ࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲㒊㛛&RPSXWHU$VVLVWHG6FLHQFH5HVHDUFK'LYLVLRQ1 㒊㛛ࢫࢱࢵࣇࢭࣥࢱ࣮ࡀᥦ౪ࡍࡿ᝟ሗฎ⌮ᩍ⫱⛉┠࡟༠ຊࡋ࡚࠸ࡿࠋ⌮Ꮫ㒊ඹ㏻⛉┠࡟࠾࠸࡚ࡣࠊࢧ࢖ࣂ࣮࣓ࢹ࢕࢔ᩍᤵ ᑠ⏣୰ ⤀஧ࢭࣥࢱ࣮࡜⌮Ꮫ㒊࡜ࡀ༠ຊࡋ࡚ࠊ⌮Ꮫ㒊ඹ㏻⛉┠࡜␎Ṕ㸸1978ᖺ3᭶ி㒔኱ᏛᕤᏛ㒊ᩘ⌮ᕤᏛ⛉༞ᴗࠊࡋ࡚ᩘ್ィ⟬ἲᇶ♏ࢆ㛤ㅮࡋ࡚࠸ࡿࠋ

1980ᖺ3᭶ி㒔኱Ꮫ኱Ꮫ㝔ᕤᏛ◊✲⛉༤ኈ๓ᮇㄢ⛬ᩘ⌮ᕤᏛᑓᨷಟ஢ࠋ2000ᖺ4᭶ࡼࡾࠊ኱㜰኱Ꮫ㸯㸬ඹ㏻ᩍ⫱࣭᝟ሗฎ⌮ᩍ⫱⛉┠ࢧ࢖ࣂ࣮࣓ࢹ࢕࢔ࢭࣥࢱ࣮ࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉ゎᯒᏛ A, ᩘᏛ₇⩦ A㸦ᑠ⏣୰ࠊ㝆᪝㸧Ꮫ◊✲㒊㛛ᩍᤵࠋ኱㜰኱Ꮫ኱Ꮫ㝔᝟ሗ⛉Ꮫ◊✲ࢧ࢖ࣂ࣮ࢧ࢖࢚ࣥࢫࡢୡ⏺㸦㝆᪝㸧⛉ࠊ⌮Ꮫ㒊ཬࡧ⌮Ꮫ◊✲⛉ව௵ࠋIEEE(Fellow)ࠊ

㸰㸬⌮Ꮫ㒊ᑓ㛛⛉┠㟁Ꮚ᝟ሗ㏻ಙᏛ఍ࠊᛂ⏝≀⌮Ꮫ఍ࠊ᪥ᮏᩘᏛ఍ྛᩘ್ィ⟬ἲᇶ♏㸦⌮Ꮫ㒊ඹ㏻ ᑠ⏣୰㸧఍ဨࠋᕤᏛ༤ኈ㸦ி㒔኱Ꮫ㸧ࠋᛂ⏝ᩘ⌮Ꮫ 7, ᐇ㦂ᩘᏛ 1㸦ᩘᏛ⛉ 㝆᪝)ㄢ㢟◊✲ a,b㸦ᩘᏛ⛉ ᑠ⏣୰ࠊ㝆᪝)㸱㸬኱Ꮫ㝔⌮Ꮫ◊✲⛉⛉┠෸ᩍᤵ 㝆᪝ ኱௓ᩘ⌮ᕤᏛᴫㄽ㸦ᩘᏛᑓᨷ 㝆᪝㸧␎Ṕ㸸 ᖺ  ᭶ᮾி኱ᏛᕤᏛ㒊≀⌮ᕤᏛ⛉༞ᴗࠊ ᖺ  ᭶ᮾி኱Ꮫ኱Ꮫ㝔ᕤᏛ⣔◊✲⛉≀㸲㸬኱Ꮫ㝔᝟ሗ⛉Ꮫ◊✲⛉⛉┠⌮ᕤᏛᑓᨷಟኈㄢ⛬ಟ஢ࠋྠᖺ  ᭶ᮾி኱Ꮫᕤࢥࣥࣆ࣮ࣗࢱᐇ㦂ᩘᏛ㸦᝟ሗᇶ♏ᩘᏛᑓᨷ 㝆Ꮫ㒊≀⌮ᕤᏛ⛉ຓᡭࢆ⤒࡚ࠊ ᖺ  ᭶ࡼࡾி㒔᪝㸧, ᝟ሗᇶ♏ᩘᏛ◊✲ Ia,Ib㸦᝟ሗᇶ♏ᩘᏛᑓ኱Ꮫᩘ⌮ゎᯒ◊✲ᡤຓᡭࠊ ᖺ  ᭶ࡼࡾ኱㜰኱ᨷ 㝆᪝㸧ࠊIIa,IIb㸦᝟ሗᇶ♏ᩘᏛᑓᨷ ᑠ⏣୰ࠊᏛࢧ࢖ࣂ࣮࣓ࢹ࢕࢔ࢭࣥࢱ࣮ࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉㝆᪝㸧Ꮫ㒊㛛ㅮᖌࠋ ᖺ  ᭶ࡼࡾྠ㒊㛛ຓᩍᤵࠋ኱㜰኱Ꮫ኱Ꮫ㝔᝟ሗ⛉Ꮫ◊✲⛉ࠊ⌮Ꮫ◊✲⛉ව௵ࠋ᪥

