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FOREFRONT OF ANALYSIS METHODS FOR FLOOD FLOWS AND BED VARIATIONS AND PROSPECTS OF SEDIMENT TRANSPORT RESEARCH

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(1)

ㄽᩥ Ἑᕝᢏ⾡ㄽᩥ㞟➨ᕳᖺ᭶

ᐇົ㠃࠿ࡽࡳࡓὥỈὶ࣭Ἑᗋኚືゎᯒἲࡢ

᭱๓⥺࡜௒ᚋࡢㄪᰝ◊✲ࡢ᪉ྥᛶ

FOREFRONT OF ANALYSIS METHODS FOR FLOOD FLOWS AND BED VARIATIONS AND PROSPECTS OF SEDIMENT TRANSPORT RESEARCH

⚟ᒸᤩ஧

Shoji FUKUOKA

1ࣇ࢙࣮ࣟ㸪ᕤ༤㸪3K' ୰ኸ኱Ꮫ◊✲㛤Ⓨᶵᵓᩍᤵ 㸦ࠛ112-8551 ᮾி㒔ᩥி༊᫓᪥1㸫13㸫27㸧

The present paper deals with a forefront of analysis methods of flood flows and bed variations in rivers. It is emphasized at first that to give time variations of measured-water surface profiles is important specifically for assessing time changes of river bed variations in addition to water-level hydrographs as the boundary conditions. Secondly, many issues concerning sediment transports in gravel bed rivers are presented and discussed. Then, focuses of discussions are paid to new findings of sediment transports in gravel-bed rivers by the numerical movable bed channel developed. Prospects of flood flows and sediment transport researches are discussed from river engineering points of views.

Key Words : Floods, bed variation ,water surface profile, gravel bed river, BVC method, numerical movable bed channel

㸬ࡲ࠼ࡀࡁ

ᡃࡀᅜ࡛ࡣ᫛࿴ᖺ௦࠿ࡽᖺ௦ࡢἙᕝࡢὥỈὶࡸ

ᅵ◁㍺㏦ࡢㄪᰝ࣭◊✲ࡣ㸪Ἑᕝࡢᐇົࢆ⾜࠺ᶵ㛵ࡀ୰ᚰ

࡟࡞ࡾ㸪኱ࢫࢣ࣮ࣝࡢἙᕝỈ⌮ᶍᆺࢆ⏝࠸࡚ὥỈὶ࡜Ἑ ᗋኚືࡢ᳨ウࡀ⾜ࢃࢀ࡚ࡁࡓ㸬୍᪉㸪኱Ꮫ➼ࡢ◊✲ᶵ㛵

࡛ࡣ㸪ὥỈὶ㸪ᅵ◁⛣ືࡢ◊✲ࡣ୺࡟Ỉ⌮ᐇ㦂࠿ࡽᇶ♏

ࢹ࣮ࢱࢆᚓ࡚㸪ࡇࢀࡽ࡟ᇶ࡙࠸࡚ὥỈࡸᅵ◁⛣ື࡟㛵ࢃ

ࡿỈ⌮⌧㇟ࡢゎᯒࡀ⾜ࢃࢀ࡚࠸ࡓ㸬ὥỈὶࡢゎᯒࡣ୙➼

ὶィ⟬ࡀ୺ὶ࡛࠶ࡗࡓ㸬ࡋ࠿ࡋ㸪ὥỈὶࡸᅵ◁⛣ື㸪Ἑ ᗋኚື➼ࡢほ ࢹ࣮ࢱࡀᑡ࡞࠿ࡗࡓࡓࡵ࡟㸪ἙᕝࡢὥỈ ὶࡸᅵ◁⛣ືࡢ⌮ゎࡀ༑ศ࡛࡞࠿ࡗࡓ㸬

᫛࿴ᖺ௦࡟ධࡾ㸪ἙᕝࡢὥỈὶ㸪Ἑᗋኚື➼ࡢほ 

⤖ᯝࡀᚎࠎ࡟㞟✚ࡉࢀ㸪ࡲࡓࢥࣥࣆ࣮ࣗࢱࡢィ⟬⬟ຊࡢ

ྥୖ㸪ࢥࣥࣆ࣮ࣗࢱࢆ⏝࠸࡚ࡢィ⟬ᢏ⾡ࡢ㐍ᒎ࡟ࡼࡾ㸪 ἙᕝࡢὥỈ㸪ᅵ◁㍺㏦ࡢ⌮ゎࡀᚎࠎ࡟῝ࡲࡗ࡚ࡁࡓ㸬ࡋ

࠿ࡋ㸪୙ᛮ㆟࡞ࡇ࡜࡟㸪ὥỈὶࡣἙᕝࡢタィእຊ࡛࠶ࡿ

࡟ࡶ࠿࠿ࢃࡽࡎ㸪ᡃࡀᅜ࡛ࡣ㸪ὥỈὶࡢఏ᧛ᶵᵓࡸἙᗋ ኚື➼㸪ὥỈὶࡢຊᏛ࡟ࡘ࠸࡚ࡣ㸪῝ࡃ᳨ウࡉࢀ࡚᮶࡞

࠿ࡗࡓࡼ࠺࡟ぢ࠼ࡿ㸬஦ᐇ㸪Ỉ⌮Ꮫࡢᩍ⛉᭩࡛ࡢὥỈὶ

࡟㛵ࡍࡿグ㏙ࡣ㸪⌧ᅾ࡛ࡶ30ᖺ๓࡜࡯࡜ࢇ࡝ኚࢃࡗ࡚࠸

ࡎ㸪ᩘᏛⓗྲྀࡾᢅ࠸ࡢࡳ࡛㸪ᐇ㝿ࡢὥỈὶࡀ࡝ࡢࡼ࠺࡞

ࡶࡢ࡛࠶ࡿ࠿࡟ࡘ࠸࡚࡯࡜ࢇ࡝᭩࠿ࢀ࡚࠸࡞࠸ࡢࡀ⌧≧

࡛࠶ࡿ㸬ࡇࡢ⌮⏤ࡣ㸪ὥỈὶࡣ㠀ᐃᖖᛶࡀᙅࡃ㸪‽ᐃᖖ ὶࡢྲྀࡾᢅ࠸ࡀฟ᮶㸪࠿ࡘ␲ఝ➼ὶⓗ࡞ὶࢀ࡛࠶ࡿࡇ࡜㸪

἞Ỉィ⏬࡛ࡣࣆ࣮ࢡὶ㔞ࡸࣆ࣮ࢡỈ఩ࡀ㔜せ࡛࠶ࡾ㸪ࡑ

ࢀࡽࡀศ࠿ࢀࡤ㸪࠾࠾ࡼࡑィ⏬ࢆ❧࡚ࡿࡇ࡜ࡀฟ᮶ࡓࡇ

࡜㸪ὥỈほ ࡢປຊࡀ኱ࡁ࠸ࡇ࡜㸪ࡲࡓ㸪Ἑᕝ⟶⌮ࡣᐁ ࡀ⾜ࡗ࡚࠾ࡾ㸪ほ ࡉࢀࡓὥỈࢹ࣮ࢱࡣእ㒊ࡢ◊✲⪅ࡀ

฼⏝ࡋ࡙ࡽ࠸≧ἣ࡟࠶ࡗࡓࡇ࡜➼ࡀ㛵ಀࡋ࡚࠸ࡓࡼ࠺࡟

ᛮ࠺㸬ࡋ࠿ࡋ㸪ࡑࡢᚋࡢἙᕝὥỈࡢほ ࢆ㏻ࡋ࡚ὥỈὶ ࡀ‽ᐃᖖ࡛㸪␲ఝ➼ὶ࡛࠶ࡿ࡜࠸࠺ࡇ࡜ࡣ㸪࠿࡞ࡾ⾲㠃

ⓗ࡞ぢ᪉࡛࠶ࡿࡇ࡜㸪㠀ᐃᖖᛶࡀὥỈὶࡢ≉ᚩࢆつᐃࡋ

࡚࠸ࡿࡇ࡜㸪ࡑࡢࡇ࡜ࡀࡲࡓ㸪ᅵ◁㍺㏦ࡸἙᗋኚື࡟኱

ࡁࡃᙳ㡪ࡋ࡚࠸ࡿࡇ࡜㸪➼ࡀ᫂ࡽ࠿࡟࡞ࡗ࡚ࡁࡓ㸬ࡇࢀ

࡟ࡣ㸪㏆ᖺἙᕝἢ࠸ከᆅⅬ࡟ᅽຊᘧỈ఩ィࢆẚ㍑ⓗᏳ౯

࡟ᐜ᫆࡟タ⨨ࡍࡿࡇ࡜ࡀྍ⬟࡜࡞ࡾ㸪ᚋ㏙ࡍࡿࡼ࠺࡟㸪 ほ ࡉࢀࡓỈ㠃ᙧࡢ᫬㛫ኚ໬ࢆゎᯒ࡟⏝࠸ࡿࡇ࡜࡟ࡼࡾ㸪 ὥỈὶ࡜ᅵ◁⛣ືࡢᮏ㉁ࡀ᫂ࡽ࠿࡟࡞ࡗ࡚ࡁࡓࡇ࡜࡜ᐦ ᥋࡟㛵ಀࡍࡿ1)

ゎᯒᢏ⾡ࡢ୍ᒙࡢ㐍ᒎ࡟ࡼࡾ㸪኱ᆺࡢἙᕝỈ⌮ᶍᆺᐇ 㦂࡟௦ࢃࡗ࡚㸪ᐇἙᕝࢆᑐ㇟࡜ࡋࡓᩘ್ゎᯒ࡟ࡼࡿ᳨ウ ࡀ㸪௒ࡸἙᕝࡢỈ⌮ၥ㢟◊✲ࡢ୺ὶ࡟࡞ࡗ࡚࠸ࡿ㸬㏆ᖺ ࡢὥỈ⅏ᐖࡢከⓎࡸ⥔ᣢ⟶⌮ࢆ☜ᐇ࡟⾜࠺ࡇ࡜ࡀᚲせ࡞

᫬௦࡟࡞ࡾ㸪Ⓨ⏕ࡋࡓὥỈ⅏ᐖ࡟ᑐࡋ࡚㸪ࡑࡢཎᅉゎ᫂

ࡢࡓࡵ࡟ὥỈὶ࡜ᅵ◁⛣ື࡟㛵ࡋ࡚༑ศ࡞⌮ゎࡀᚲせ࡜

࡞ࡾ㸪ṇࡋ࠸ᢏ⾡ⓗุ᩿ࡀồࡵࡽࢀࡿࡼ࠺࡟࡞ࡗࡓࡇ࡜㸪

ࡲࡓ㸪Ἑᕝ⎔ቃ࡟ཬࡰࡍὥỈὶ࡜ᅵ◁⛣ືࡢ㔜せᛶࡀㄆ

㆑ࡉࢀࡿࡼ࠺࡟࡞ࡗࡓࡇ࡜➼ࡀ㸪ᚑ᮶ࡢᯟࢆ㉸࠼ࡓㄪᰝ㸪

◊✲ࢆ⾜࠺ᚲせᛶ࡜⎔ቃࡀᩚࡗࡓࡇ࡜࡜ࡶ㛵ಀࡋ࡚࠸ࡿ㸬 ᮏ◊✲࡛ࡣ㸪Ἑ㐨ィ⏬㸪Ἑᕝ⟶⌮ࡢࡓࡵࡢ᭱ࡶᇶᮏ࡛

࠶ࡿὥỈὶ࡜ᅵ◁⛣ືࡢゎᯒᢏ⾡࡟ࡘ࠸࡚㸪ᐇົ㠃࠿ࡽ

(2)

