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1 㒊㛛ࢫࢱࢵࣇ

2 ᩍ⫱࣭◊✲ᴫせᩍᤵ ᑠ⏣୰ ⤀஧

2.1 ᩍ⫱ࡢᴫせ␎Ṕ㸸1978ᖺ3᭶ி㒔኱ᏛᕤᏛ㒊ᩘ⌮ᕤᏛ⛉༞ᴗࠊࢧ࢖ࣂ࣮࣓ࢹ࢕࢔ࢭࣥࢱ࣮࡟࠾ࡅࡿᩍ⫱ཬࡧᩍ⫱

1980ᖺ3᭶ி㒔኱Ꮫ኱Ꮫ㝔ᕤᏛ◊✲⛉༤ኈ๓ᮇㄢᨭ᥼άື࡜ࡋ࡚ࠊᤵᴗᨭ᥼ࢩࢫࢸ࣒ CLE ࡸィ⟬ᶵࢆ⛬ᩘ⌮ᕤᏛᑓᨷಟ஢ࠋ2000ᖺ4᭶ࡼࡾࠊ኱㜰኱Ꮫ฼⏝ࡋࡓ⛉Ꮫᢏ⾡ィ⟬ᩍ⫱ࢆ㐍ࡵ࡚࠸ࡿࠋඹ㏻ᩍ⫱ࢧ࢖ࣂ࣮࣓ࢹ࢕࢔ࢭࣥࢱ࣮ࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉࡟࠾࠸࡚ࡣࠊࢭࣥࢱ࣮ࡀᥦ౪ࡍࡿ᝟ሗฎ⌮ᩍ⫱⛉┠Ꮫ◊✲㒊㛛ᩍᤵࠋ኱㜰኱Ꮫ኱Ꮫ㝔᝟ሗ⛉Ꮫ◊✲⛉ࠊ㸦ࢧ࢖ࣂ࣮ࢧ࢖࢚ࣥࢫࡢୡ⏺㸧࡟༠ຊࡋ࡚࠸ࡿࠋ⌮⌮Ꮫ㒊ཬࡧ⌮Ꮫ◊✲⛉ව௵ࠋIEEE(Fellow)ࠊ㟁ᏊᏛ㒊ඹ㏻⛉┠࡟࠾࠸࡚ࡣࠊࢧ࢖ࣂ࣮࣓ࢹ࢕࢔ࢭࣥࢱ᝟ሗ㏻ಙᏛ఍ࠊᛂ⏝≀⌮Ꮫ఍ࠊ᪥ᮏᩘᏛ఍ྛ఍ဨࠋ࣮࡜⌮Ꮫ㒊࡜ࡀ༠ຊࡋ࡚ࠊ⌮Ꮫ㒊ඹ㏻⛉┠࡜ࡋ࡚ᩘᕤᏛ༤ኈ㸦ி㒔኱Ꮫ㸧ࠋ್ィ⟬ἲᇶ♏ࢆ㛤ㅮࡋ࡚࠸ࡿࠋࡲࡓࠊ⌮Ꮫ㒊ᩘᏛ⛉࡟࠾ࡅࡿィ⟬ᶵᩍ⫱ࢆᨭ᥼ࡋ࡚࠸ࡿࠋ2013 ᖺᗘࡣࠊ௨ୗࡢᏛෆㅮ⩏ࢆᢸᙜࡋࡓࠋ෸ᩍᤵ 㝆᪝ ኱௓␎Ṕ㸸1990 ᖺ 3 ᭶ᮾி኱ᏛᕤᏛ㒊≀⌮ᕤᏛ⛉༞ᴗࠊ1992 ᖺ 3 ᭶ᮾி኱Ꮫ኱Ꮫ㝔ᕤᏛ⣔◊✲⛉≀㸯㸬ඹ㏻ᩍ⫱࣭᝟ሗฎ⌮ᩍ⫱⛉┠⌮ᕤᏛᑓᨷಟኈㄢ⛬ಟ஢ࠋྠᖺ 4 ᭶ᮾி኱ᏛᕤゎᯒᏛ A, ᩘᏛ₇⩦ A (ᑠ⏣୰, 㝆᪝)Ꮫ㒊≀⌮ᕤᏛ⛉ຓᡭࢆ⤒࡚ࠊ1997 ᖺ 4 ᭶ࡼࡾி㒔኱ࢧ࢖ࣂ࣮ࢧ࢖࢚ࣥࢫࡢୡ⏺ (㝆᪝)Ꮫᩘ⌮ゎᯒ◊✲ᡤຓᡭࠊ2001 ᖺ 4 ᭶ࡼࡾ኱㜰኱Ꮫࢧ㸰㸬⌮Ꮫ㒊ᑓ㛛⛉┠࢖ࣂ࣮࣓ࢹ࢕࢔ࢭࣥࢱ࣮ࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ㒊㛛ᩘ್ィ⟬ἲᇶ♏ (⌮Ꮫ㒊ඹ㏻㸪ᑠ⏣୰)ㅮᖌࠋ2002 ᖺ 4 ᭶ࡼࡾྠ㒊㛛ຓᩍᤵࠋ኱㜰኱Ꮫ኱Ꮫᛂ⏝ᩘ⌮Ꮫ 7, ᐇ㦂ᩘᏛ 1(ᩘᏛ⛉㸪㝆᪝)㝔᝟ሗ⛉Ꮫ◊✲⛉ࠊ⌮Ꮫ◊✲⛉ව௵ࠋ᪥ᮏᩘᏛ఍ࠊㄢ㢟◊✲ a,b(ᩘᏛ⛉, 㝆᪝)᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍(⌮஦)ࠊ᪥ᮏィ⟬ᩘ⌮ᕤᏛ఍ྛ఍㸱㸬኱Ꮫ㝔⌮Ꮫ◊✲⛉⛉┠
ᩘ⌮ᕤᏛᴫㄽ (ᩘᏛᑓᨷ, 㝆᪝)ဨࠋ༤ኈ(ᕤᏛ)(ᮾி኱Ꮫ)ࠋ