3 ◊✲ᴫせᮏᩘᏛ఍ࠊ᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍ ⌮஦ ࠊ᪥ᮏィ⟬ᩘ⌮ᕤᏛ఍ྛ఍ဨࠋ༤ኈ ᕤᏛ ᮾி኱Ꮫ ࠋᆅ⌫⎔ቃࠊ᝟ሗࠊ⏕࿨ࠊࢼࣀࢸࢡࣀࣟࢪ࣮࡞࡝ࡢ⛉Ꮫᢏ⾡ศ㔝࡟࠾࠸࡚ࠊᵝࠎ࡞ᩘ⌮ࣔࢹࣝࡀᒎ㛤ࡋࠊᣍ࡬࠸ᩍဨ࣭◊✲ဨࢥࣥࣆ࣮ࣗࢱࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ㏻ࡋ࡚ࠊࡑࡢ⌮ゎᣍ࡬࠸෸ᩍᤵ ᅜΎ㎮ஓ㸦ࣝࢿࢧࢫ࢚ࣞࢡࢺࣟࢽࢆ῝ࡵࠊ᪂ࡓ࡞▱ぢࢆᚓࡿヨࡳࡀ኱ࡁࡃ㐍ᒎࡋ࡚࠸ࢡࢫ㸧ࡿࠋࡇࡢࡓࡵࠊᩘᏛⓗ࡟ᇶ♏௜ࡅࡽࢀࡓィ⟬ࣔࢹࣝᣍ࡬࠸◊✲ဨ ᓥ⏣▱Ꮚ㸦኱㜰ᡂ㋣኱Ꮫ㸧ࡢᵓ⠏ࡸᩘᏛⓗᡭἲ࡟ࡼࡿࣔࢹࣝ㝵ᒙࢆ᫂ࡽ࠿࡟ࡍࡿࡇ࡜ࡀ┈ࠎ㔜せ࡟࡞ࡗ࡚࠸ࡿࠋࡲࡓࠊࡇࡢࡼ࠺࡞2 ᩍ⫱࠾ࡼࡧᩍ⫱ᨭ᥼ᴗ⦼㐣⛬ࡣࠊ᪂ࡓ࡞ᩘᏛࣔࢹࣝࢆᵓᡂࡋࠊᩘᏛ࣭ᩘ್ゎᯒ࡜ඹ࡟ᩘ್ィ⟬ᡭἲࡸ࢔ࣝࢦࣜࢬ࣒ࢆᵓ⠏ࡍࡿᶵᮏᖺᗘࡣࠊ௨ୗࡢᏛෆㅮ⩏ࢆᢸᙜࡋࡓࠋࢧ࢖ࣂ࣮࣓ࢹ࢕࢔ࢭࣥࢱ࣮࡟࠾ࡅࡿᩍ⫱ཬࡧᩍ⫱ᨭ᥼άື࡜఍࡛ࡶ࠶ࡾࠊ࠸ࢃࡺࡿ͆ᛂ⏝ᩘᏛ͇ࢆⓎᒎࡉࡏࡿᶵ఍࡛ࡶ࠶ࡿࠋࡋ࡚ࠊᤵᴗᨭ᥼ࢩࢫࢸ࣒ CLE ࡸィ⟬ᶵࢆ฼⏝ࡋࡓ⛉ࢥࣥࣆ࣮ࣗࢱᐇ㦂⛉Ꮫ◊✲㒊㛛ࡣࠊ㠀⥺ᙧ೫ᚤศᏛᢏ⾡ィ⟬ᩍ⫱ࢆ㐍ࡵ࡚࠸ࡿࠋඹ㏻ᩍ⫱࡟࠾࠸࡚ࡣࠊ᪉⛬ᘧ࡟ᇶ࡙ࡃᩘ⌮ࣔࢹࣝࡸィ⟬ࣔࢹࣝࡢᵓᡂࢆ୰