ぢ࡚ࡢ᭱๓⥺ࢆ♧ࡍ㸬ḟ࡟㸪▼♟Ἑᕝࡢᅵ◁⛣ື࡛ᮍゎ Ỵࡢ㔜せ࡞Ꮫ⾡ⓗ㸪ᢏ⾡ⓗㄢ㢟ࢆᥦ♧ࡋ㸪ࡑࢀࡽࡢゎỴ

ࢆᅗࡿ㐨ࢆ᥈ࡿ᭱ᚋ࡟㸪᪂ࡋࡃ㛤Ⓨࡉࢀࡓᩘ್⛣ືᗋ Ỉ㊰࠿ࡽᚓࡽࢀࡿᡂᯝࡣ࡝ࡢࡼ࠺࡞ࡶࡢ࡛㸪ࡇࢀࢆᐇἙ ᕝ⟶⌮࡟ά࠿ࡍࡓࡵࡢ᪉⟇ࢆ㆟ㄽࡍࡿ㸬

㸬ὥỈὶ㸪Ἑᗋኚືゎᯒࡢᒎ㛤㸫ほ Ỉ㠃ᙧࡢ᫬

㛫ኚ໬ࢆቃ⏺᮲௳࡟୚࠼㸪ὥỈὶ࡜Ἑᗋኚືࢆ୍

యⓗ࡟ゎࡃࡇ࡜ࡢ㔜せᛶ

Ἑᕝ⟶⌮࡟ᚲせ࡞ὥỈὶ࡜Ἑᗋኚືࡢ᳨ウ᪉ἲࡀ࠸ࡃ ࡘ࠿࠶ࡿࡀ㸪ࡑࡢ୰࡛㸪ලయⓗ࡟⏝࠸ࡽࢀ㸪᭷ຠᛶࡀ☜

࠿ࡵࡽࢀ࡚࠸ࡿゎᯒᢏ⾡ࡣ㸪ὥỈ᫬ࡢỈ㠃ᙧࡢ᫬㛫ኚ໬

ࡢほ ್ࢆ᪤▱㔞࡜ࡋ࡚㸪㐠ື᪉⛬ᘧ࡜Ἑᗋኚືࡢᘧࢆ

୍యⓗ࡟ゎࡃ᪉ἲ࡛࠶ࡿ1)2)㸬ᚑ᮶㸪ὥỈࡢỈ⌮Ꮫ࡛ࡣ㸪

ୖὶ➃࡛ὥỈὶ㔞ࣁ࢖ࢻࣟࢢࣛࣇࢆ㸪ୗὶ➃Ỉ఩ࣁ࢖ࢻ

ࣟࢢࣛࣇࢆ୚࠼࡚㸪Ỉ఩ࡸὶ㏿ሙࢆゎࡃ᪉ἲࡀ୍⯡ⓗ࡟

⏝࠸ࡽࢀ࡚᮶ࡓ㸬ࡑࡇ࡛ࡣỈ఩ࣁ࢖ࢻࣟࢢࣛࣇࡣᮍ▱㔞

࡜ࡋ࡚ᢅࢃࢀ࡚ࡁࡓ㸬ࡇࢀࡣ㸪Ἑᗋ㧗ࡀὥỈ୰࡟࡯࡜ࢇ

࡝ኚືࡏࡎ㸪ᅛᐃᗋ࡜ࡋ࡚ᢅ࠼ࡿࡼ࠺࡞ቃ⏺㠃࡛࠶ࢀࡤ㸪

୚࠼ࡓὶ㔞ࣁ࢖ࢻࣟࢢࣛࣇ࡟ᑐࡋ࡚㸪Ỉ఩ࣁ࢖ࢻࣟࢢࣛ

ࣇࢆᮍ▱㔞࡜ࡋ࡚ゎࡃࡇ࡜ࡣ⪃࠼ᚓࡿ᪉ἲ࡛࠶ࡿ㸬

㏆ᖺ㸪Ỉ఩ࢆྠ᫬ከⅬ࡛ ࡿࡇ࡜ࡀᐜ᫆࡟࡞ࡾ㸪Ἑᕝ ࡢỈ㠃ᙧࡢ᫬㛫ኚ໬ࢆ㧗⢭ᗘ࡟ᐜ᫆࡟ồࡵࡿࡇ࡜ࡀྍ⬟

࡟࡞ࡗࡓ㸬ࡇࡢࡼ࠺࡟Ỉ఩ࡀὶ㔞ࡼࡾࡶ㧗⢭ᗘ࡟ከⅬ࡛

 ࢀࡿ࡞᫬௦࡛ࡣ㸪ᚑ᮶ࡢࡼ࠺࡟ὶ㔞ࣁ࢖ࢻࣟࢢࣛࣇࢆ

ୖὶ➃ࡢቃ⏺᮲௳࡜ࡍࡿࡼࡾࡶ㸪Ἑᗋኚືࢆྵࡴ⦪ᶓ᩿

㠃ᙧࡢኚ໬➼ࡢ᝟ሗࡀ཯ᫎࡋ࡚࠸ࡿほ Ỉ㠃ᙧࡢ᫬㛫ኚ

໬ࢆ᪤▱㔞࡜ࡋ㸪ୖὶ➃ቃ⏺᮲௳㸪ୗὶ➃ቃ⏺᮲௳࡟Ỉ

఩ࣁ࢖ࢻࣟࢢࣛࣇ࡛୚࠼㸪ὶ㔞ࣁ࢖ࢻࣟࢢࣛࣇࢆᮍ▱㔞

࡜ࡍࡿィ⟬ἲࡀ㸪ᐇἙᕝࡢゎᯒ࡟ࡩࡉࢃࡋ࠸㸬

ὥỈ୰࡟኱ࡁ࡞Ἑᗋኚືࡀ࠶ࡿ࡜ࡁࡣ㸪ゎᯒࡢ୰࡛Ỉ 㠃ᙧࡢ᫬㛫ኚ໬ࢆ⪃៖ࡍࡿࡇ࡜ࡣ㸪⛣ືᗋࡢሙྜࡣ㸪ࡉ

ࡽ࡟㔜せ࡟࡞ࡿ㸬Ỉ㠃ᙧࡣἙᗋኚື࡟ᛂࡌ࡚㸪Ἑ㐨㈓␃

㔞㸪Ἑ㐨㐟Ỉ㔞3)࡟ࡼࡗ࡚᫬✵㛫ⓗ࡟ኚ໬ࡍࡿ㸬ࡋࡓ ࡀࡗ࡚㸪ࡇࢀࡽࡢἙᕝࡢỈ⌮⌧㇟ࢆ┤᥋཯ᫎࡋ࡚࠸ࡿほ  Ỉ఩ࡢ᫬✵㛫ศᕸࢆᡤ୚ࡢ᮲௳࡜ࡋ࡚⏝࠸㸪ὶ㔞ࣁ࢖

ࢻࣟࢢࣛࣇ࡜Ἑᗋኚືࡢ᫬✵㛫ศᕸࢆᮍ▱㔞࡜ࡍࡿࡇ࡜

Ỉ㠃ᙧ᫬⣔ิࢹ࣮ࢱ࡟ᇶ࡙ࡃὥỈὶ࣭Ἑᗋኚືゎᯒࣇ࣮ࣟ

㡯┠

Ỉ㠃ᙧ᫬㛫ኚ໬(Ỉ఩᫬✵㛫ኚ໬)(ᚲ㡲**) ὥỈᚋ䛾ᖹᆒἙᗋ㧗䛾⦪᩿ศᕸ ὶ㔞(䛒䜛᩿㠃䛾ὶ㏿) ほ Ỉ㠃ᙧ

᫬⣔ิ䝕䞊䝍

ቃ⏺᮲௳タᐃ䝕䞊䝍

ୖὶタᐃỈ఩᫬⣔ิ

ୗὶタᐃỈ఩᫬⣔ิ

⤥◁㔞䠄ୖὶᖹ⾮ὶ◁㔞䠅

ึᮇ≧ែ䛾ᆅᙧ䝕䞊䝍 ᖹ㠃ᙧ≧䠈᩿㠃ᙧ≧

ゎᯒ䝯䝑䝅䝳䝕䞊䝍 䝯䝑䝅䝳ᖹ㠃ᙧ≧䠈Ἑᗋ㧗䠈ᆅ

⿕≧ἣ(䝯䝑䝅䝳䛾✀㢮)䛺䛹

ึᮇ≧ែ䛾ᆅ⿕≧ἣ

⢒ᗘศᕸ䠈 ᶞᮌ᢬ᢠಀᩘศᕸ

ቃ⏺᮲௳

ୖὶ➃ቃ⏺᮲௳(ୖὶ➃Ỉ఩ㄪᩚ)

ୗὶ➃ቃ⏺᮲௳(ୗὶ➃Ỉ఩ㄪᩚ)

ୖὶὶ◁㔞(ᖹ⾮ὶ◁㔞)