㸲㸬኱Ꮫ㝔᝟ሗ⛉Ꮫ◊✲⛉⛉┠
ᣍ࡬࠸ᩍဨ࣭◊✲ဨࢥࣥࣆ࣮ࣗࢱᐇ㦂ᩘᏛ(᝟ሗᇶ♏ᩘᏛᑓᨷ㸪㝆ᣍ࡬࠸ᩍᤵ ▼ᕝΎᚿ 㸦ࣝࢿࢧࢫ࢚ࣞࢡࢺࣟࢽࢡ᪝), ᝟ሗᇶ♏ᩘᏛ◊✲ Ia,Ib(᝟ሗᇶ♏ᩘᏛᑓᨷ㸪ࢫ㸦ᰴ㸧㸧ᑠ⏣୰, 㝆᪝), IIa,IIb(᝟ሗᇶ♏ᩘᏛᑓᨷ 㝆ᣍ࡬࠸ᩍᤵ ௒ᮧಇᖾ 㸦⊂❧⾜ᨻἲே⌮໬Ꮫ◊✲᪝)ᡤィ⟬⛉Ꮫ◊✲ᶵᵓ㸧ᣍ࡬࠸෸ᩍᤵ ᅜΎ㎮ஓ㸦ࣝࢿࢧࢫ࢚ࣞࢡࢺࣟࢽࢡ

2.2 ◊✲ࡢᴫせᆅ⌫⎔ቃࠊ᝟ሗࠊ⏕࿨ࠊࢼࣀࢸࢡࣀࣟࢪ࣮࡞࡝ࡢࢫ㸦ᰴ㸧㸧⛉Ꮫᢏ⾡ศ㔝࡟࠾࠸࡚ࠊᵝࠎ࡞ᩘ⌮ࣔࢹࣝࡀᒎ㛤ࡋࠊࢥࣥࣆ࣮ࣗࢱࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ㏻ࡋ࡚ࠊࡑࡢ⌮ゎࢆ῝ࡵࠊ᪂ࡓ࡞▱ぢࢆᚓࡿヨࡳࡀ኱ࡁࡃ㐍ᒎࡋ࡚࠸ࡿࠋࡇࡢࡓࡵࠊᩘᏛⓗ࡟ᇶ♏௜ࡅࡽࢀࡓィ⟬ࣔࢹࣝ－ 31 －ࡢᵓ⠏ࡸᩘᏛⓗᡭἲ࡟ࡼࡿࣔࢹࣝ㝵ᒙࢆ᫂ࡽ࠿࡟ࡍᨭ᥼ࢆ᥎㐍ࡍࡿࡇ࡜࡟ࡼࡗ࡚ࠊᙜ㒊㛛࡜௻ᴗ࡜ࡢඹࡿࡇ࡜ࡀ┈ࠎ㔜せ࡟࡞ࡗ࡚࠸ࡿࠋࡲࡓࠊࡇࡢࡼ࠺࡞

ྠ◊✲ࢸ࣮࣐(኱つᶍ࣭኱㡿ᇦ༙ᑟయࢹࣂ࢖ࢫࢩ࣑ࣗ㐣⛬ࡣࠊ᪂ࡓ࡞ᩘᏛࣔࢹࣝࢆᵓᡂࡋࠊᩘᏛ࣭ᩘ್ゎ࣮ࣞࢩࣙࣥࡢ◊✲)ࡀᖹᡂ㸰㸴ᖺᗘ JHPCN ◊✲ㄢ㢟ᯒ࡜ඹ࡟ᩘ್ィ⟬ᡭἲࡸ࢔ࣝࢦࣜࢬ࣒ࢆᵓ⠏ࡍࡿᶵ࡟᥇ᢥࡉࢀࡓࠋࡉࡽ࡟ࠊඹ㏻ᴗົ࡜ࡋ࡚௨ୗࡢጤဨ఍࡟ཧ⏬ࡋࡓࠋ఍࡛ࡶ࠶ࡾࠊ࠸ࢃࡺࡿ͆ᛂ⏝ᩘᏛ͇ࢆⓎᒎࡉࡏࡿᶵ ࣭㧗ᛶ⬟ィ⟬ᶵጤဨ఍㸦ᑠ⏣୰㸧఍࡛ࡶ࠶ࡿࠋࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲㒊㛛ࡣࠊ㠀⥺ᙧ೫ᚤศ ࣭ᗈሗጤဨ఍㸦㝆᪝㸧᪉⛬ᘧ࡟ᇶ࡙ࡃᩘ⌮ࣔࢹࣝࡸィ⟬ࣔࢹࣝࡢᵓᡂࢆ୰ᚰ࡟ࡋ࡚ࠊࢥࣥࣆ࣮ࣗࢱࢩ࣑࣮ࣗࣞࢩࣙࣥࡢ⌮ㄽⓗ4 2013 ᖺᗘ◊✲ᴗ⦼ᇶ♏ࢆ⠏ࡃィ⟬ᩘᏛ࣭ᩘ್ゎᯒࡢ◊✲ࠊࡑࡢᛂ⏝࡜ࡋ࡚኱つᶍࢥࣥࣆ࣮ࣗࢱࢩ࣑࣮ࣗࣞࢩࣙࣥᢏ⾡࡟㛵

4.1 㔞Ꮚ࢚ࢿࣝࢠ࣮㍺㏦ࣔࢹࣝ࡟ࡼࡿඛ➃ MOSFETࡍࡿ◊✲ࢆయ⣔ⓗ࡟㐍ࡵ࡚࠸ࡿ◊✲㒊㛛࡛࠶ࡿࠋࢩ࣑࣮ࣗࣞࢩࣙࣥࡢ◊✲2013ᖺᗘࡢ୺࡞◊✲ࢸ࣮࣐ࡣࠊ༙ᑟయ㍺㏦ࡢᩘ⌮ࣔࢹࣝ࡟㛵ࡍࡿ◊✲ࠊ㔞Ꮚὶయ᪉⛬ᘧࡸ཯ᛂ⛣ὶᣑ