― 33 ―ᚰ࡟ࡋ࡚ࠊࢥࣥࣆ࣮ࣗࢱࢩ࣑࣮ࣗࣞࢩࣙࣥࡢ⌮ㄽⓗ⏝࠸ࡽࢀ࡚࠸ࡿࠋࡋ࠿ࡋ࡞ࡀࡽࠊୖ఩ࡢ㝵ᒙ࡟࠶ࡿᇶ♏ࢆ⠏ࡃィ⟬ᩘᏛ࣭ᩘ್ゎᯒࡢ◊✲ࠊࡑࡢᛂ⏝࡜㔞Ꮚὶయ(QHD)ࣔࢹࣝࡸ㔞Ꮚ࢚ࢿࣝࢠ࣮㍺㏦(QET)ࡋ࡚኱つᶍࢥࣥࣆ࣮ࣗࢱࢩ࣑࣮ࣗࣞࢩࣙࣥᢏ⾡࡟㛵ࣔࢹࣝࡢ≀⌮ࣔࢹࣝࡸᩘ್ゎἲࡣ༑ศ࡟ࡣ◊✲ࡉࡍࡿ◊✲ࢆయ⣔ⓗ࡟㐍ࡵ࡚࠸ࡿ◊✲㒊㛛࡛࠶ࡿࠋࢀ࡚࠸࡞࠸ࠋ⌧ᅾࡢ୺࡞◊✲ࢸ࣮࣐ࡣࠊ༙ᑟయ㍺㏦ࡢᩘ⌮ࣔࢹ4-࣓ࣔࣥࢺࣔࢹࣝࢆᇶ♏࡟ࡋࡓ QET ࣔࢹࣝࢆ᪂ࣝ࡟㛵ࡍࡿ◊✲ࠊ㔞Ꮚὶయ᪉⛬ᘧࡢᩘ್ゎᯒ࣭ᩘ್ࡓ࡟ᥦ᱌ࡋࡓࠋ ࡉࡽ࡟ࠊ㔞Ꮚ࢚ࢿࣝࢠ࣮㍺㏦᪉⛬ࢫ࣮࣒࢟࡟㛵ࡍࡿ◊✲ࠊ༙ᑟయࢩ࣑࣮ࣗࣞࢩࣙࣥᡭᘧ࡟ᑐࡍࡿᩘ್ゎἲ㸦཯᚟ゎἲ࡜ᩘ್ࢫ࣮࣒࢟㸧ࡢἲ࡜ࡑࡢᛂ⏝࡟㛵ࡍࡿ◊✲ࠊ೫ᚤศ᪉⛬ᘧࡢಖᏑ࣭◊✲ࢆ㐍ࡵ࡚ࠊ2 ḟඖᩘ್ࢩ࣑࣮ࣗࣞࢩࣙࣥࢆᐇ⌧ᩓ㐓๎ࢆ෌⌧ࡍࡿᩘ್ィ⟬ἲ࡟㛵ࡍࡿ◊✲ࠊኚศཎࡋ࡚࠸ࡿࠋࡇࢀ࡟ࡼࡗ࡚ࠊSi MOSFET ࡔࡅ࡛࡞ࡃࠊ⌮࡟ᇶ࡙ࡃᩘ⌮ࣔࢹࣝ࡟㛵ࡍࡿ◊✲ࠊᩘ್ィ⟬ἲࡢ