ὥỈὶ(BVCἲ)䞉Ἑᗋኚືゎᯒ

ᚇยἙὊἑ

ㄪᩚ䞉ಟṇ*

ᚐௌኽௐỉ౨ᚰ ゎᯒ䝰䝕䝹䛾᳨ド ẚ㍑

ゎᯒ⤖ᯝ

Ỉ㠃ᙧ䛾᫬㛫ኚ໬(Ỉ఩᫬✵㛫ኚ໬) ὶ㔞䝝䜲䝗䝻䜾䝷䝣䛾⦪᩿ศᕸ

ὶ㏿ศᕸ䛾᫬✵㛫ኚ໬(ᗏ㠃ὶ㏿䛾᫬✵㛫ኚ໬) Ἑᗋ㧗䛾᫬✵㛫ኚ໬

ᚐௌᵆ൦ྸᵇἙὊἑồỉ٭੭

* ὥỈὶ䛾ୖ᪼ᮇ䞉ୗ㝆ᮇ䛾⦆䜔䛛䛺Ỉ㠃ᙧኚ໬䛻㏣㝶䛩䜛᢬ᢠศᕸ䛾್䜢ồ䜑䜛䛣䛸䛿ᐜ᫆䛷䛒䜛

** Ỉ㠃ᙧ䝕䞊䝍䛿ほ 䝕䞊䝍䛷၏୍᫬✵㛫ศᕸ䜢䜒䛴

Ỉ㠃ᙧ᫬⣔ิࢹ࣮ࢱ࡟ᇶ࡙ࡃὥỈὶ࣭Ἑᗋኚືゎᯒࡢ

࢖࣓࣮ࢪ

BVCἲࡢᇶ♏ᘧ࡜ᮏ᳨ウ࡛⏝࠸ࡓἙᗋኚືゎᯒᡭἲ

්ᡮЎࠋύࡁ්᩿ᡮᵆᵠᵴᵡඥᵇ ඕ࠿٭ѣᚐௌඥ

ὥỈ๓Ἑᗋᙧ≧

ὥỈ䝢䞊䜽Ἑᗋᙧ≧

ὥỈᚋἙᗋᙧ≧

Ỉ㠃ᙧ᫬⣔ิ䝕䞊䝍 ὥỈ๓䛾ᖹᆒἙᗋ㧗 ὥỈᚋ䛾ᖹᆒἙᗋ㧗 ほ 䝕䞊䝍

ୗὶタᐃỈ఩

ୗὶ➃

ୖὶ➃

ୖὶタᐃỈ఩

ୖ᪼ᮇỈ㠃ᙧ(ᐇ⥺)

ୗ㝆ᮇỈ㠃ᙧ(◚⥺)

૾ᆉࡸύᚸ̖ࡸ

ᵆᵏᵇ ൦ข࠯ר්ᡮ ᢃѣ૾ᆉࡸί൦࠯૾Ӽὸ ᵆᵐᵇ ൦ข ᡲዓࡸ

ᵆᵑᵇ ൦ขᆢЎพࡇ ൦ขᆢЎพࡇ૾ᆉࡸ

ᵆᵒᵇ ൦ᘙ්᩿ᡮ ൦ᘙ᩿ỉᢃѣ૾ᆉࡸ

ᵆᵓᵇ ൦ข࠯רᤲႺ්ᡮ ᵵỉ଺᧓٭҄᣽ỉἯỴἏὅ૾ᆉࡸ

ᵆᵔᵇ ࡁ᩿ןщ ᢃѣ૾ᆉࡸίᤲႺ૾Ӽὸ ᵆᵕᵇ ࡁ්᩿ᡮ ൦ขᆢЎẲẺพࡇỉܭ፯ࡸ

ᵆᵏᵇ ੈ්ჿ᣽ ᑱဋὉᢊɥỉࡸ

ᵆᵐᵇ ූᢂჿỉූɥ᣽ ெ̽Ὁެỉࡸ

ᵆᵑᵇ ූᢂჿຜࡇ ɤഏΨᆆ්ਘ૝૾ᆉࡸ

ᵆᵒᵇ ඕ࠿٭ѣ᣽ ්ჿỉᡲዓࡸ

ව൦්

ᵆᵠᵴᵡඥᵇ

ඕ࠿٭ѣ

சჷ᣽

(3)

ࡣ㸪⛣ືᗋၥ㢟࡛ࡣᮏ㉁ⓗ࡛࠶ࡾ≉࡟㔜せ࡛࠶ࡿ㸬

⚟ᒸࡽࡣ1)2)3)4)㸪ࡇࡢࡼ࠺࡞⪃࠼ࡢࡶ࡜࡟㸪ከࡃࡢἙᕝ

࡛Ỉ㠃ᙧࡢ᫬㛫ኚ໬ࢆ᪤▱㔞࡜ࡋ㸪ᅗ࡟♧ࡍࣇ࣮ࣟ

ࢳ࣮ࣕࢺ࡟ᚑࡗ࡚ὥỈὶ࡜Ἑᗋኚືࢆゎ࠸࡚࠸ࡿ㸬ୖὶ

➃㸪ୗὶ➃ࡢỈ఩ࣁ࢖ࢻࣟࢢࣛࣇࢆቃ⏺᮲௳࡜ࡋ࡚㸪㠀 ᐃᖖከḟඖὥỈὶゎᯒ࡜஧ḟඖἙᗋኚືィ⟬ࢆ⤌ࡳྜࢃ

ࡏ㸪ྛ᫬㛫ࡢᐇ Ỉ㠃ᙧ࡜୍⮴ࡍࡿࡼ࠺࡟ὶࢀ࡜Ἑᗋኚ

ືࢆゎࡁ㸪ὶ㏿ศᕸ࡜Ἑᗋ㧗㸪ὶ㔞➼ࡢ᫬✵㛫ศᕸ➼ࢆ

ồࡵ࡚࠸ࡿ㸬ࡇࡢࡇ࡜ࢆูࡢゝ࠸᪉ࢆࡍࢀࡤ㸪ὥỈ୰࡟

ྛ᫬㛫ࡢἙᗋᗏ㠃ࡢ㧗ࡉࡣኚ໬ࡍࡿࡀ㸪Ỉ㠃ᙧࡀ᪤▱࡛

࠶ࡿࡢ࡛ࡇࢀࢆ⏝࠸ࡓᇶ♏ᘧࡼࡾỈ῝ࡀỴࡲࡾ㸪ὶ㔞ࡀ

࡝ࡢ᩿㠃࡛ࡶồࡲࡿࡇ࡜࡟࡞ࡿ㸬⏝࠸ࡿὶࢀࡢ㐠ື᪉⛬

ᘧࡣ㸪㠀ᐃᖖ‽஧ḟඖゎᯒἲ㸪㠀ᐃᖖᖹ㠃஧ḟඖゎᯒἲ㸪 㠀ᐃᖖ‽୕ḟඖ୍⯡ᗏ㠃ゎᯒἲ㸦௨ୗ࡛BVCἲ࡜࿧ࡪ㸧

➼ࡀ࠶ࡿࡀ㸪࡝ࢀࢆ⏝࠸ࡿ࠿ࡣᑐ㇟࡜ࡍࡿἙ㐨ࡢ≉ᛶ࡟

ࡼࡿ㸬‴᭤ࡸ」㞧࡞Ἑᗋᵓ㐀㸪Ἑᕝᶓ᩿ᵓ㐀≀➼ࢆᣢࡘ Ἑ㐨࡛ࡣ㸪Ἑᗋኚືゎᯒࡢ⢭ᗘࡀ㔜せ࡟࡞ࡿࡢ࡛㸪୍⯡

ⓗ࡟ࡣ%9&ἲࡀ᥎ዡࡉࢀࡿ㸬BVCἲ5)ࡣ㸪ὸỈὶࡢ௬ᐃ

ࢆ⏝࠸࡞࠸Ỉ῝✚ศࣔࢹ࡛ࣝ࠶ࡾ㸪Ἑᗋࡢ᢬ᢠホ౯ࡸἙ ᗋኚືゎᯒ࡟ᚲせ࡞ᗏ㠃ᅽຊ࡜ᗏ㠃ὶ㏿ࢆồࡵࡿࡇ࡜ࡀ ฟ᮶㸪」㞧࡞ὶࢀሙ࡟ά⏝ྍ⬟࡞≉ᚩࢆᣢࡘ㸬ᅗ ࡣ㸪 ほ Ỉ㠃ᙧࡢ᫬㛫ኚ໬ࡀ୚࠼ࡽࢀࢀࡤ㸪ᑐᛂࡍࡿἙᗋኚ