Wigner-Boltzmann ᪉⛬ᘧࡢ࣮࣓ࣔࣥࢺᒎ㛤࠿ࡽ㔞ᩓ᪉⛬ᘧࡢᩘ್ゎᯒ࣭ᩘ್ࢫ࣮࣒࢟࡟㛵ࡍࡿ◊✲ࠊᏊὶయࣔࢹࣝࡀᑟฟࡉࢀࠊྂ඾ⓗὶయࣔࢹࣝ࡜ࡢᑐ༙ᑟయࢩ࣑࣮ࣗࣞࢩࣙࣥᡭἲ࡜ࡑࡢᛂ⏝࡟㛵ࡍࡿ◊ᛂࢆࡶࡗࡓ࣐ࢡࣟࣔࢹࣝࡢ㝵ᒙࡀᙧᡂࡉࢀࡿࠋ✲ࠊ೫ᚤศ᪉⛬ᘧࡢಖᏑ࣭ᩓ㐓๎ࢆ෌⌧ࡍࡿᩘ್ィࡇࡢ୰࡛ࠊୖ఩ࡢ㝵ᒙ࡟࠶ࡿ㔞Ꮚὶయ(QHD)ࣔࢹ⟬ἲ࡟㛵ࡍࡿ◊✲ࠊኚศཎ⌮࡟ᇶ࡙ࡃᩘ⌮ࣔࢹࣝ࡟ࣝࡢᣑᩓ㏆ఝ࠿ࡽ㔞Ꮚ࢚ࢿࣝࢠ࣮㍺㏦(QET)ࣔࢹࣝ

㛵ࡍࡿ◊✲ࠊᩘ್ィ⟬ἲࡢᏳᐃᛶࢆ⏕࠿ࡋࡓᩘ⌮࢔ࢆ㛤Ⓨࡋࠊ㔞Ꮚ㛢ࡌ㎸ࡵ㍺㏦࡜ඹ࡟࣍ࢵࢺ࢟ࣕࣜ࢔ࣝࢦࣜࢬ࣒ࡢ㛤Ⓨ࡛࠶ࡿࠋࡲࡓࠊ୪ิィ⟬࡟㛵ࡍࡿຠᯝࡀࣔࢹࣜࣥࢢ࡛ࡁࡿ≀⌮ࣔࢹࣝࢆᵓᡂࡋࡓࠋࡉ࢔ࣝࢦࣜࢬ࣒ࡢ㛤Ⓨࡸホ౯ࡶ㐍ࡵ࡚࠸ࡿࠋࡽ࡟ࠊ㏆ᖺ㛤Ⓨࡀ㐍ࡴⷧ⭷ MOSFET ᵓ㐀࡟ᑐᛂࡍࡿࡓࡵࠊ4-࣓ࣔࣥࢺࣔࢹࣝࢆᇶ♏࡟ࡋࡓ QET ࣔࢹࣝࢆ3 ᩍ⫱࣭◊✲➼࡟ಀࡿ඲Ꮫᨭ᥼᪂ࡓ࡟ᥦ᱌ࡋࡓࠋ
ࡇࢀ࡟ࡼࡗ࡚ࠊSi MOSFET ࡔࡅ࡛࡞ࡃࠊ17nm ୡᙜ㒊㛛ࡣࠊ඲Ꮫᨭ᥼ᴗົ࡜ࡋ࡚ࢫ࣮ࣃ࣮ࢥࣥࣆࣗ௦௨㝆ࡢḟୡ௦ࢹࣂ࢖ࢫ࡜ࡋ࡚ᮇᚅࡉࢀ࡚࠸ࡿ㧗⛣࣮ࢱ฼⏝⪅ᨭ᥼ࢆ⾜ࡗ࡚࠸ࡿࠋ2013 ᖺᗘࡣࠊᨭ᥼άື ᗘ ᮦ ᩱ ࡢ ࢳ ࣕ ࢿ ࣝ ࢆ ᭷ ࡍ ࡿ Ge ࡸ InGaAsືࡢᙉ໬ࡢࡓࡵ࡟ࠊࢫ࣮ࣃ࣮ࢥࣥࣆ࣮ࣗࢱ฼⏝⪅ᨭ

MOSFET ෆࡢ࣍ࢵࢺ࢟ࣕࣜ࢔ຠᯝࢆకࡗࡓ㔞Ꮚ㛢᥼ WG ࢆ᪂ࡓ࡟❧ࡕୖࡆࡓࠋࡇࡢ୰࡛ࠊᙜ㒊㛛ࡣࠊࡌ㎸ࡵ㍺㏦ࢆゎᯒࡋࠊࡑࡢࢹࣂ࢖ࢫ≉ᛶࡢணࢫ࣮ࣃ࣮ࢥࣥࣆ࣮ࣗࢱࡢ௻ᴗ฼⏝᥎㐍ࢆྵࡴ฼⏝⪅ࡵࡓࠋࡉࡽ࡟ࠊ࣐ࣝࢳࢤ࣮ࢺ MOSFET ᵓ㐀࡟࠾࠸࡚ࠊᨭ᥼ࠊㅮ⩦఍ࡢ㛤ദ௻⏬ཬࡧㅮ⩦఍ࡢᐇ᪋㸦㝆᪝ᢸSi ࢳࣕࢿࣝ࡜㧗⛣ືᗘᮦᩱࢳࣕࢿࣝࡢ≉ᛶࢆẚ㍑ゎᙜ㸸ࢫࣃࢥࣥ࡟㏻ࡌࡿ୪ิࣉࣟࢢ࣑ࣛࣥࢢࡢᇶ♏,ᯒࡋࡓࠋࢆ㐍2013 ᖺ 6 ᭶ 27 ᪥, ୪ิィ⟬ධ㛛, 2013 ᖺ 9 ᭶ 3 ᪥㸧ࠊࢫ࣮ࣃ࣮ࢥࣥࣆ࣮ࣗࢱ஦ᴗ࣮࣒࣮࣍࣌ࢪࡢ඲㠃ᨵಟࠊ