22nm ௨㝆ࡢḟୡ௦ࢹࣂ࢖ࢫ࡜ࡋ࡚ᮇᚅࡉࢀ࡚࠸ࡿᏳᐃᛶࢆ⏕࠿ࡋࡓᩘ⌮࢔ࣝࢦࣜࢬ࣒ࡸ୪ิィ⟬࡟㛵Ge MOSFET ෆࡢ࣍ࢵࢺ࢟ࣕࣜ࢔ຠᯝࢆకࡗࡓ㔞Ꮚࡍࡿ࢔ࣝࢦࣜࢬ࣒ࡢ㛤Ⓨ࡛࠶ࡿࠋ㛢ࡌ㎸ࡵ㍺㏦ࢆゎᯒࡋࠊࡑࡢࢹࣂ࢖ࢫ≉ᛶࡢண ࢆ㐍ࡵ࡚࠸ࡿࠋ

4 2012 ᖺᗘ◊✲ᴗ⦼
4.2 ㉮໬ᛶࣔࢹࣝࡢᩘ್ゎἲ࡟㛵ࡍࡿ◊✲
4.1 㔞Ꮚὶయࣔࢹࣝ࡜ᩘ್ゎἲ࡟㛵ࡍࡿ◊✲཯ᛂ⛣ὶᣑᩓ᪉⛬ᘧ⣔࡟ࡼࡗ࡚ࠊ⏕≀⣔࡟࠾ࡅࡿ
Schrödinger ᪉ ⛬ ᘧ ࡢ ὶ య ⾲ ⌧ ࡢ ◊ ✲ ࡣ , Deࣃࢱ࣮ࣥᙧᡂ⌧㇟ࡸ⣽⬊ෆࡢ࢖࢜ࣥࢳࣕࢿࣝ⌧㇟࡞Broglie, Madelung, Bohm ࡽ࡟ࡼࡗ࡚ࡣࡌࡵࡽࢀࠊ

࡝ࢆグ㏙ࡍࡿࡇ࡜ࡀ࡛ࡁࡿࠋ㏆ᖺࠊ㉮໬ᛶࣂࢡࢸࣜ

Schrödinger ᪉⛬ᘧࢆ Madelung ኚ᥮ࡸ Wigner-Wyle࢔ࡢࣃࢱ࣮ࣥᙧᡂࡀᐇ㦂ⓗ࡟ぢฟࡉࢀࠊ⣽⬊ศ⿣࡟ኚ᥮ࡋ࡚ Wigner-Boltzmann ᪉⛬ᘧࢆᑟฟࡋ࡚ࠊ≀ࡼࡿቑṪຠᯝࢆ⤌ࡳධࢀࡓ㉮໬ᛶࣔࢹࣝࡢึᮇ್ቃ⌮࣭໬Ꮫ⌧㇟ࡢࣔࢹࣝ᪉⛬ᘧࡀᑟ࠿ࢀ࡚࠸ࡿࠋ⏺್ၥ㢟࠿ࡽ㉮໬ᛶࣂࢡࢸࣜ࢔ࡢࣃࢱ࣮ࣥᙧᡂࡀ⌮༙ᑟయ࡟࠾ࡅࡿ㔞Ꮚὶయࣔࢹࣝࡶࠊ