ືࡶ᥎ᐃࡀࡘࡃ࡜࠸࠺⪃࠼ࢆ㸪ᅗࡢὥỈὶ㸪Ἑᗋኚື

ゎᯒࡢࣇ࣮ࣟࢳ࣮ࣕࢺࡢ࢖࣓࣮ࢪ࡛♧ࡋࡓࡶࡢ࡛࠶ࡿ㸬 ḟ࡟㸪◁♟Ἑᕝ࡛࠶ࡿ▼⊁ᕝࡢ᫛࿴56ᖺ8᭶ὥỈࢆᑐ

㇟࡜ࡋ㸪ほ Ỉ㠃ᙧࡢ᫬㛫ኚ໬ࢆ୚࠼࡚ゎ࠸ࡓὥỈὶ㸫 Ἑᗋኚືゎᯒࡢ⤖ᯝࢆ♧ࡍ6)㸬⾲࡟ὥỈὶࡢゎᯒ࡟⏝

࠸ࡓBVCἲࡢᇶ♏ᘧ࡜㸪Ἑᗋኚືゎᯒ࡟⏝࠸ࡓᘧࢆࡑࢀ

ࡒࢀ♧ࡍ㸬ᅗ̾ ࡣ▼⊁ᕝ࡟࠾ࡅࡿ⦪᩿Ỉ㠃ᙧࡢ᫬㛫ኚ

໬ࡢほ ⤖ᯝ࡜ゎᯒ⤖ᯝࢆ♧ࡍ㸬ᤲὶ◁㔞ᘧ࡟࠿࠿ࢃࡽ

ࡎỈ㠃ᙧࡀⰋዲ࡟෌⌧࡛ࡁ࡚࠸ࡿ㸬ᅗࡣ㸪ὥỈ๓ᚋ࡛

⏕ࡌࡓἙᗋ㧗⦪᩿ᙧࡢኚ໬ࢆ♧ࡍ㸬ᤲὶ◁㔞ᘧ࡟ࡼࡿప Ỉ㊰ᖹᆒἙᗋ㧗ࡢ㐪࠸ࡀᑠࡉࡃ㸪࠸ࡎࢀࡢゎᯒ⤖ᯝࡶ0k

㹼8k༊㛫࡟࠾ࡅࡿἙᗋపୗࢆⰋዲ࡟෌⌧࡛ࡁ࡚࠸ࡿ㸬 ࡑࢀ࡟ᑐࡋ࡚㸪᭱῝Ἑᗋ㧗ࡣ㸪኱ࡁ࡞ᤲὶ◁㔞ࡀ⟬ᐃ ࡉࢀࡿⰱ⏣࣭㐨ୖᘧࢆ⏝࠸ࡓゎᯒ࡛ࡣ㸪3k㹼6k௜㏆ࡢ⺬

⾜༊㛫࡛ࡣ㸪Ὑ᥀῝ࡀ௚ࡢゎᯒࡸᐇ ್࡜ẚ࡭࡚኱ࡁࡃ ィ⟬ࡉࢀ㸪⏝࠸ࡿᤲὶ◁㔞ᘧ࡟ࡼࡾᕪࡀ⏕ࡌࡿ㸬㠀ᐃᖖ ᖹ㠃஧ḟඖゎᯒ࡛ࡣ㸪BVCἲ࡜ྠᵝ࡟ほ Ỉ㠃ᙧࢆゎᯒ

࡟⏝࠸࡚ࡶἙᗋኚືࡣ༑ศ࡟ㄝ࡛᫂ࡁ࡞࠿ࡗࡓ㸬ࡇࡢࡇ

࡜ࡣ㸪▼⊁ᕝࡢࡼ࠺࡞⺬⾜Ἑᕝࡢὶࢀࡢゎᯒ࡟ࡣ㸪BVC ἲࡢࡼ࠺࡟୕ḟඖᛶࢆ⪃៖ࡀฟ᮶ࡿࡇ࡜ࡀ㔜せ࡛࠶ࡿࡇ

࡜ࡀศ࠿ࡿ㸬

Ἑ㐨࡜ᵓ㐀≀ࢆ୍యⓗ࡟ᤊ࠼㸪␗࡞ࡿ᫬✵㛫 ࢫࢣ࣮ࣝ࠿ࡽ࡞ࡿ✀ࠎࡢὥỈ࣭Ἑᗋኚືࢆᗈ⠊ᅖ㸪

⤫ྜⓗ࡟ゎᯒࡍࡿ

Ἑᕝࡣ㸪ᒣᆅᇦ࠿ࡽᾏᓊᇦࡲ࡛ኚ໬ࡢ኱ࡁ࠸ᆅᙧ㸪ᆅ

㉁ࢆ࿊ࡋ㸪ὶ㊰⺬⾜㸪◁ᕞ㸪ἙᖜࡸἙᗋᮦᩱ➼㸪Ἑ㐨ࡣ

␗࡞ࡿ኱ࡁࡉࡢࢫࢣ࣮ࣝ࠿ࡽᵓᡂࡉࢀ㸪ࡑࢀ࡟ᛂࡌࡓỈ

⌮⌧㇟ࡀ⏕ࡌ࡚࠸ࡿ㸬⌧ᅾࡢὥỈゎᯒᢏ⾡ࡣ㸪㛗࠸Ἑ㐨

༊㛫࡛⏕ࡌ࡚࠸ࡿΰᅾࡍࡿࢫࢣ࣮ࣝࡢ␗࡞ࡿỈ⌮⌧㇟ࢆ

୍యⓗ㸪⤫୍ⓗ࡟ゎᯒ࡛ࡁࡿᢏ⾡࡟࡞ࡾᚓ࡚࠸࡞࠸㸬ࡇ ࡢࡓࡵ࡟ࡣ㸪኱ࡁ࡞እຊ࠿ࡽᑠࡉ࡞እຊࡲ࡛ࢆྵࡴ␗࡞

ࡿࢫࢣ࣮࡛ࣝつᐃࡉࢀࡿἙ㐨ࡢỈ⌮⌧㇟ࢆ᫬࣭✵㛫ⓗ࡟

⤫ྜࡋ࡚ᢅ࠺ࡇ࡜ࡀྍ⬟࡞ゎᯒ࣭タィᢏ⾡ࡀồࡵࡽࢀ࡚

࠸ࡿ7)㸬ࡇࢀ࡟ࡣ㸪ෆ⏣㸪⚟ᒸ࡟ࡼࡿBVCἲ5)ࡀ᭷ຠ࡛࠶

ࡿ㸬BVCἲࡣ㸪✵㛫ࢫࢣ࣮ࣝࡢ㐪࠸࡟ࡼࡿᚲせ࡞ゎᯒせ

⣲ࡀྵࡲࢀࡓ୍ࡘࡢ᪉⛬ᘧ⣔࡛⾲⌧ࡉࢀ࡚࠸ࡿ㸬⪃࠼᪉ ࡢᇶᮏࡣ㸪ᖹᆒὶࡣ㸪Ỉ῝✚ศࡉࢀࡓᖹ㠃஧ḟඖᘧ࡛࠶

ࡿࡇ࡜㸪୍ḟඖ㸪஧ḟඖⓗ࡞ὶࢀࡢἙ㐨༊㛫ࡣ㸪୍ḟඖ㸪

஧ḟඖゎᯒࡀ⾜ࢃࢀ㸪୕ḟඖⓗ࡞ゎᯒࡀᚲせ࡞ὶࢀࡢἙ 㐨༊㛫࡛ࡣ㸪୕ḟඖⓗ࡞ゎᯒࡀᐇ⾜ฟ᮶ࡿࡼ࠺࡟㸪ὥỈ ὶ࡜Ἑᗋኚືࡀ⧅ࡀࡾࢆᣢࡗ࡚㐃⥆ⓗ࡟ィ⟬ฟ᮶ࡿࡇ࡜

࡛࠶ࡿ㸬

௨ୗ࡟␗࡞ࡿ᫬✵㛫ࢫࢣ࣮ࣝࡢ✀ࠎࡢỈ⌮⌧㇟ࢆ⤫ྜ

ᅗ⦪᩿Ỉ㠃ᙧࡢほ ⤖ᯝ࡜ゎᯒ⤖ᯝࡢẚ㍑

ᅗ⦪᩿Ἑᗋᙧ≧ࡢほ ⤖ᯝ࡜ゎᯒ⤖ᯝࡢẚ㍑

ಙ⃰ᕝୗὶࡢὶᇦᅗ

Ჴ൦ˮᚇย৑

Ჴȝȳȗ੎൦ೞئ

(4)

ⓗ࡟ゎᯒࡋࡓᐇ౛࡜ࡋ࡚㸪」㞧࡞Ἑᕝࢩࢫࢸ࣒࡜↓ሐ 㒊ࢆ᭷ࡍࡿಙ⃰ᕝୗὶᇦ඲ᕝࡢὥỈὶ࣭Ἑᗋኚືゎᯒ⤖

ᯝࢆ♧ࡍ㸬

ಙ⃰ᕝୗὶࡢὶᇦᅗࢆᅗ࡟♧ࡍ㸬ᮏᕝࡼࡾࡶ኱ࡁ

࡞ὶ㔞ࢆᣢࡘᗄࡘ࠿ࡢᨭᕝὶධ㸪ศὴ࣭ྜὶࡍࡿὴᕝ୰

ࣀཱྀᕝ㸪ከ㔞ࡢ࣏ࣥࣉ᤼Ỉ㔞㸪ἑᒣࡢἙᕝᵓ㐀≀ࡢᏑᅾ

࡞࡝」㞧࡞Ἑᕝ࡟࠾ࡅࡿὥỈὶ࡜Ἑᗋኚືࢆㄝ᫂ࡍࡿࡓ

ࡵ࡟ࡣ㸪Ἑ㐨㈓␃࡜㏫ὶࢆక࠺ὶࢀ㸪す㔝ᆅ༊ࡢỏ℃㸪

୰ࣀཱྀᕝࡢศྜὶ➼ࡀಙ⃰ᕝୗὶᇦ඲యࡢὶࢀ࡟ᙳ㡪ࢆ

ཬࡰࡋ࡚࠸ࡿࡇ࡜࡟╔┠ࡋ㸪ಙ⃰ᕝୗὶ඲ᕝࢆᑐ㇟࡟㸪 ᅗ㸪ᅗ࡛♧ࡋࡓ኱ὥỈ᫬ࡢỈ㠃ᙧࡢ᫬㛫ኚ໬࡟ᇶ࡙

࠸ࡓὥỈὶ㸪Ἑᗋኚືࡢ᳨ウࢆ⾜ࡗࡓ㸬ὥỈὶゎᯒ࡟ࡣ㸪 ࡇࡢࡼ࠺࡞」㞧࡞Ἑ㐨ὶࢀ࡟㐺ࡋࡓBVCἲࢆ㐺⏝ࡋࡓ㸬 ゎἲࡣ⾲࡟♧ࡋࡓ࡜࠾ࡾ࡛࠶ࡿ㸬ࡇࡇ࡛㸪ᘧ(5)㸪(6)