4.2 ㉮໬ᛶࣔࢹࣝࡢᩘ್ゎἲ࡟㛵ࡍࡿ◊✲㧗ᰯ⏕ࡢࢫ࣮ࣃ࣮ࢥࣥࣆ࣮ࣗࢸ࢕ࣥࢢࢥࣥࢸࢫࢺ㛤཯ᛂ⛣ὶᣑᩓ᪉⛬ᘧ⣔࡟ࡼࡗ࡚ࠊ⏕≀⣔࡟࠾ࡅࡿദ࡟㛵ࡍࡿᨭ᥼ࢆ⾜ࡗࡓࠋࡲࡓࠊ㠉᪂ⓗࣁ࢖ࣃ࣮ࣇ࢛࣮࣐ࣥࢫ࣭ࢥࣥࣆ࣮ࣗࣃࢱ࣮ࣥᙧᡂ⌧㇟ࡸ⣽⬊ෆࡢ࢖࢜ࣥࢳࣕࢿࣝ⌧㇟࡞ࢸ࢕ࣥࢢ࣭࢖ࣥࣇࣛ㸦HPCI㸧άືࠊࠕࢿࢵࢺ࣮࣡ࢡ

࡝ࢆグ㏙ࡍࡿࡇ࡜ࡀ࡛ࡁࡿࠋ㏆ᖺࠊ㉮໬ᛶࣂࢡࢸࣜᆺࠖᏛ㝿኱つᶍ᝟ሗᇶ┙ඹྠ฼⏝࣭ඹྠ◊✲ᣐⅬ࢔ࡢࣃࢱ࣮ࣥᙧᡂࡀᐇ㦂ⓗ࡟ぢฟࡉࢀࠊ⣽⬊ศ⿣࡟

㸦JHPCN㸧άືࠊ⚄ᡞ኱Ꮫ༠ᐃㅮᗙࠕ኱つᶍᩘ್ࢩࡼࡿቑṪຠᯝࢆ⤌ࡳධࢀࡓ㉮໬ᛶࣔࢹࣝࡢึᮇ್ቃ

࣑࣮ࣗࣞࢩࣙࣥ≉ㄽࠖ࡟༠ຊࡋ࡚࠸ࡿࠋJHPCN άື⏺್ၥ㢟࠿ࡽ㉮໬ᛶࣂࢡࢸࣜ࢔ࡢࣃࢱ࣮ࣥᙧᡂࡀᩘ

－ 32 －⾜࡞࠸ࠊࡉࡽ࡟ࡇࢀࢆண ᏊಟṇᏊἲࡢணᏛⓗ࡟ཬࡧᩘ್ゎᯒⓗ࡟◊✲ࡉࢀ࡚࠸ࡿࠋ

Ꮚ࡜ࡋࡑࡢ୰࡛ࠊMimura-Tsujikawa ࣔࢹࣝࡶ཯ᛂ⛣ὶᣑ࡚⏝࠸ࡿゎἲ࡟ࡼࡾࠊᵓ㐀ࢆಖᏑࡋࡘࡘ㧗㏿࡟ィ⟬ᩓ᪉⛬ᘧ⣔࡟ࡼࡗ࡚グ㏙ࡉࢀࠊࡇࡢࣔࢹࣝ࠿ࡽ㉮໬ࢆྍ⬟࡜ࡋࡓࠋࡇࢀࢆ㧗ḟ Cahn-Hilliard ᪉⛬ᘧ࡟ᛶࣂࢡࢸࣜ࢔ࡢᵝࠎ࡞ࣃࢱ࣮ࣥᙧᡂࡀᑟࡁฟࡉࢀࡿ㐺⏝ࡋࠊ⌮ㄽ㏻ࡾࡢ⤖ᯝࢆᚓ࡚࠸ࡿࠋࡲࡓࠊࡇࡢከࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿࠋᡃࠎࡣ㉮໬ᛶ⌧㇟ࢆࣔࢹࣝ໬ẁ㝵໬࡟ࡣ୍ᐃࡢ⮬⏤ᗘࡀ࠶ࡿࡀࠊࡇࡢ⮬⏤ᗘࡢタࡍࡿ⛣ὶ࣭ᣑᩓ࣭཯ᛂ᪉⛬ᘧࡢ㞳ᩓ໬࡟ᑐࡋ࡚ࠊ᭷ᐃ࡟ࡼࡾᩘ್ⓗ࡟Ᏻᐃ࡛࠶ࡿ࠿ࡀ␗࡞ࡗ࡚ࡃࡿࠋࡇ㝈య✚ἲ࡟࠾ࡅࡿ 6FKDUIHWWHU*XPPHO ᆺࣇࣛࢵࢡࢀ࡟ᑐࡋࠊḟඖࢆᣑᙇࡋࡓ✵㛫࡛ Lyapunov ᛶࡀ‶ࢫࡀᵓᡂ࡛ࡁࡿࡇ࡜ࢆ♧ࡋࠊᩘ್ࢫ࣮࣒࢟ࡢ㧗⢭ᗘࡓࡉࢀࡿሙྜ࡟ᩘ್Ᏻᐃᛶࡀࡶࡓࡽࡉࢀࡿ࡜ࡢ௬ㄝ

