃ␗࡞ࡿࠋࡑࡢ㐪࠸ࡢ୍ࡘࡣࠊどⅬࡢ఩⨨࡟࠿࠿ࢃࡿࡶࡢ࡛࠶ࡿࠋ㸱ḟඖୡ⏺ࡣࠊ࡝ࡇ࡟どⅬࢆ⨨࠸࡚ぢ࡚ࡶࠊࡑࡇ࠿ࡽぢࡓ“ṇࡋ࠸᝟ᬒ”ࡀぢ࠼ࡿࠋ୍᪉ࠊ⏬ീ࡟ࡣࠊࡑࢀࢆ᧜ᙳࡋࡓ᫬ࡢどⅬ㸦ࡘࡲࡾࣞࣥࢬ୰ᚰ㸧ࡀ௜㝶ࡋ࡚࠾ࡾࠊࡑࡢ
Ⅼࡀࠊࡑࡢ⏬ീࢆ═ࡵࡿ“ṇࡋ࠸どⅬ”࡛࠶ࡿࠋࡑࢀ௨እࡢどⅬ࠿ࡽ⏬ീࢆ═ࡵࡿ࡜ࠊ“ṇࡋࡃ࡞࠸᝟ᬒ”ࢆぢ࡚࠸ࡿࡇ࡜࡟࡞ࡿࠋࡓ࡜࠼ࡤࠕ┤᪉యࡢ⏬ീࡣࠊࣞࣥࢬ୰ᚰ௨እࡢどⅬ࠿ࡽぢࡓ࡜ࡁ࠸࠿࡞ࡿ┤᪉యࡶ᚟ඖ࡛ࡁ࡞࠸ࠖࡇ࡜ࡀド࡛᫂ࡁࡿࠋࡇࡇ࡟ࠊ❧యࢆㄗࡗ࡚▱ぬࡋ࡚ࡋࡲ࠺㘒ぬࡢཎᅉࡀ₯ࢇ࡛࠸ࡿࠋලయⓗ࡟ࡣࠊ⏬ീࢆ᧜ᙳࡍࡿ࡜ࡁࡢࣞࣥࢬ୰ᚰࡼࡾ㏆࠸఩⨨࡛⏬ീࢆ═ࡵࡿ࡜ࠊᐇ㝿ࡼࡾዟ⾜ࡁࡀὸࡃឤࡌࡽࢀࠊ㏫࡟ࣞࣥࢬ୰ᚰࡼࡾ㐲࠸఩⨨࡛⏬ീࢆ═ࡵࡿ࡜ࠊᐇ㝿ࡼࡾዟ⾜ࡁࡀ῝ࡃឤࡌࡽࢀࡿࠋ
 どⅬࡢ㐪࠸ࡀࡶࡗ࡜῝้࡟࡞ࡿࡢࡣࠊ」ᩘࡢ⏬ീࢆྜᡂࡍࡿሙྜ࡛࠶ࡿࠋ⏬ീ࡟௜㝶ࡍࡿࡣ
ࡎࡢどⅬ఩⨨ࡀ୍⮴ࡋ࡞࠸ྜᡂ⏬ീࡣࠊ࡝ࡇ࡟どⅬࢆ⨨࠸࡚ぢ࡚ࡶࠊ“ṇࡋ࠸᝟ᬒ”ࢆぢ࡚࠸ࡿࡇ࡜࡟ࡣ࡞ࡽ࡞࠸ࠋࡓ࡜࠼ࡤࠊ✵ࡁᆅࡢᐇ෗⏬ീ࡜ࠊࡑࡇ࡟❧࡚ࡿணᐃࡢᘓ≀ࡢࢥࣥࣆ࣮ࣗࢱ
ࢢࣛࣇ࢕ࢵࢡࢫ⏬ീࢆྜᡂࡋ࡚ࠊᘓ≀ࡢ᏶ᡂண᝿ᅗࢆసࡿሙ㠃࡛ࡣࠊࡇࡢどⅬ఩⨨ࢆࡎࡽࡍࡇ
࡜࡟ࡼࡗ࡚ࠊᘓ≀ࡢᅽ㏕ឤࢆᐇ㝿ࡼࡾᑠࡉࡃឤࡌࡉࡏࡿ࡜࠸࠺᧯సࡀྍ⬟࡟࡞ࡿࠋ ࡇࢀࡽࡢᛶ㉁ࡣࠊၟရࡢㄗࡗࡓ༳㇟ࢆ୚࠼ࡿᗈ࿌⏬ീࡢไసᢏ⾡࡟ࡶ㏻ࡌࡿࡶࡢ࡛࠶ࡾࠊࡑ
ࡢᢅ࠸ࡣὀពࢆせࡍࡿࠋࠕ᧜ᙳ᫬ࡢࣞࣥࢬ୰ᚰ࡜ࡣ␗࡞ࡿ఩⨨࠿ࡽ═ࡵࡿࡼ࠺࡞⎔ቃ࡛ᗈ࿌⏬
ീࢆ࿊♧ࡋ࡞࠸ࠖࠊ