ࢆ↓どࡍࢀࡤ㸪ὸỈὶࡢ௬ᐃࢆ⏝࠸ࡓ‽୕ḟඖὥỈὶゎ ᯒ࡜࡞ࡿࡇ࡜࠿ࡽ㸪ᑐ㇟࡜ࡍࡿὶࢀࡢࢫࢣ࣮ࣝ࡜Ỉ⌮⌧

㇟࡟ᛂࡌ࡚㸪BVCἲࢆ౑࠸ศࡅࡿࡇ࡜ࡀྍ⬟࡛࠶ࡿ㸬࡞

࠾㸪ᮏ⠇࡛ࡣ඲ᕝࢆᑐ㇟࡜ࡋࡓᗈ࠸⠊ᅖࡢὥỈ࣭Ἑᗋኚ

ື≉ᛶࡢᢕᥱࡀᚲせ࡛࠶ࡿࡇ࡜࠿ࡽ㸪ὥỈὶゎᯒ࡟ࡣὸ Ỉὶࡢ௬ᐃࢆ⏝࠸ࡓBVCἲࢆ⏝࠸ࡓ㸬ὥỈ୰࡟ࡣὙሖࡀ

඲㛢࡜࡞ࡿࡓࡵಙ⃰ᕝୖὶ➃࠿ࡽࡢὶධ㔞ࡣࢮ࡛ࣟ࠶ࡿ㸬 ᨭᕝ࠿ࡽࡢὶධቃ⏺᮲௳ࡣ㸪ᮏᕝࡢほ Ỉ㠃ᙧࡢ᫬㛫ኚ

໬ࢆㄝ࡛᫂ࡁࡿࡼ࠺࡟୚࠼ࡓ㸬ࡲࡓ㸪㛵ᒇศỈ㊰࡜ᮏᕝ

ୗὶࡢୗὶ➃Ỉ఩࡟ࡣ㸪᪂₲኱ሖ࡜す ࡢほ Ỉ఩ࣁ࢖

ࢻࣟࢢࣛࣇࢆࡑࢀࡒࢀ୚࠼ࡓ㸬ᑐ㇟⠊ᅖࡢἙᗋᮦᩱࡣࢩ

ࣝࢺ࣭⢓ᅵศ㹼⣽♟ศ࡛ᵓᡂࡉࢀ㸪ᖹᆒ⢏ᚄࡣ㹼 0.5mm⛬ᗘ࡛࠶ࡿ㸬

ᅗ࡟Ỉ㠃ᙧࡢ᫬㛫ኚ໬࡜Ἑᗋ㧗ࡢ⦪᩿ศᕸࡢゎᯒ

್࡜ほ ್ࡢẚ㍑ࢆ♧ࡍ㸬15㹼21k࡟࠾࠸࡚ࡣ㸪඲యⓗ

࡟ぢ࡚ゎᯒỈ఩ࡣほ Ỉ఩ࢆㄝ࡛᫂ࡁ࡚࠾ࡾ㸪ࣆ࣮ࢡ᫬

ࡢỈ఩ࡣὥỈ⑞㊧Ỉ఩࡜ᴫࡡ୍⮴ࡋ࡚࠸ࡿ㸬ࡲࡓ㸪ᖹᆒ Ἑᗋ㧗ࡢゎᯒ್࡜ᐇ⦼್ࢆẚ㍑ࡍࡿ࡜㸪㛵ᒇศỈ㊰ࡢᅵ

◁ࣇࣛࢵࢩࣗ࡟ࡼࡿἙᗋపୗࡸ㸪39㹼41kࡢሁ✚࡟ࡘ࠸

࡚༑ศ⾲⌧࡛ࡁ࡚࠸࡞࠸ࡶࡢࡶ࠶ࡿࡀ㸪඲యⓗ࡟ࡳ࡚ゎ ᯒ್ࡣᐇ ್ࢆᴫࡡㄝ࡛᫂ࡁ࡚࠸ࡿ㸬

ᅗ࡟ὶ㔞ࣁ࢖ࢻࣟࢢࣛࣇ㸪ᅗ࡟↓ሐ༊㛫ࡢす㔝 ᆅ༊ࡢỏ℃࣮࣒࣎ࣜࣗࡢゎᯒ್࡜ᐇ⦼್ࡢẚ㍑ࢆ♧ࡍ㸬 ࡇࢀ࡟ࡼࡿ࡜㸪ὶ㔞ࣁ࢖ࢻࣟࢢࣛࣇࡢゎᯒ್ࡣほ ್ࢆ

ᴫࡡ⾲⌧࡛ࡁ࡚࠾ࡾ㸪ࡲࡓ㸪す㔝ᆅ༊࡛ࡣ᭱኱୓P ࡢỏ℃ࡀⓎ⏕ࡋࡓ࡜᥎ᐃࡉࢀࡿࡀ㸪ᮏゎᯒ࡛ࡣỏ℃㔞ࡢ Ἴᙧ࡜࣮࣒࣎ࣜࣗ࡟ࡘ࠸࡚ᐇ⦼್ࢆᴫࡡㄝ࡛᫂ࡁ࡚࠸ࡿ

ࡇ࡜ࡀศ࠿ࡿ㸬

ಙ⃰ᕝୗὶࡢὥỈὶࡣ㸪ࡑࡢἙ㐨≉ᛶ࠿ࡽ㸪Ἑ㐨ἢ࠸

ࡢከࡃࡢ࣏ࣥࣉ᤼Ỉࢆཷࡅ࡞ࡀࡽ㸪す㔝ᆅ༊ࡢ↓ሐ㒊ࡢ

‣ỈࢆྵࡵἙ㐨ෆࡢከࡃࡢ⟠ᡤ࡛㈓␃ࢆ⏕ࡌ㸪ὶୗࡋ࡚

࠸ࡿ㸬ほ Ỉ㠃ᙧࡢ᫬㛫ኚ໬ࢆ⏝࠸ࡓゎᯒἲࡣ㸪ࡇࢀࡽ

ࢆ㐺ษ࡟⪃៖ฟ᮶ࡿ᪉ἲ࡛࠶ࡾ㸪ᐇ㝿࡟㉳ࡇࡗࡓὥỈ㸪 Ἑᗋኚື⌧㇟ࢆࡼࡃㄝ᫂ࡋ࡚࠸ࡿ㸬

ᵓᵎᵎ ᵏᵊᵎᵎᵎ ᵏᵊᵓᵎᵎ ᵐᵊᵎᵎᵎ ᵐᵊᵓᵎᵎ ᵑᵊᵎᵎᵎ ᵑᵊᵓᵎᵎ ᵒᵊᵎᵎᵎ ᵒᵊᵓᵎᵎ ᵓᵊᵎᵎᵎ

ᵕᵍᵐᵗᴾᵏᵐᵘᵎᵎ ᵕᵍᵑᵎᴾᵎᵘᵎᵎ ᵕᵍᵑᵎᴾᵏᵐᵘᵎᵎ ᵕᵍᵑᵏᴾᵎᵘᵎᵎ ᵕᵍᵑᵏᴾᵏᵐᵘᵎᵎ

්᣽ίᵍᶑ

ᒰထίᚐௌ͌ὸ ɶἠӝ൦ᧉίᚐௌ͌ὸ

ெʟίᚐௌ͌ὸ ࠔჽ೛ίᚐௌ͌ὸ

ᒰထίᚇย͌ὸ ɶἠӝ߷൦ᧉίᚇย͌ὸ

ெʟίᚇย͌ὸ ࠔჽ೛ίᚇย͌ὸ

‧•

‣••

‣‧•

․••

․‧•

‥••

‥‧•

…••

…‧•


‡․‫‒‣․‬•• 
‡‥•‒•‬•• 
‡‥•‒‣․‬•• 
‡‥‣‒•‬••

ᙱ᣼עғ↝൩຦᣽≋ɢ 

ᙱ᣼עғ൩຦∂∐∋∞∆

‚ᚘም͌‛

ᙱ᣼עғ൩຦∂∐∋∞∆

≋ඹؤܱጚ൦ˮⅺ↸↝ਖ਼ܭ͌≌

ὶ㔞ࣁ࢖ࢻࣟࢢࣛࣇࡢゎᯒ್࡜ほ ್ࡢẚ㍑ す㔝ᆅ༊ࡢỏ℃࣮࣒࣎ࣜࣗࡢ᫬㛫ኚ໬

ඹؤ

ރ߃ ᔓҾٻؤ

А᜿ဋ߷ӫެᵮ

ᒰထ ɤவɦ൦ᵮ

ૼ߷ᵮ

̬ଢૼဋ ဋɥᣂᵮ

ᵏᵔ ᵏᵖ ᵐᵎ ᵐᵐ

ᵕᵍᵐᵗᴾᵏᵔᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵐᵗᴾᵏᵖᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵐᵗᴾᵐᵎᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵑᵎᴾᵎᵘᵎᵎᴾᚐௌ͌

ᵕᵍᵑᵎᴾᵑᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵑᵎᴾᵗᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵑᵎᴾᵏᵒᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵑᵎᴾᵏᵖᵘᵎᵎᴾᚐௌ͌

И஖ඕ࠿᭗ ව൦ࢸඕ࠿᭗

ඹؤ ރ߃

ᔓҾٻؤ

А᜿ဋ߷ӫެᵮ ᒰထ

ɤவɦ൦ᵮ

ૼ߷ᵮ ဋɥᣂᵮ̬ଢૼဋ

൦ဋᵮ ݱ᪰ৎ೛

ᐵʟ೛

ٻᅸᵮ ᙾែ඾ᵮ

ૼᣒދ ᯓދ᣼๽ᵮ

ࠔჽ೛

̮ຜ߷൦ᧉίɥὸ

ૼ๽ٻؤᵆɥᵇ

ᵋᵔ ᵋᵒ ᵋᵐ ᵏᵎ ᵏᵐ ᵏᵒ ᵏᵔ ᵏᵖ ᵐᵎ ᵐᵐ

ᵎ ᵏ ᵐ ᵑ ᵒ ᵓ ᵔ ᵕ ᵖ ᵗ ᵏᵎ ᵏᵏ ᵏᵐ ᵏᵑ ᵏᵒ ᵏᵓ ᵏᵔ ᵏᵕ ᵏᵖ ᵏᵗ ᵐᵎ ᵐᵏ ᵐᵐ ᵐᵑ ᵐᵒ ᵐᵓ ᵐᵔ ᵐᵕ ᵐᵖ ᵐᵗ ᵑᵎ ᵑᵏ ᵑᵐ ᵑᵑ ᵑᵒ ᵑᵓ ᵑᵔ ᵑᵕ ᵑᵖ ᵑᵗ ᵒᵎ ᵒᵏ ᵒᵐ ᵒᵑ ᵒᵒ ᵒᵓ ᵒᵔ ᵒᵕ ᵒᵖ ᵒᵗ ᵓᵎ ᵓᵏ

ុᩉίᶉὸ

೅᭗ίᵲᵌᵮᵌᶋὸ

ᵕᵍᵐᵗᴾᵏᵔᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵐᵗᴾᵏᵖᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵐᵗᴾᵐᵎᵘᵎᵎᴾᚐௌ͌

ᵕᵍᵑᵎᴾᵎᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵑᵎᴾᵑᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵑᵎᴾᵗᵘᵎᵎᴾᚐௌ͌

ᵕᵍᵑᵎᴾᵏᵒᵘᵎᵎᴾᚐௌ͌ ᵕᵍᵑᵎᴾᵏᵖᵘᵎᵎᴾᚐௌ͌ ව൦ࢸඕ࠿᭗

ྑᓊሐ㜵 ᕥᓊሐ㜵

㻴㼃㻸

䖃䚷⑞㊧Ỉ఩䚷ᕥᓊ 䕿䚷⑞㊧Ỉ఩䚷ྑᓊ 䕦䚷ほ ್ 䕻䚷ᖹᆒἙᗋ㧗䠄ᐇ⦼䠅

᧙ދЎ൦ែ

ὥỈᚋἙᗋ㧗䠄ゎᯒ⤖ᯝ䠅

஬༑ᔒᕝྜὶ ส㇂⏣ᕝྜὶ

୰䝜ཱྀᕝศὴ ຍⱱᕝྜὶ

ᑠ㜿㈡㔝ᕝྜὶ

ୗ᮲ᕝྜὶ

୰䝜ཱྀᕝྜὶ ᮏᕝୗὶ

ᖹᡂᖺ᭶ὥỈ࡟࠾ࡅࡿỈ㠃ᙧࡢ᫬㛫ኚ໬ཬࡧἙᗋ㧗⦪᩿ศᕸࡢゎᯒ್࡜ᐇ ್ࡢẚ㍑㸦ಙ⃰ᕝ㸧

(5)