໬ࡸ㈇ࡢ⃰ᗘၥ㢟ࡢᅇ㑊ࢆᩘ್ᐇ㦂࡟ࡼࡗ᳨࡚ドࡋࠊࢆࡓ࡚ࠊ୍㒊ࡢ⣔࡟ࡘ࠸࡚ࡇࢀࢆ᳨ドࡋࡓࠋࡲࡓࠊᖖᚤศ᪉⛬ᘧࡢ࢚ࢿࣝࢠ࣮ࢆಖᏑࡍࡿゎἲ㛤Ⓨࡋࡓᩘ್ࢫ࣮࣒࢟ࡢඃ఩ᛶࢆ♧ࡋࡓࠋ࡜ࡋ࡚ᥦ᱌ࡉࢀࡓ Greenspan ࡢ➨஧ゎἲࢆ೫ᚤศ᪉
4.3 ೫ᚤศ᪉⛬ᘧࡢಖᏑ࣭ᩓ㐓๎ࢆ෌⌧ࡍࡿᩘ್ィ⛬ᘧ࡟ᣑᙇࡍࡿ◊✲ࡶ⾜ࡗࡓࠋᐇ౛࡜ࡋ࡚ࡇࢀࢆ⟬ἲ࡟㛵ࡍࡿ◊✲

Korteweg-de Vries ᪉⛬ᘧ࡟㐺⏝ࡋࠊⰋዲ࡞⤖ᯝࢆᚓࡓࠋࡇࡢゎἲ࡟ࡘ࠸࡚ࡣ」ᩘࡢಖᏑ㔞ࢆྠ᫬࡟ಖᏑᵝࠎ࡞◊✲ศ㔝࡟࠾࠸࡚㠀⥺ᙧၥ㢟࡟ᑐࡍࡿᩘ್ィ⟬ࡢ㔜せᛶࡣ㧗࠸ࠋᮏ◊✲࡛ࡣ≉࡟㠀⥺ᆺᛶࡀ㔜࡛ࡁࡿྍ⬟ᛶࡀぢ㎸ࡲࢀࡿࡓࡵࠊࡉࡽ࡞ࡿ◊✲ࢆ㐍ࡵࡿணᐃ࡛࠶ࡿࠋ

せ࡛࠶ࡿࡼ࠺࡞೫ᚤศ᪉⛬ᘧࡢᩘ್ゎἲࡢᵓᡂ࢔ࣝ
ࢦࣜࢬ࣒࡟ࡘ࠸࡚㛤Ⓨࢆ㐍ࡵ࡚ࡁࡓࠋ㠀⥺ᆺ೫ᚤศ

4.4 ᏶඲ᚤศᙧ࡟⮳ࡽ࡞࠸≧ἣ࡬ࡢ✚ศᅉᏊἲᣑᙇ᪉⛬ᘧࡢከࡃࡣ࢚ࢿࣝࢠ࣮ಖᏑᛶࡸ⤌ᡂಖᏑᛶ࡞࡝ࡢಖᏑ๎ࡸᩓ㐓๎ࢆせㄳࡉࢀࡿࡶࡢࡀከ࠸ࡇ࡜࡟╔ᖖᚤศ᪉⛬ᘧࡢᩘ್ゎἲ࡜ࡋ࡚ྂࡃ࠿ࡽ▱ࡽࢀࡿ┠ࡋ Lyapunov 㛵ᩘࢆ㞳ᩓⓗ࡟ᵓᡂࡍࡿ࢔࢖ࢹ࢕࢔✚ศᅉᏊἲࡣࠊᖖᚤศ᪉⛬ᘧ࡟㐺ษ࡞㛵ᩘࢆ᥃ࡅࡿ࡟ᇶ࡙࠸࡚㞳ᩓኚศᑟ㛵ᩘἲ࡜࠸࠺ࢫ࣮࣒࢟ᵓᡂἲࡇ࡜࡟ࡼࡾ᏶඲ᚤศᙧ࡟ኚᙧࡋࠊࡇࡢ᏶඲ᚤศᙧࡼࢆᥦ᱌ࡋࡓࠋࡾᩘ್ゎࢆィ⟬ࡍࡿ᪉ἲ࡛࠶ࡿࠋ᏶඲ᚤศᙧࡣ㛵ᩘࡇࡢ㐺⏝⠊ᅖࢆᗈࡆࡿ◊✲ࡢ㐍ᒎ࡟ࡼࡾࠊゎᯒⓗ࡟ࡣཝᐦゎࡀồࡲࡗࡓ≧ែ࡛࠶ࡿࡢ࡛ࠊᩘ್

Hamilton ⣔ࢆྵࡴ࢚ࢿࣝࢠ࣮ಖᏑ⣔ࡸ Fujita-typeゎἲ࡜ࡋ࡚ࡣඖࡢᖖᚤศ᪉⛬ᘧࢆ┤᥋ゎࡃࡼࡾࡶᮏ⇿Ⓨၥ㢟⣔ࠊ⢓⳦ࡢᣲືࢆグ㏙ࡍࡿ Keller-Segel ⣔㉁ⓗ࡟ᐜ࡛᫆࠶ࡾࠊィ⟬㔞ࡶㄗᕪࡶῶᑡࡏࡋࡵࡿࡇ࡞࡝ࡢ㐃❧೫ᚤศ᪉⛬ᘧ⣔ࠊ㠀⥺ᙧ Schroedinger ၥ࡜ࢆᮇᚅ࡛ࡁࡿࠋࡋ࠿ࡋࠊ≉ᐃࡢᙧᘧࡢᖖᚤศ᪉⛬㢟࡞࡝ࡢ」⣲ၥ㢟➼ࢆࡣࡌࡵࠊ㠀⥺ᆺ㛗Ἴ㛗㏆ఝ᪉ᘧࢆ㝖ࡅࡤ᏶඲ᚤศᙧ࡟⮳ࡿࡇ࡜⮬㌟ࡀᅔ㞴࡛࠶ࡾࠊ⛬ᘧ࡜ࡋ࡚㏆ᖺᥦၐࡉࢀࡓ Bao-Feng Feng ᪉⛬ᘧࠊ✚ศᅉᏊἲࡣ࠸ࢃࡤࠕ࡛ࡁࡓࡽ⣲ᬕࡽࡋ࠸ࡀ㏻ᖖࡣ