ㄽⓗ࡟ཬࡧᩘ್ⓗ࡟◊✲ࡉࢀ࡚࠸ࡿࠋ

Wigner-Boltzmann ᪉⛬ᘧࡢ࣮࣓ࣔࣥࢺᒎ㛤࠿ࡽࠊ㝵ࡑࡢ୰࡛ࠊMimura-Tsujikawa ࣔࢹࣝࡶ཯ᛂ⛣ὶᣑᒙᵓ㐀ࢆࡶࡗࡓࣔࢹࣝ࡜ࡋ࡚ᑟฟࡉࢀࠊྂ඾ⓗὶయᩓ᪉⛬ᘧ⣔࡟ࡼࡗ࡚グ㏙ࡉࢀࠊࡇࡢࣔࢹࣝ࠿ࡽ㉮໬ࣔࢹࣝ࡜ࡢᑐᛂࢆࡶࡗࡓ࣐ࢡࣟࣔࢹࣝࡢ㝵ᒙࡀᙧᛶࣂࢡࢸࣜ࢔ࡢᵝࠎ࡞ࣃࢱ࣮ࣥᙧᡂࡀᑟࡁฟࡉࢀࡿᡂࡉࢀࡿࠋࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿࠋᡃࠎࡣࡇࢀ࡟ᑐࡋࠊ୍⯡ᛶࡢ࠶ࡿ㧗⢭ᗘ࡞ಖᏑࢫ࣮࣒࢟ࢆᥦ᱌ࡋࠊࢢࣜࢵࢻ౫Ꮡᛶࡸ㈇ࡢ⃰ᗘၥ㢟ࡢゎᯒࢆᩘ್ᐇ㦂࡟ࡼࡗ࡚㐍ࡵࠊᥦ᱌ࡋ࡚࠸ࡿᩘ್ࢫ࣮࣒࢟ࡢホ౯ࢆ㐍ࡵ࡚࠸ࡿࠋ
4.3 ೫ᚤศ᪉⛬ᘧࡢಖᏑ࣭ᩓ㐓๎ࢆ෌⌧ࡍࡿᩘ್ィ⟬ἲ࡟㛵ࡍࡿ◊✲ᵝࠎ࡞◊✲ศ㔝࡟࠾࠸࡚㠀⥺ᙧၥ㢟࡟ᑐࡍࡿᩘ್ィ⟬ࡢ㔜せᛶࡣ㧗࠸ࠋᮏ◊✲࡛ࡣ≉࡟㠀⥺ᆺᛶࡀ㔜ࡇࡢ୰࡛ࠊ㔞Ꮚࢻࣜࣇࢺ-ᣑᩓࣔࢹࣝࡣࠊᩘᏛゎせ࡛࠶ࡿࡼ࠺࡞೫ᚤศ᪉⛬ᘧࡢᩘ್ゎἲࡢᵓᡂ࢔ࣝᯒ࡜ᩘ್ゎᯒࡢ୧㠃࠿ࡽ◊✲ࡉࢀࠊ཯᚟ゎἲࡸᩘ್ࢦࣜࢬ࣒࡟ࡘ࠸࡚㛤Ⓨࢆ㐍ࡵ࡚ࡁࡓࠋ㠀⥺ᆺ೫ᚤศࢫ࣮࣒࢟ࡢ㛤Ⓨࡶ㐍ࡵࡽࢀ࡚ࠊྂ඾ࣔࢹࣝ࡜ඹ࡟ࠊ᪉⛬ᘧࡢከࡃࡣ࢚ࢿࣝࢠ࣮ಖᏑᛶࡸ⤌ᡂಖᏑᛶ࡞࡝༙ᑟయ⏘ᴗ⏺ࡢ୰࡛⣲Ꮚタィࣔࢹࣝ࡜ࡋ࡚ᖜᗈࡃࡢಖᏑ๎ࡸᩓ㐓๎ࢆせㄳࡉࢀࡿࡶࡢࡀከ࠸ࡇ࡜࡟╔― 34 ―┠ࡋ Lyapunov 㛵ᩘࢆ㞳ᩓⓗ࡟ᵓᡂࡍࡿ࢔࢖ࢹ࢕࢔