㸬ᩘ್⛣ືᗋỈ㊰ࡢά⏝࡟ࡼࡿ⛣ືᗋỈ⌮Ꮫࡢ᪂ ࡓ࡞ᆅᖹࢆ㛤ࡃ

␗࡞ࡿᙧ≧㸪⢏ᗘศᕸࡢἙᗋᮦᩱ࠿ࡽ࡞ࡿ▼♟Ἑ ᕝࡢᩘ್⛣ືᗋỈ㊰࡟ࡼࡿ⢏Ꮚ࡟స⏝ࡍࡿὶయຊ㸪᥋ゐ ຊ㸪⢏ᚄูὶ◁㔞ࡢ⟬ᐃ

๓❶ࡲ࡛ὥỈὶ࡜Ἑᗋኚືࡢゎᯒᢏ⾡ࡢᐇ⏝㠃࠿ࡽࡳ

ࡓ᭱๓⥺࡟ࡘ࠸࡚㏙࡭ࡓ㸬◁♟Ἑᕝ࡛ࡣ㸪ほ Ỉ㠃ᙧࢆ

⏝࠸ࡓ⢭ᗘࡢ㧗࠸ὥỈὶゎᯒࢆᅵ◁⛣ືゎᯒ࡜୍యⓗ࡟

⾜࠺ࡇ࡜࡟ࡼࡗ࡚㸪◁♟Ἑᕝ࡛㉳ࡇࡗ࡚࠸ࡿከࡃࡢၥ㢟 ࡀゎ᫂ࡉࢀ࡚ࡁࡓ㸬ࡇࢀࡣ㸪◁♟Ἑᕝ࡛ࡣ㸪ὥỈὶ࡜◁

♟ࡢ㛫࡛㉳ࡇࡿ┦஫ᖸ΅ࡢᙳ㡪ࡀࡑࢀ࡯࡝኱ࡁࡃ࡞࠸ࡇ

࡜ࡀ⌮⏤࡟ᣲࡆࡽࢀࡿ㸬ࡋ࠿ࡋ㸪▼♟Ἑᕝ࡛ࡣ㸪▼♟ࡢ

኱ࡁࡉ㸪ᙧ≧ࡢ㐪࠸ࡢࡓࡵ࡟㸪ࡲࡓ⛣ື㔞ࡢከࡉࡢࡓࡵ

࡟㸪◁♟Ἑᕝࡢゎᯒἲࡀࡑࡢࡲࡲ౑࠼ࡿࢃࡅ࡛ࡣ࡞࠸㸬 ᮏ⠇࡛ࡣ㸪▼♟Ἑᕝࡢὶ◁ၥ㢟࡜௒ᚋࡢᒎ㛤ࡢ㐨➽࡟

ࡘ࠸࡚㆟ㄽࡍࡿ㸬▼♟Ἑᕝࡣ㸪኱ࡁ࠸▼♟ࢆྵࡴᗈ࠸⢏

ᗘศᕸ࠿ࡽ࡞ࡾ㸪Ἑᗋࡢ⾲㠃ࡢพฝ࡟ࡼࡿ✵㝽ᵓ㐀ࡀ⢏

Ꮚ㐠ື࡟㔜せ࡞ᙺ๭ࢆᣢࡘ㸬ࡇࡢࡓࡵ㸪◁♟Ἑᕝ࡛㐺⏝

ྍ⬟࡞ὶ◁㔞ᘧࢆ⏝࠸ࡓἙᗋኚືゎᯒἲࡣ㸪ࡑࡢ㐺⏝ᛶ ࡀప࠸ࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗ࡚࠸ࡿ9)10)㸬ⴭ⪅ࡽࡣ㸪ᖖ㢪 ᑎᕝ࡟࠾࠸࡚㸪⌧ᆅᐇ㦂ࢆᐇ᪋ࡋ㸪▼♟Ἑᕝࡢ᪂ࡋ࠸஧

ḟඖἙᗋኚືゎᯒࣔࢹࣝࢆᵓ⠏ࡋࡓ㸬ࡇࡢࣔࢹࣝ࡟ὥỈ

᫬ࡢỈ㠃ᙧࡢ᫬㛫ኚ໬ࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡾ㸪ᖖ㢪ᑎᕝ㸪 ᮐෆᕝ➼ࡢ▼♟ἙᕝࡢὥỈὶ࡜Ἑᗋኚືࢆ࠿࡞ࡾࡢ⢭ᗘ

࡛ㄝ᫂ࡍࡿࡇ࡜ࡀྍ⬟࡟࡞ࡗࡓ11)㸬ࡋ࠿ࡋ㸪▼♟Ἑᕝࡢ ᮏ㉁ⓗ࡞ຊᏛ㐣⛬࡛࠶ࡿ▼♟࡜ὶࢀࡢ┦஫స⏝ࡸ▼♟࡜

▼♟ࡢ㛫ࡢ⾪✺࡟ࡼࡿ㐠ື㔞஺᥮➼ࡀࡇࡢࣔࢹ࡛ࣝࡣ⪃

៖ࡉࢀ࡚࠸ࡎ㸪஧┦ὶ࡜ࡋ࡚ࡢྲྀࡾᢅ࠸ࡀㄢ㢟࡜ࡋ࡚ṧ ࡉࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ㸪ࡇࢀࡽࡢ┦஫స⏝ࢆ┤᥋ィ ࡍࡿ