regularized long wave ᪉⛬ᘧࡸ Camassa-Holm ᪉⛬㐺⏝࡛ࡁ࡞࠸ࠖゎἲ࡛࠶ࡿࠋࡇࢀ࡟ᑐࡋࠊ✚ศᅉᏊᘧࠊࣃࢱ࣮ࣥᙧᡂၥ㢟ࡢࣔࢹࣝ᪉⛬ᘧ࡜ࡋ࡚▱ࡽࢀἲࡢኚᙧ㐣⛬ࢆ୎ᑀ࡟⪃ᐹࡍࡿࡇ࡜࡟ࡼࡗ࡚ࠊ᏶඲

ࡿ Swift-Hohenberg ᪉⛬ᘧࡸ㠀⥺ᙧ Klein- Gordon ᪉ᚤศᙧ࡟⮳ࡽࡎ࡜ࡶࡑࡢ㏵୰ࡢᙧᘧ࠿ࡽᩘ್ィ⟬ࢆ⛬ᘧࠊᣑᙇᆺ Fisher-Kolmogorov ᪉⛬ᘧࠊ࢚ࣝࢦ࣮ࢻ

⾜࠺ࡇ࡜࡟ࡼࡗ࡚ᩘ್ィ⟬ୖࡢ฼Ⅼࢆᚓࡽࢀ࡞࠸࠿

ᛶࢆㄪ࡭ࡿࡓࡵ࡟⏝࠸ࡽࢀࡓ Fermi-Pasta-Ulam ᪉࡜࠸࠺ࡢࡀࡇࡢ◊✲࡛࠶ࡿࠋࡇࡢ࢔࢖ࢹ࢕࢔࡟ᇶ࡙⛬ᘧ㸪ࢯࣜࢺࣥࡢᏑᅾᛶࡀၥ㢟࡜࡞ࡗ࡚࠸ࡿ

ࡁࠊ30 ௨ୖࡢࢣ࣮ࢫ࡟࠾࠸࡚ᐇ㝿࡟ィ⟬ࢆ⾜࠸ࠊከ

modified Camassa-Holm ᪉⛬ᘧ࡞࡝ࠊከᒱ࡟Ώࡿၥ㢟ࡃࡢሙྜ࡟࠾࠸࡚ࡇࡢ╔┠Ⅼࡀṇࡋ࠸ࡇ࡜ࡀᙉࡃᮇࡀᮏ᪉ἲㄽࡢᑐ㇟࡜࡞ࡗ࡚࠸ࡿࠋᚅ࡛ࡁࡿ⤖ᯝࢆᚓࡓࠋࡉࡽ࡟ࡇࡢ᪉ἲࡢ⌮ㄽⓗഃ㠃ࡲࡓࠊィ⟬࡟࠾ࡅࡿ㠀⥺ᙧᛶࢆᙅࡃࡍࡿࡓࡵ࡟

ࢆ㏣ồࡍࡿⓎᒎࡀぢ㎸ࡲࢀࡿࠋ

linearization ࡜࿧ࡤࢀࡿ᫬㛫᪉ྥࡢከẁ㝵໬࡟ࡼࡿᡭἲࢆᣑᙇࡋ࡚㞳ᩓኚศᑟ㛵ᩘἲ࡟ᑟධࡍࡿ◊✲ࢆ－ 33 －

5 ♫఍㈉⊩࡟㛵ࡍࡿᴗ⦼✲ຓᡂᇶ㔠ຓᡂ㔠 ᇶ┙◊✲(B) “㞳ᩓ㛵ᩘゎᯒ࡜ኚศ⌮ㄽ࠿ࡽ࡞ࡿᕪศἲࡢᇶ♏⌮ㄽᵓ⠏” (ᖹ5.1. ᩍ⫱㠃࡟࠾ࡅࡿ♫఍㈉⊩ᡂ 25㹼29 ᖺᗘ) ௦⾲

5.1.1 Ꮫෆάືz(௨ୖ 㝆᪝)኱㜰኱Ꮫ࠸ࡕࡻ࠺⚍㒊㛛බ㛤(2013ᖺ5᭶3᪥)ᴾ
5.5 ࡑࡢ௚ࡢάື

5.1.2 ௚኱Ꮫ㠀ᖖ໅ㅮᖌ➼z⚄ᡞ኱Ꮫ༠ᐃㅮᗙࠕ኱つᶍᩘ್ࢩ࣑࣮ࣗࣞࢩࣙ

5.5.1 ఍㆟㐠Ⴀࣥ≉ㄽࠖ, ⚄ᡞ኱Ꮫ, 2013ᖺ7᭶24,25᪥㸦ᑠ⏣୰ࠊ(1) The Fourth Workshop on Computer-Assisted Science(➨ 4 ᅇࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲఍), ኱㜰኱Ꮫ,㝆᪝㸧ᴾ2014 ᖺ 2 ᭶ 17 ᪥.
5.2. ◊✲㠃࡟࠾ࡅࡿ♫఍㈉⊩5.2.1 Ꮫ఍άື ᖺᗘ◊✲Ⓨ⾲ㄽᩥ୍ぴz

IEEE SISPAD, Chair, Steering Committeezᛂ⏝≀⌮Ꮫ఍ࢩࣜࢥࣥࢸࢡࣀࣟࢪ࣮ศ⛉఍, ᖿᏛ⾡ㄽᩥㄅ஦(1) T. Matsuo, and D. Furihata, ”A stabilization of㸦௨ୖ ᑠ⏣୰㸧

multistep linearly implicit schemes for dissipativez᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍ ࢿࢵࢺ࣮࣡ࢡጤဨ, ஦ᴗጤsystems,” J. Comput. Appl. Math., 264(2014),

ဨpp.38-48.