ࠕどⅬ఩⨨ࡢ୍⮴ࡋ࡞࠸ྜᡂ⏬ീࡣၟရᗈ࿌࡟౑ࢃ࡞࠸ࠖ࡞࡝ࡢ࣐ࢼ࣮ࡀᚲ
せ࡛࠶ࡿࠋ࠶ࡿ࠸ࡣࡶࡗ࡜✚ᴟⓗ࡟ࡣࠊᬑ㏻ࡢேࡀᬑ㏻࡟⏬ീࢆ═ࡵࡓ᫬ࠊ࡛ࡁࡿࡔࡅࡦࡎࡳ
ࡢᑡ࡞࠸❧య▱ぬࡀ࡛ࡁࡿ⎔ቃࢆࠊつไࡢᙧ࡛ᐃࡵࡿࡇ࡜ࡀᚲせ࡛࠶ࡿࠋࡑࡢࡓࡵ࡟ࡣࠊどⅬ఩⨨ࡢࡎࢀࡀ❧య▱ぬ࡟࡝ࡢࡼ࠺࡞ࡦࡎࡳࢆ⏕ࡳฟࡍ࠿ࡢᐃ㔞ⓗᢕᥱࡀᚲせ࡜࡞ࡿࡀࠊࡑࡢࡓ
ࡵࡢゎᯒ᪉ἲࢆసࡿࡇ࡜ࡀ࡛ࡁࡓࠋ ࡋ࠿ࡋࠊࡶ࠺୍᪉࡛ࠊ⮬⏤࡞どⅬࡢ㑅ᢥࡣࠊ࣐ࣝࢳࣃ࣮ࢫ࣌ࢡࢸ࢕ࣈ࡞࡝࡜ࡼࡤࢀࡿ⾲⌧ᢏ⾡ࡢഃ㠃ࡶᣢࡗ࡚࠸ࡿࠋࡋࡓࡀࡗ࡚ࠊᗈ࿌⏬ീไసࡢ࣐ࢼ࣮࣭つไࡣࠊ⾲⌧ࡢ⮬⏤࡜ࡢᩚྜᛶ
ࡶྲྀࡽ࡞ࡅࢀࡤ࡞ࡽ࡞࠸ࠋࡇࢀࡀḟࡢㄢ㢟࡛࠶ࡿࠋ



Simulation Groupᄂᆮಒᙲ⏡␉␏␖␢⏡␑␝ྰᐯࠁኵጢႎἣἑὊὅ࢟঺ೞನỉᴾἳἕἉἷဃ঺ồỉᢘဇɥ‫̮ٻޛ‬UEYAMA Daishin৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹϱ૙੉ȷ҅ෙᢊ‫ܖٻ‬‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ྵᝋૠྸ‫ܖ‬ᲦҦٟᲢྸ‫ܖ‬Უᄂ ᆮ ϋ ܾᲴ ǷȟȥȬȸǷȧȳૅੲᚐௌ

ᴾ
Simulation Groupᄂᆮಒᙲ ⮬↛⏺࡟ࡣᵝࠎ࡞ࣃࢱ࣮࣭ࣥᶍᵝࡀᏑᅾࡍࡿࠋࡑࢀࡽࡣ⮬ᕫ⤌⧊ⓗ࡟ᙧᡂࡉࢀࡿࡶࡢࡀከࡃ㸪ࡑࡢ࣓࢝ࢽࢬ࣒ࡣ㸪ᩘ⌮⛉Ꮫ㸪≀⌮Ꮫ㸪໬Ꮫ㸪⏕≀Ꮫ࡜࠸ࡗࡓᵝࠎ࡞ศ㔝࠿ࡽࡢ࢔ࣉ࣮ࣟࢳ࡟