ࡇ࡜ࡀ஦ᐇୖᅔ㞴࡞ࡓࡵ࡟㸪⌧ᆅほ ࡸỈ⌮ᐇ㦂࠿ࡽࡇ ࡢᶵᵓࢆᐃ㔞໬ࡍࡿࡇ࡜࡟ࡣ㝈⏺ࡀ࠶ࡿ㸬

ỗ⏝ࡉࢀ࡚࠸ࡿከࡃࡢἙᗋኚືゎᯒࡣ㸪◁⢏Ꮚࢫࢣ࣮

ࣝࡢὶࢀ㸪◁⢏Ꮚࡢ㐠ືࡸᑠつᶍ࡞Ἑᗋᙧែ➼ࡣᗏ㠃ࡏ

ࢇ᩿ᛂຊ࡜ὶ◁㔞ᘧࡢ㛵ಀᘧ࡟ᢲࡋ㎸ࡳ㸪Ἑᗋᗏ㠃௜㏆

ࡢ⢏Ꮚ⛣ືࡢຊᏛࡣࣈࣛࢵࢡ࣎ࢵࢡࢫ໬ࡉࢀࡓ୰࡛ㄽࡌ

ࡽࢀ࡚ࡁࡓ㸬ࡲࡓ㸪ὥỈὶゎᯒ࡛⏝࠸ࡽࢀ࡚ࡁࡓὸỈὶ ᪉⛬ᘧࡀ㸪㖄┤᪉ྥࡢ㐠ື㔞㍺㏦࡞࡝ࡀ⪃៖࡛ࡁ࡞࠸࡞

࡝㸪ὶࢀࡢゎᯒࣔࢹࣝ࡜ࡋ࡚୙༑ศ࡞ࡲࡲ࡛㸪⤒㦂ⓗゎ 㔘࡟㢗ࡾ✚ᴟⓗ࡞ゎỴࢆᅗࡗ࡚ࡇ࡞࠿ࡗࡓ㸬ࡉࡽ࡟㸪ࡇ

ࢀࡲ࡛⾜ࢃࢀ࡚ࡁࡓ⛣ືᗋࡢᩘ್ィ⟬ࡣ㸪⢏Ꮚࢫࢣ࣮ࣝ

ࡢὶࢀࢆゎ࠿ࡎ࡟⤒㦂ⓗ࡞ᢠຊಀᩘ࡞࡝ࢆ⏝࠸࡚⢏Ꮚ࡟

స⏝ࡍࡿὶయຊࢆホ౯ࡋᡭ࠸ࡿ㸬ࡋ࠿ࡋ㸪ࡇࡢゎᯒἲ࡛

ࡣ㸪ΰྜ⢏ᚄ⢏Ꮚࡀከ㔞࡟⛣ືࡍࡿᗏ㠃㏆ഐ࡟࠾࠸࡚ࡣ㸪 㐺ษ࡞ᢠຊಀᩘࢆ୚࠼ࡿࡇ࡜ࡣᅔ㞴࡛࠶ࡾ㸪㐠ື㔞㍺㏦

ࡸ᢬ᢠ๎ࢆṇࡋࡃぢ✚ࡶࡿࡇ࡜ࡣ㞴ࡋ࠸㸬

࡜ࡣ࠸࠼㸪⠇㸪⠇࡛♧ࡋࡓࡼ࠺࡟‽୕ḟඖゎᯒἲ➼

ጤ࡛ᗏ㠃㏆ഐࡢὶࢀࢆ࠿࡞ࡾࡢ⛬ᗘゎᯒ࡛ࡁࡿࡼ࠺࡟

࡞ࡗ࡚ࡁࡓ⌧ᅾ㸪Ἑᗋኚືゎᯒࡀ᭷ࡍࡿၥ㢟Ⅼࢆ✚ᴟⓗ

࡟ゎᾘࡋ࡚࠸ࡃࡇ࡜ࡀᚲせ࡛࠶ࡿ㸬ࡇࢀࡣࡲࡓ㸪ὶ◁࡟

㛵ࡍࡿ㐠ື᪉⛬ᘧࡢ᪂ࡓ࡞㆟ㄽ࡟ࡘ࡞ࡀࡿࡇ࡜࡟࡞ࡿ㸬

⌧≧ࡢࡲࡲ࡛ࡣ㸪ዴఱ࡟㧗⢭ᗘ࡟ὥỈὶࡢ᪉⛬ᘧࢆゎ࠸

࡚ࡶ㸪Ἑᗋኚືࡀ㐺ษ࡟ㄝ࡛᫂ࡁ࡞࠸ሙྜࡀከ࠸㸬ࡑࡢ ௦⾲౛ࡣ㸪ὶࢀ࡜ᅵ◁⛣ືࡢᒁᡤⓗ࡞㠀ᖹ⾮ᛶࡀᙉ࠸ሙ

࡛࠶ࡿ㸬Ἑᕝࡀྜὶࡍࡿ࡜ࡇࢁ㸪Ỉ⾪㒊㸪ᵓ㐀≀࿘㎶➼

࠸ࡎࢀࡶ✌ാࡢᏳ඲ᛶ࡟ᐦ᥋࡟㛵ಀࡍࡿሙᡤࡀ┦ᙜࡍࡿ㸬 ࡋ࠿ࡋ㸪㏆ᖺ࡛ࡣ㸪⌧㇟ゎ᫂ࡢࢶ࣮ࣝ࡜ࡋ࡚኱ᆺࡢᩘ

್ゎᯒࡀྍ⬟࡜࡞ࡾ㸪ゎ᫂ࡀᅔ㞴࡜⪃࠼ࡽࢀ࡚ࡁࡓㄢ㢟

ࢆᢅ࠼ࡿࡼ࠺࡟࡞ࡗ࡚᮶ࡓ12)㸬ࡇࢀࡽᮍゎỴࡢὶ◁ၥ㢟

࡟ᑐࡋ࡚⚟⏣࣭⚟ᒸࡽ13)14)ࡀ㐍ࡵ࡚࠸ࡿ௵ពᙧ≧⢏Ꮚ⩌

ࡢಶࠎࡢ⢏Ꮚ㐠ື࡟╔┠ࡋ㸪ὶࢀࢆEulerⓗ࡟㸪⢏Ꮚ㐠ື

ࢆLagrangeⓗ࡟┤᥋ゎᯒࡍࡿᩘ್⛣ືᗋỈ㊰ࢆ⏝࠸ࡓゎ

ᯒࡣ᪂ࡋ࠸ᆅᖹࢆ㛤ࡃྍ⬟ᛶࡀ㧗࠸㸬

ᅗ̾ࡣ㸪୙つ๎࡞ᙧ࡛ᗈ࠸⢏ᗘศᕸ࠿ࡽ࡞ࡿᩘ್⛣

ືᗋỈ㊰ࢆ♧ࡍ㸬ᐇ㦂ࡣἙᗋᮦᩱࡼࡾࡶᑠࡉ࡞ィ⟬᱁Ꮚ

ࢆ⏝࠸኱つᶍィ⟬ࢆ⾜࠸㸪኱㔞࡟⛣ືࡍࡿ⢏Ꮚ࿘ࡾࡢὶ

ࢀ࡜⢏Ꮚ࡟స⏝ࡍࡿὶయຊ㸪⢏Ꮚ㛫ࡢ᥋ゐຊ➼ࢆ┤᥋ồ

ࡵࡿࡶࡢ࡛࠶ࡿ㸬ࡇࡢࡼ࠺࡟ὶࢀ࡜▼♟⢏Ꮚࡢ㐠ືࢆᩘ

್ⓗ࡟┤᥋ゎࡃࡇ࡜ࡣ㸪኱ኚ࡞ィ⟬᫬㛫ࢆせࡍࡿࡀ㸪኱

㔞ࡢ௵ពᙧ≧⢏Ꮚ⩌ࡢ㐠ືࡸ⢏ᚄูὶ◁㔞➼ࢆホ౯ฟ᮶

ࡿ᪉ἲ࡛࠶ࡿ㸬ᅗ ࡣ㸪ᩘ್⛣ືᗋᐇ㦂࡛ồࡵࡽࢀࡓ

⢏ᚄูὶ◁㔞࡛࠶ࡾ㸪⏝࠸ࡓ⢏ᗘศᕸࡢ᮲௳࡛ࡣ㸪⌫ࡢ ᪉ࡀ▼♟ࡼࡾࡶὶ◁㔞ࡀከࡃ㸪኱ࡁ࡞⢏ᚄ㞟ᅋࡢὶ◁㔞 ࡣᑠࡉ࡞⢏ᚄ㞟ᅋࡼࡾࡶከ࠸ࡇ࡜ࡀศ࠿ࡿ15)㸬ࡇࡢ᪉ἲ

࡟ࡼࡗ࡚㸪ࡇࢀࡲ࡛ㄪ࡭ࡿࡇ࡜ࡀ࡛ࡁ࡞࠿ࡗࡓἙᗋ㏆ഐ ࡢ⢏Ꮚ㐠ື࡜ὶయ㐠ືཬࡧࡑࢀࡽࡢ┦஫స⏝ࢆㄪ࡭ࡿࡇ

࡜ࡀฟ᮶㸪ࡇࢀࡼࡾὶࢀࡢ᢬ᢠ๎➼Ἑᗋࡢᵓ㐀㸪ὶ◁㐠

ືඪࡀ᫂ࡽ࠿࡟࡞ࡿ࡜⪃࠼࡚࠸ࡿ㸬

ࡇࢀࡽࡢ᳨ウࡀ㐍ࡴ࡜㸪ᚑ᮶ࡢ⛣ືᗋỈ⌮ࡢ⪃࠼᪉ࡢၥ 㢟㸪⏝࠸ࡽࢀ࡚࠸ࡿ⌮ㄽࡢጇᙜᛶࡸ㐺⏝㝈⏺ࡀ᫂ࡽ࠿࡟

࡞ࡿ㸬ࡉࡽ࡟㸪ὶ◁ࣔࢹࣝࡢ㛤Ⓨࡢࡓࡵࡢ⛣ືᗋὶࢀࡢ ᩘ್⛣ືᗋᐇ㦂Ỉ㊰ㅖඖ

Ỉ㊰໙㓄࣭

㏻Ỉ๓Ἑᗋ໙㓄㸸 P

P

P

ὶ◁㔞™㸦㹫㹱㸧ὶ◁㔞™10-3㸦㹫3/㹱㸧

ὶ◁㔞ࡢ᫬㛫ኚ໬ୖ⌫ୗ▼♟

(6)