㸦௨ୖ 㝆᪝㸧ᅜ㝿఍㆟఍㆟㘓 S.Sho, S.Odanaka, and A.Hiroki, “Analysis of5.3 ⏘Ꮫ㐃ᦠcarrier transport in Si and Ge MOSFETs includingヱᙜ࡞ࡋquantum confinement and hot carrier effects”,
Proceedings of 16th International Workshop on

5.4 ◊✲ࣉࣟࢪ࢙ࢡࢺάື

Computational Electronics, pp.160-161, Nara, 2013.

⌧ᅾࠊ௨ୗࡢ◊✲ࣉࣟࢪ࢙ࢡࢺ࡟ཧ⏬ࡋ࡚࠸ࡿࠋ

(2) Daisuke Furihata, An attempt to design a fast andstructure preserving scheme for the Feng equation,(1) ᩥ 㒊 ⛉ Ꮫ ┬  ⛉ Ꮫ ◊ ✲ ㈝ ⿵ ຓ 㔠 ᇶ ┙ ◊ ✲The Third International Conference: Nonlinear(B)“࢚ࢿࣝࢠ࣮ᩓ㐓ⓗ㠀⥺ᙧಖᏑ๎ࡢゎࡢ᫬㛫Waves -Theory and Applications, Beijing, China

኱ᇦᵓ㐀”(ᖹᡂ 23㹼26 ᖺᗘ)㐃ᦠ(2013 June 12--15).

㸦௨ୖ ᑠ⏣୰㸧(2) ᩥ㒊⛉Ꮫ┬ ⛉Ꮫ◊✲㈝⿵ຓ㔠ᣮᡓⓗⴌⱆ “㠀(3) Daisuke Furihata, An attempt to create fast
numerical schemes with the discrete variationalᵓ㐀໬࣓ࢵࢩࣗୖࡢ࣎ࣟࣀ࢖᱁Ꮚᕪศ࡟ࡼࡿᵓ

derivative method, Equadiff13, Prague, Czecho㐀ಖᏑᩘ್ゎἲ” (ᖹᡂ 23㹼25 ᖺᗘ) ௦⾲(3) ᩥ 㒊 ⛉ Ꮫ ┬  ⛉ Ꮫ ◊ ✲ ㈝ ⿵ ຓ 㔠 ᇶ ┙ ◊ ✲(B)“᭷㝈య✚ἲࡢᩘᏛⓗᇶ┙⌮ㄽࡢ☜❧” (ᖹᡂ(2013 Aug. 26--30).
 Daisuke Furihata, An iteration method for thenumerical solution of the discrete variational23㹼26 ᖺᗘ)ศᢸ

derivative schemes, Czech-Japanese Seminar in(4) ᩥ㒊⛉Ꮫ┬ ⛉Ꮫ◊✲㈝⿵ຓ㔠 ᣮᡓⓗⴌⱆ "࣋

Applied Mathematics 2013, Meiji university (2013ࢡࢺ್ࣝⓎᒎ᪉⛬ᘧ࡟ᑐࡍࡿᗄఱᵓ㐀ᆺᩘ್ゎἲ" (ᖹᡂ 24㹼26 ᖺᗘ)ศᢸ
(5) ᪥ᮏᏛ⾡᣺⯆఍ ⛉Ꮫ◊✲㈝⿵ຓ㔠ཬࡧᏛ⾡◊

Sep. 5--8).
(5) Daisuke Furihata, Predictor corrector algorithm with－ 34 －thediscretevariational

derivativemethod,

International Conference on Scientific Computationᩘ୙➼ᘧ࡟ࡘ࠸࡚, ឡ፾኱Ꮫゎᯒࢭ࣑ࢼ࣮, ឡ፾and Differential Equations, Valladolid, Spain (2013኱Ꮫ, 2013 ᖺ 6 ᭶.

Sep. 16--20).

(12) .㝆⡡ ኱௓, ᙅ㠀⥺ᙧ㞳ᩓኚศᑟ㛵ᩘࢫ࣮࣒࢟࡟ࡘ࠸࡚, ᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍ 2013 ᖺᗘᖺ఍, ⚟ᒸ2013 ᖺ 9 ᭶.

ཱྀ㢌Ⓨ⾲㸦ᅜෆ◊✲఍࡞࡝㸧(13) 㝆⡡ ኱௓, ࣎ࣟࣀ࢖࣓ࢵࢩࣗ --᭷㝈య✚ἲ࡟㐺ࡋࡓ✵㛫㞳ᩓ໬ἲ--, ᮾி኱Ꮫᩘ್ゎᯒࢭ࣑ࢼ࣮

(1) ᮧୖ೺ኴ, ᑠ⏣୰⤀஧, 㙂ⳡᘅ, “㉮໬ᛶ⌧㇟ࢆࣔࢹࣝ໬ࡍࡿ⛣ὶ࣭ᣑᩓ࣭཯ᛂ᪉⛬ᘧ࡟ᑐࡍࡿ㧗⢭ᗘ࡞㠀⥺ᙧࢫ࣮࣒࢟”, ᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍ᖺ఍ㅮ

(UTNAS), ᮾி኱Ꮫ, ᮾி㸪2013 ᖺ 11 ᭶.
(14) 㝆⡡ ኱௓, ᵓ㐀ಖᏑᩘ್ゎἲධ㛛 --㞳ᩓኚศᑟ㛵ᩘἲ--, ᛂ⏝ᩘᏛຮᙉ఍, Ⱚᾆᕤᴗ኱Ꮫ, ࡉ࠸₇ண✏㞟, pp.301-302, 2013 ᖺ 9 ᭶.
(2) 㙂 ⳡᘅ, ᑠ⏣୰⤀஧, “㔞Ꮚ࢚ࢿࣝࢠ࣮㍺㏦ࣔࢹࣝࢆ⏝࠸ࡓඛ➃ MOSFET ࢩ࣑࣮ࣗࣞࢩࣙࣥ,” ᛂࡓࡲᕷ, 2013 ᖺ 12 ᭶.
(15) 㝆⡡ ኱௓, 㠀ᑐ⛠ศゎ࡟ᇶ࡙ࡃ㞳ᩓኚศᑟ㛵ᩘἲࡢ⦆࿴, ໭ᾏ㐨኱Ꮫ MMC ࢭ࣑ࢼ࣮, ໭ᾏ㐨኱⏝≀⌮Ꮫ఍ศ⛉఍ࠕࣉࣟࢭࢫ࣭ࢹࣂ࢖ࢫ࣭ᅇ㊰ࢩ࣑࣮ࣗࣞࢩࣙࣥ࠾ࡼࡧ୍⯡ࠖ, pp.32-37, 2013 ᖺ 11᭶.

Ꮫ㟁Ꮚ◊, ᮐᖠᕷ, 2014 ᖺ 1 ᭶.
(16) 㝆⡡ ኱௓, 㠀⥺ᙧ೫ᚤศ᪉⛬ᘧ࡟ᑐࡍࡿᵓ㐀ಖᏑゎἲࡢ㧗㏿໬ࡢヨࡳ, ᖖᚤศ᪉⛬ᘧࡢᩘ್ゎ(3) 㙂 ⳡᘅ, ᑠ⏣୰⤀஧, “༙ᑟయ࡟࠾ࡅࡿ㔞Ꮚ࢚ࢿἲ࡜ࡑࡢ࿘㎶ 2014, 㟼ᒸ⌮ᕤ⛉኱Ꮫ, 㟼ᒸ┴⿄஭ࣝࢠ࣮㍺㏦ࣔࢹࣝࡢࡓࡵࡢᩘ್ィ⟬”, ➨㸲ᅇࢥᕷ, 2014 ᖺ 3 ᭶.

ࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲఍, 2014 ᖺ 2 ᭶.
(4) 㙂 ⳡᘅ, “㔞Ꮚ࢚ࢿࣝࢠ࣮㍺㏦ࣔࢹࣝࢆ⏝࠸ࡓゎㄝࡑࡢ௚

Si ࡜㧗⛣ືᗘᮦᩱࢆࡶࡘ MOSFET ࡢࢩ࣑࣮ࣗࣞヱᙜ࡞ࡋࢩࣙࣥ◊✲”, ᛂ⏝≀⌮Ꮫ఍㛵すᨭ㒊ࢭ࣑ࢼ࣮ࠕ༙

ᑟయࢹࣂ࢖ࢫ࡟࠾ࡅࡿ㟁Ꮚ⇕㍺㏦ࡢ≀⌮ࠖ, 2014
ᖺ 3 ᭶.
(5) 㔝ᮧ ࿴ྐ, “⛎᭩ၥ㢟ࡢ೵Ṇつ๎ࡢ཯᚟ᨵၿἲ”,᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍ 2014 ᖺᖺ఍, ⚟ᒸ, 2013 ᖺ 9 ᭶.
(6) 㔝ᮧ ࿴ྐ, “୍⯡໬ࡋࡓ⛎᭩ၥ㢟ࡢ཯᚟ᩘ್ゎ ᖺᗘ≉ู◊✲ሗ࿌࣭ಟኈㄽᩥ࣭༤ኈㄽᩥ༤ኈㄽᩥ(1) S.Sho, “A study of a quantum energy-transportmodel for semiconductorsࠊ”Ph.D. Thesis, Graduateἲ”, ᛂ⏝ᩘᏛྜྠ◊✲㞟఍, 㱟㇂኱Ꮫ, 2013 ᖺ 12

School of Information Science and Technology,᭶.

Osaka University, March 2014.

(7) 㔝ᮧ ࿴ྐ, "୍⯡໬ࡋࡓ⛎᭩ၥ㢟ࡢ཯᚟ᩘ್ゎἲ", ➨ 4 ᅇࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲఍, 2014 ᖺ 2᭶.
(8) ㏆⸨ Ⰻ௓, "Greenspan ࡢ᪉ἲࡢ೫ᚤศ᪉⛬ᘧ࡬ಟኈㄽᩥ(1) ㏆⸨ Ⰻ௓䠄᝟ሗ⛉Ꮫ䠅, Greenspan 䛾᪉ἲ䛾೫ᚤศ᪉⛬ᘧ䜈䛾ᣑᙇ, Feb. 2014.

ࡢᣑᙇ", ➨ 4 ᅇࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲఍,2014 ᖺ 2 ᭶.

(2) ⾜⃝ ⩧ኴ䠄᝟ሗ⛉Ꮫ䠅, ✚ศᅉᏊἲ䛾୍⯡໬, Feb.

(9) ⛅ᒣ ඲அ㍜, "㞳ᩓኚศᑟ㛵ᩘἲ࡟ࡘ࠸࡚", ➨ 4ᅇࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲఍, 2014 ᖺ 2 ᭶.
(10) ⾜⃝ ⩧ኴ, "✚ศᅉᏊἲࡢ୍⯡໬", ➨ 4 ᅇࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲఍, 2014 ᖺ 2 ᭶.
(11) 㝆⡡ ኱௓(኱㜰኱Ꮫ), 㞳ᩓኚศᑟ㛵ᩘἲ࠾ࡼࡧࡑࡢ⥺ᙧ໬࡜㸪ࡑࡢゎᯒ࡟࠶ࡽࢃࢀࡿ㞳ᩓⓗ࡞㛵－ 35 －2014.