ࡘࠊ᥇⏝ࡋࡓ㈨※ࡢ㡰఩࡛ࡣ࡞ࡃホ౯㛵ᩘࢆホ౯್࡟ᇶ࡙࠸࡚㞳ᩓኚศᑟ㛵ᩘἲ࡜࠸࠺ࢫ࣮࣒࢟ᵓᡂἲᖹᆒ࡜ࡍࡿࡼ࠺࡞ሙྜࡢၥ㢟࡟ᑐࡋ࡚ࡣ◊✲ࡶᑡ࡞ࢆᥦ᱌ࡋࡓࠋࡃࠊ࠿ࡘࠊᩘᏛⓗ࡟᫂ᛌ࡞ุ᩿ᇶ‽ࢆᚓࡿࡇ࡜ࡣ㠀ࡇࡢ㐺⏝⠊ᅖࢆᗈࡆࡿ◊✲ࡢ㐍ᒎ࡟ࡼࡾࠊ
Hamilton ⣔ࢆྵࡴ࢚ࢿࣝࢠ࣮ಖᏑ⣔ࡸ Fujita-typeᖖ࡟ᅔ㞴࡛࠶ࡿࠋࡋ࠿ࡋᐇ⏝ୖࡢၥ㢟ࡣࡇ࠺ࡋࡓᛶ㉁ࢆᣢࡘࡢ࡛࠶ࡿࠋ⇿Ⓨၥ㢟⣔ࠊ⢓⳦ࡢᣲືࢆグ㏙ࡍࡿ Keller-Segel ⣔ࡇࢀ࡟ᑐࡋࠊࢃࢀࢃࢀࡣ௵ព᫬㛫ࡼࡾඛ࡟ᚓࡽࢀ࡞࡝ࡢ㐃❧೫ᚤศ᪉⛬ᘧ⣔ࠊ㠀⥺ᙧ Schroedinger ၥࡿホ౯್ᖹᆒ࡜ࡑࡢ᫬Ⅼ࡛ࡢ㈨※ホ౯್ࢆẚ㍑ࡋ

㢟࡞࡝ࡢ」⣲ၥ㢟➼ࢆࡣࡌࡵࠊ㠀⥺ᆺ㛗Ἴ㛗㏆ఝ᪉࡚ࠊᚋ⪅ࡀୖᅇࡗࡓࡽ᥇⏝ࡍࡿ࡜࠸࠺⮬ᕫ᧐╔ⓗ࢔⛬ᘧ࡜ࡋ࡚㏆ᖺᥦၐࡉࢀࡓ Bao-Feng Feng ᪉⛬ᘧࠊࣝࢦࣜࢬ࣒ࢆᥦ᱌ࡍࡿࠋࡇࢀࡣ㠀ᖖ࡟༢⣧࡞ᩘᏛⓗregularized long wave ᪉⛬ᘧࡸ Camassa-Holm ᪉⛬≧ែ௨እ࡛ࡣᩘᏛⓗ࡞ゎࡣᮃࡵ࡞࠸ࡀࠊࢩ࣑࣮ࣗࣞᘧࠊࣃࢱ࣮ࣥᙧᡂၥ㢟ࡢࣔࢹࣝ᪉⛬ᘧ࡜ࡋ࡚▱ࡽࢀࢩࣙࣥࢆ཯᚟ࡍࡿࡇ࡜࡛ᩘ್ⓗ࡞࢔ࣝࢦࣜࢬ࣒࡜ࡋ

ࡿ Swift-Hohenberg ᪉⛬ᘧࡸ㠀⥺ᙧ Klein- Gordon ᪉࡚ࡣᐇ⿦ྍ⬟࡛࠶ࡾࠊᐇ㝿࡟ࡇࢀࢆᐇ⿦ࡋ࡚ࠋ㠀ᖖ⛬ᘧࠊᣑᙇᆺ Fisher-Kolmogorov ᪉⛬ᘧࠊ࢚ࣝࢦ࣮ࢻ࡟㧗࠸ᛶ⬟࡜ᐇ⏝ᛶࢆࡶࡘࡶࡢ࡛࠶ࡿࡇ࡜ࢆ☜ㄆࡋᛶࢆㄪ࡭ࡿࡓࡵ࡟⏝࠸ࡽࢀࡓ Fermi-Pasta-Ulam ᪉ࡓࠋ⛬ᘧ㸪ࢯࣜࢺࣥࡢᏑᅾᛶࡀၥ㢟࡜࡞ࡗ࡚࠸ࡿ
modified Camassa-Holm ᪉⛬ᘧ࡞࡝ࠊከᒱ࡟Ώࡿၥ㢟