ᇶ♏ࢹ࣮ࢱࢆྲྀᚓࡍࡿࡇ࡜ࡀ࡛ࡁ㸪ࡑࡢ ࢹ࣮ࢱࡀබ㛤 ࡉࢀࡿࡇ࡜࡟ࡼࡾ㸪ከࡃࡢ◊✲⪅࡟ࡼࡗ࡚ᗈࡃά⏝ࡉࢀ

ࡿࡇ࡜࡟࡞ࡿ㸬ࡇࢀࡣ㸪஘ὶ◊✲࡟࠾࠸࡚஘ὶࢩ࣑ࣗ

࣮ࣞࢱࡀᯝࡓࡋࡓᙺ๭࡜ྠᵝ࡟㸪⛣ືᗋᩘ್ࢩ࣑࣮ࣗࣞ

ࢱ࡟ࡼࡗ࡚ὶ◁ຊᏛࡀ㣕㌍ⓗ࡟㐍Ṍࡋ㸪᪂ࡋ࠸ᆅᖹࡀ㛤

࠿ࢀࡿࡇ࡜ࡀᮇᚅࡉࢀࡿ㸬

ᐇຠᛶࡢ࠶ࡿ⛣ືᗋᩘ್ゎᯒἲࡢᒎ㛤

ᩘ್⛣ືᗋỈ㊰࡛ࡢ◊✲ᡂᯝࢆἙᕝ⟶⌮㸪Ἑ㐨タィࡢ ᐇົ࡟࡝ࡢࡼ࠺࡟⏕࠿ࡍ࠿ࡀḟࡢㄢ㢟࡜࡞ࡿ㸬⢏Ꮚ㐠ື

ࢆEuler㸫Lagrange Coupling ἲ࡟ࡼࡾヲ⣽࡟ゎᯒࡍࡿᩘ

್⛣ືᗋỈ㊰ࡣ㸪ィ⟬㈇Ⲵࡢ㠃࠿ࡽᐇἙᕝࡢἙᗋኚື࡟

㐺⏝ࡍࡿࡇ࡜ࡣ㸪⌧≧ࡢComputerࡢィ⟬⬟ຊ࡛ࡣ↓⌮ࡀ

࠶ࡿ㸬▼♟ἙᕝࡢἙᗋኚືゎᯒἲࢆᐇົ࡟౑࠼ࡿᙧ࡛ᵓ

⠏ࡍࡿࡓࡵ࡟ࡣ㸪ᐇົࡢゎᯒ࡟㐺ࡋࡓEulerⓗ࡞ᩘ್⛣ື

ᗋỈ㊰࡛᫂ࡽ࠿࡜࡞ࡗࡓLagrangeⓗ⢏Ꮚ㐠ືࡢຊᏛ࡜⢏

Ꮚ࿘ᅖࡢỈࡢὶࢀࢆ⢏Ꮚ⩌ᛂຊ࡟ኚ᥮ࡋ㸪⢏Ꮚ࡜Ỉࡀΰ ᅾࡍࡿሙࡢὶࢀ࡜⢏Ꮚ㐠ືࢆࡑࢀࡒࢀEuler㐠ື᪉⛬ᘧࡢ

஧┦ὶࢀ࡜ࡋ࡚⾲⌧ࡍࡿࡇ࡜ࡀࡲࡎᚲせ࡛࠶ࡿ㸬ࡇࢀ࡟

ࡣ㸪ᙜ↛㸪㠀ᖹ⾮ὶ◁ࡢ㐠ື᪉⛬ᘧࡢ⾲ࡋ᪉ࡸ▼♟⢏Ꮚ ࡢὶ◁㔞ᘧࡢ᳨ウ➼ከࡃࡢ୓ྎࡀྵࡲࢀࡿ㸬

㸳㸬 ࠶࡜ࡀࡁ

ὥỈὶ࡜Ἑᗋኚືࡣ㸪Ἑ㐨ࡢỈ⌮ࡢ᭱ࡶ㔜せ࡞᳨ウ㡯

┠࡛࠶ࡿ㸬࡟ࡶ࠿࠿ࢃࡽࡎ㸪࡞ࡐ࠿ㄪᰝ࣭◊✲㠃࡛ࡣⓎ

ᒎᛶࡢప࠸㨩ຊࡢᑠࡉ࠸ศ㔝࡟࡞ࡗ࡚ࡋࡲࡗࡓࡼ࠺࡟ᛮ

࠺㸬⚾ࡀ◊✲⪅࡜ࡋ࡚ࢫࢱ࣮ࢺࡋࡓⱝ࠸᫬௦㸪ὶ◁ၥ㢟 ࡀỈᕤᏛࡢ୰ᚰㄢ㢟࡛㨩ຊⓗ࡞◊✲ศ㔝࡛࠶ࡗࡓ㸬ࡇࡢ ㄽᩥࡣ㸪㛗ᖺ㸪ὥỈὶ㸪ὶ◁ၥ㢟࡟㛵ࢃࡗ࡚ࡁࡓࡶࡢࡢ

୍ே࡜ࡋ࡚㸪⌧ᅾࡢ≧ἣ࡟㈐௵ࢆឤࡌ㸪ⱝ࠸◊✲⪅࣭ᢏ

⾡⪅࡟㸪ὥỈὶ࡜ὶ◁ၥ㢟ࢆ㨩ຊࡢ࠶ࡿศ㔝࡟Ⓨᒎࡉࡏ

࡚࡯ࡋ࠸࡜ࡢᛮ࠸ࢆ㎸ࡵ࡚᭩࠸ࡓ㸬

ὥỈὶ࡜ὶ◁ࡢၥ㢟ࡣ㸪ࡑࡢ㔜せᛶ࡟ࡶ࠿࠿ࢃࡽࡎ㸪 ᚑ᮶ࡢᯟ⤌ࡳ࠿ࡽฟࡿࡇ࡜ࢆࡏࡎ㸪⮬ࡽࡢ◊✲ࢆࠕᑡࡋ

࡙ࡘࠖಟṇࡍࡿࡇ࡜࡛◊✲ࡢ‶㊊ࢆぢฟࡋ࡚࠸ࡿ࠿ࡽ࡛

ࡣ࡞࠸ࡢ࠿࡜ᛮ࠺㸬ࡶࡗ࡜⮬ศࡢ㐍ࡵ࡚࠸ࡿ◊✲࡟᪂ࡋ ࡉࢆぢࡘࡅ㸪୺ᙇࡋ㸪ᖖ࡟㆟ㄽࢆᡓࢃࡏࡿࢳࣕࣞࣥࢪࣥ

ࢢ࡞ጼໃࡀᚲせ࡛࠶ࡿ࡜ᛮ࠺㸬

᭱ᚋ࡟㸪ᮏㄽᩥࢆࡲ࡜ࡵࡿ࡜㸪௨ୗࡢ࡜࠾ࡾ࡛࠶ࡿ㸬

◁♟ἙᕝࡢἙᗋኚືࢆᕤᏛⓗ࡟ព࿡ࡢ࠶ࡿ⢭ᗘ࡛ồࡵࡿ

࡟ࡣ㸪ὥỈỈ㠃ᙧࡢ᫬㛫ኚ໬ࢆほ ࡋ㸪ࡇࢀࢆ⏝࠸㸪 BVCゎᯒ㸪Ἑᗋኚືィ⟬ࢆᐇ⾜ࡍࡿࡢࡀ᭱ၿࡢ᪉ἲ࡛࠶

ࡿ㸬୍᪉㸪▼♟Ἑᕝ࡟ࡘ࠸࡚ࡣ㸪ྠᵝ࡟ほ Ỉ㠃ᙧࢆ⏝

࠸㸪▼♟Ἑᕝࡢ஧ḟඖἙᗋኚືィ⟬ἲࢆ⏝࠸ࡿࡢࡀࡼ࠸

ࡀ㸪ゎỴࡍ࡭ࡁㄢ㢟ࡀṧࡉࢀ࡚࠸ࡿ㸬

ᩘ್⛣ືᗋỈ㊰ࢆ⏝࠸㸪ὶࢀ࡜▼♟⢏Ꮚࡢ㐠ືࢆゎࡃ Euler-Lagrange Coupling ᪉ἲࡣ㸪▼♟ࡢ㍺㏦ࡸἙᗋ㠃ࡢ

᢬ᢠ➼㸪ᵓ㐀➼㸪◁♟⢏Ꮚ࡛ࣞ࣋ࣝゎࡃゎᯒἲ࡛࠶ࡿ㸬

ࡇࢀ࡟ࡼࡗ࡚㸪ᚑ᮶ࡢ⛣ືᗋỈ⌮ࡢᯟ⤌ࡳࡢጇᙜᛶ࡜㝈

⏺ᛶࡀ᫂ࡽ࠿࡟࡞ࡾ㸪⛣ືᗋỈ⌮◊✲ࡢ᪂ࡋ࠸ᒎ㛤ࡢ㐨

➽ࢆ๰ࡾฟࡍྍ⬟ᛶࡀ㧗࠸㸬ࡋ࠿ࡋ㸪ዴఱ࡟ࡋ࡚ࡇࡢ⤖

ᯝࢆᐇ⏝࡟౪ࡍࡿᙧࡲ࡛⡆␎໬ࡍࡿ࠿ࡣ㸪௒ᚋࡢ኱ࡁ࡞

௙஦࡛࠶ࡿ㸬

ὥỈὶ㸪Ἑᗋኚືၥ㢟࡛ࡣ㸪Ἑᕝࡢᮃࡲࡋ࠸Ἑᖜࡸ᩿

㠃ᙧࢆ࡝ࡢࡼ࠺࡟Ỵࡵࡿ࠿ࡣ㸪㑊ࡅ࡚㏻ࢀ࡞࠸㔜せ࡞ၥ 㢟࡛࠶ࡿ16)㸬ࡇࡢၥ㢟࡟ࡘ࠸࡚ࡣูࡢᶵ఍࡟㆟ㄽࡍࡿࡇ

࡜࡟ࡋࡓ࠸㸬

ཧ⪃ᩥ⊩

1) ⚟ᒸᤩ஧㸸ὥỈὶࡢỈ㠃ᙧほ ࡢព⩏࡜Ỉ㠃ᙧ࡟ᇶ࡙ࡃἙᕝ ࡢ⥔ᣢ⟶⌮ᢏ⾡㸪Ἑᕝᢏ⾡ㄽᩥ㞟㸪➨12ᕳ㸪pp.1-6,2006.

2) ⚟ᒸᤩ஧ :Ἑ㐨タィࡢࡓࡵࡢᇶᮏࡣఱ࠿-Ỉ㠃ᙧ᫬⣔ิほ ್

࡜ὥỈὶ-ᅵ◁ὶࡢゎᯒࢆ⤌ࡳྜࢃࡏࡓἙ㐨Ỉ⌮ࢩࢫࢸ࣒࡜ࡑ ࡢぢ࠼ࡿ໬ ,Ἑᕝᢏ⾡ㄽᩥ㞟 ,➨17ᕳ ,pp.83-88 , 2011.

3) ➉ᮧྜྷᬕ࣭⚟ᒸᤩ஧㸸㠀ᐃᖖᖹ㠃஧ḟඖὶࢀ࡟࠾ࡅࡿὥỈ㐟 Ỉ㔞ࡢホ౯ἲ࡜໭ୖᕝᒣ㛫⊃㝼Ἑ㐨࡟࠾ࡅࡿὥỈὶࡢὶ㔞࡜

Ỉ఩ࣁ࢖ࢻࣟࢢࣛࣇࡢఏ᧛ᶵᵓ㸪ᅵᮌᏛ఍ㄽᩥ㞟B1(Ỉᕤ )V .70㸪No.4㸪I_721- I_726㸪2014㸬

4) ⚟ᒸᤩ஧㸪Ώ㑔᫂ⱥ㸪ཎ ಇᙪ㸪⛅ᒣṇே㸸Ỉ㠃ᙧࡢ᫬㛫ኚ໬

࡜㠀ᐃᖖ஧ḟඖゎᯒࢆ⏝࠸ࡓὥỈὶ㔞ࣁ࢖ࢻࣟࢢࣛࣇ࡜㈓␃

㔞ࡢ㧗⢭ᗘ᥎⟬,ᅵᮌᏛ఍ㄽᩥ㞟㸪No.761/II-67㸪pp.45-56㸪2004.

5) ෆ⏣㱟ᙪ㸪⚟ᒸᤩ஧: ὸỈὶࡢ௬ᐃࢆ⏝࠸࡞࠸Ỉ῝✚ศࣔࢹ

ࣝ࡟ࡼࡿᗏ㠃ὶ㏿ࡢゎᯒἲ,ỈᕤᏛㄽᩥ㞟ࠊ➨56ᕳ , I_1225- 1230㸪2012.

6) ᒸᮧㄔྖ㸪ᒸ㒊࿴᠇㸪⚟ᒸᤩ஧㸸ὥỈὶࡢ⦪᩿Ỉ㠃ᙧኚ໬࡜

‽୕ḟඖὶゎᯒἲࢆ⏝࠸ࡓ▼⊁ᕝἙཱྀ㒊ࡢὥỈ୰ࡢἙᗋኚື

ゎᯒ㸪Ἑᕝᢏ⾡ㄽᩥ㞟㸪➨16ᕳ㸪pp.125-130㸪2010.

7) ShojiFukuoka and Tatsuhiko Uchida: Toward integrated multi-scale simulations of flow and sediment transport in rivers, Journal of Japan Society of Civil Engineers, Ser.B1 (Hydraulic Engineering), Vol. 69, No. 4, II_1-II_10, 2013.

8) ⏣➃ᖾ㍜,⚟ᒸᤩ஧,ෆ⸨࿴ஂ:ᖹᡂ23ᖺ7᭶㇦㞵࡟ࡼࡿಙ⃰ᕝୗ

ὶᇦࡢὥỈὶୗ≉ᛶ࡜ࡑࡢゎᯒἲ ̿஬༑ᔒᕝ,ส㇂⏣ᕝࡢྜὶ

࡜୰ࣀཱྀᕝࡢศὴࢆྵࡴἙ㐨༊㛫ࢆᑐ㇟࡜ࡋ࡚̿,ᅵᮌᏛ఍ㄽ

ᩥ㞟B1(ỈᕤᏛ)㸪Vol.69㸪No.4I_787-I_792㸪2013.

9) ⚟ᒸᤩ஧:▼♟Ἑᕝࡢ⛣ືᗋỈ⌮ࡢㅖၥ㢟࡜ゎỴ࡬ࡢ㐨➽,Ỉᕤ Ꮫ࡟㛵ࡍࡿኟᏘ◊ಟ఍ㅮ⩏㞟㸪Aࢥ࣮ࢫ 44㸪A-1-1~25㸪2008.

10)㛗⏣೺࿃, ⚟ᒸ ᤩ஧: ▼♟ἙᕝࡢἙᗋኚືᶵᵓ࡜⾲ᒙ▼♟ࡢ

พฝศᕸ࡟╔┠ࡋࡓ஧ḟඖἙᗋኚືゎᯒἲ㸪ᅵᮌᏛ఍ㄽᩥ㞟 B1,Vol. 68, No. 1㸪pp.1-20㸪2012.

11)⚟ᒸᤩ஧㸸ᮐෆᕝࡢἙ㐨ኚ㑄ࢆ⪃៖ࡋࡓ἞Ỉ࡜⎔ቃࡢㄪ࿴ࡋ ࡓᏳᐃ࡞Ἑ㐨⦪࣭ᶓ᩿ᙧ≧࡟㛵ࡍࡿ◊✲㸪໭ᾏ㐨Ἑᕝ㈈ᅋ◊

✲ᡤ⣖せ㸪(XXIV)㸪pp.123-163㸪2014㸬

12)ᚋ⸨ோᚿ㸸ᩘ್ὶ◁Ỉ⌮Ꮫ㸪᳃໭ฟ∧㸪2004㸬

13)⚟⏣ᮅ⏕㸪⚟ᒸᤩ஧㸪ෆ⏣㱟ᙪ㸸Ỉὶ࡟ࡼࡿ▼♟⢏Ꮚ⩌ࡢ⛣ືᶵ ᵓ࡜ࡑࡢࣔࢹࣝ໬㸪ỈᕤᏛㄽᩥ㞟㸪➨56ᕳ㸪I_937-I_942㸪2012.

14)⚟⏣ᮅ⏕㸪⚟ᒸᤩ஧㸪ෆ⏣㱟ᙪ㸸⛣ືᗋᩘ್ᐇ㦂Ỉ㊰ࢆὶୗ

ࡍࡿ▼♟⢏Ꮚ⩌ࡢ୕ḟඖ㐠ື㸪ᅵᮌᏛ఍ㄽᩥ㞟B1(ỈᕤᏛ)㸪 Vol.69㸪No.4㸪I_1051-I_1056㸪2013.

15)⏣ᡤ ᙎ㸪⚟⏣ᮅ⏕㸪⚟ᒸᤩ஧㸸➼౯࡞⢏ᗘศᕸࢆ᭷ࡍࡿ⌫

࡜▼♟࡛ᵓᡂࡉࢀࡿ2ࡘࡢᩘ್⛣ືᗋୖࡢ⢏Ꮚ㐠ືࡢẚ㍑᳨ウ㸪 ᅵᮌᏛ఍ㄽᩥ㞟B1(ỈᕤᏛ) Vol.70, No.4㸪I_961-I_966㸪2014.

16)⚟ᒸᤩ஧㸪ᆏཱྀ㐩ဢ:↓ḟඖὶ㔞࡟ᑐࡍࡿ↓ḟඖἙᖜ࣭Ỉ῝ࡢ

࡜ࡿ⠊ᅖ࡜ᩚഛ㏵ୖἙᕝ࡬ࡢ㐺⏝㸪ỈᕤᏛㄽᩥ㞟 ,➨56ᕳ㸪 I_1423-1428㸪2012 .

㸦ཷ௜㸧

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