ࡼࡗ࡚ᚎࠎ࡟᫂ࡽ࠿࡟࡞ࡾࡘࡘ࠶ࡿࠋ≉࡟ᩘ⌮⛉Ꮫⓗ࡞࢔ࣉ࣮ࣟࢳ࡟ࡼࡿ◊✲࡛ࡣ㸪཯ᛂᣑᩓ⣔࡜࿧ࡤࢀࡿ⣔࡟࠾ࡅࡿ◊✲ࡀ┒ࢇ࡛࠶ࡿࠋࢥࣥࣆ࣮ࣗࢱୖ࡛㸪࠶ࡿ✀ࡢ཯ᛂᣑᩓ᪉⛬ᘧࢆࢩ࣑࣮ࣗࣞࢩࣙࣥࡍࡿ࡜㸪ࡑࡇ࡟ࡣ⮬↛⏺࡟ぢࡽࢀࡿࡼ࠺࡞つ๎ṇࡋ࠸ᶍᵝࡀ⌧ࢀࡿࠋ⮬ᕫ⤌⧊ⓗᶵᵓࢆᣢࡘࣃࢱ࣮ࣥᙧᡂ࡟࠾࠸࡚ࡣ㸪౛࠼ࡤ㡿ᇦᙧ≧ࡀ」㞧࡞ሙྜ࡛ࡶ㸪ࡑࡢ」㞧࡞ᙧ≧࡟ྜࢃࡏ࡚࠾࠾ࡼࡑᆒ➼࡞ࣃࢱ࣮ࣥࢆᙧᡂࡍࡿࠋᮏ◊✲࡛ࡣࡑࡢࡼ࠺࡞ࠕᛶ㉁ࠖࢆ࣓ࢵࢩࣗ⏕ᡂ࡟ά࠿ࡏ࡞࠸࠿࡜࠸࠺࢔࢖ࢹ࢔ࢆฟⓎⅬ࡟㸪ࡑࢀࢆᐇ⌧ࡍࡿࣉࣟࢢ࣒ࣛࡢసᡂࢆ㏻ࡌ࡚㸪ࡑࡢ᭷ຠᛶࢆᥦ᱌ࡍࡿࡶࡢ࡛࠶ࡿࠋࣃࢱ࣮ࣥᙧᡂ࡟㛵ࡍࡿ⌮ㄽࡢ᪂ࡓ࡞ᛂ⏝࡜ࡋ࡚௒ᚋࡢᛂ⏝ศ㔝ࡢᣑ኱࡟ᐤ୚ࡍࡿࡶࡢ࡜⪃࠼࡚࠸ࡿࠋ

ᅗ㸸ᥦ᱌ᡭἲ࡟ࡼࡗ࡚సᡂࡉࢀࡓ࣓ࢵࢩࣗ㸦ྑ㸧ࠋ⮬ᕫ⤌⧊ⓗ࡟⏕ᡂࡉࢀࡿࢫ࣏ࢵࢺࣃࢱ࣮ࣥ㸦ᕥ㸧ࢆ฼⏝ࡋ࡚సᡂࡉࢀࡿࠋ᪉⛬ᘧ୰ࡢࣃ࣓࣮ࣛࢱࢆ㐺ษ࡟ㄪ⠇ࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪࣓ࢵࢩࣗࡢ⢒ᐦࡶ⮬⏤࡟ࢥࣥࢺ࣮࡛ࣟࣝࡁࡿࠋ

࣭ A self-organized mesh generator using pattern formation in a reaction-diffusion system, H. Notsu,
D. Ueyama, and M. Yamaguchi, Applied Mathematics Letters 26(2) (2013), pp.201-206.