5 ♫఍㈉⊩࡟㛵ࡍࡿᴗ⦼ࡀᮏ᪉ἲㄽࡢᑐ㇟࡜࡞ࡗ࡚࠸ࡿࠋࡲࡓࠊ㠀⥺ᙧᛶࢆィ⟬ୖᙅࡃࡍࡿࡓࡵ࡟ࠊ

5.1. ᩍ⫱㠃࡟࠾ࡅࡿ♫఍㈉⊩5.1.1 Ꮫෆάື

linearization ࡜࿧ࡤࢀࡿ᫬㛫᪉ྥࡢከẁ㝵໬࡟ࡼࡿᡭἲࢆᣑᙇࡋ࡚㞳ᩓኚศᑟ㛵ᩘἲ࡟ᑟධࡍࡿ◊✲ࢆz኱㜰኱Ꮫ࠸ࡕࡻ࠺⚍㒊㛛බ㛤(2012.4.30)ᴾ࠾ࡇ࡞ࡗ࡚࠾ࡾ Cahn-Hilliard ᪉⛬ᘧ࡞࡝࡟㐺⏝ࡋ୍࡚ᐃࡢᡂᯝࢆᚓ࡚࠸ࡿࠋࡑࡋ࡚ࠊࡇࡢከẁ㝵໬࡟

5.2. ◊✲㠃࡟࠾ࡅࡿ♫఍㈉⊩ࡣ୍ᐃࡢ⮬⏤ᗘࡀ࠶ࡿࡀࠊࡇࡢ⮬⏤ᗘࡢタᐃ࡟ࡼࡾ5.2.1 Ꮫ఍άືᩘ್ⓗ࡟Ᏻᐃ࡛࠶ࡿ࠿ࡀ␗࡞ࡗ࡚ࡃࡿࠋࡇࢀ࡟ᑐࡋࠊzᛂ⏝≀⌮Ꮫ఍ࢩࣜࢥࣥࢸࢡࣀࣟࢪ࣮ศ⛉఍,ᖿ஦ḟඖࢆᣑᙇࡋࡓ✵㛫࡛ Lyapunov ᛶࡀ‶ࡓࡉࢀࡿሙྜ࡟ᩘ್Ᏻᐃᛶࡀࡶࡓࡽࡉࢀࡿ࡜ࡢ௬タࢆࡓ࡚ࠊ㒊㸦௨ୖ ᑠ⏣୰㸧ࡢ⣔࡟ࡘ࠸࡚ࡇࢀࢆ᳨ドࡋࡓẁ㝵࡛࠶ࡿࠋz᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍ ⌮஦㸪ࢿࢵࢺ࣮࣡ࢡጤဨ㛗,஦ᴗጤဨ

4.4 ᫬㛫ไ⣙ୗ࡛ࡢ☜⋡ⓗ⛎᭩ၥ㢟࡟ᑐࡍࡿᐇ⏝ⓗ㸦௨ୖ 㝆᪝㸧࡞࢔ࣝࢦࣜࢬ࣒
5.3 ⏘Ꮫ㐃ᦠ᫬㛫ࢆ࠾࠸࡚㞳ᩓⓗ࡟ᚓࡽࢀࡿ㈨※ೃ⿵ิ࡟ᑐ

(1) ヱᙜ࡞ࡋࡋࠊ࡝ࡢࡼ࠺࡞ᇶ‽࡛᥇⏝Ỵᐃࢆୗࡍ࠿࡜࠸࠺ᡓ␎࡟㛵ࡍࡿၥ㢟ࡣྂࡃ࠿ࡽ⛎᭩ၥ㢟ࠊ⤖፧ၥ㢟࡞࡝࡜

5.4 ◊✲ࣉࣟࢪ࢙ࢡࢺάື

ࡼࡤࢀࠊᩘᏛⓗ࡟ࡶᐇ⏝ୖࡶ㔜せ࡞ၥ㢟࡛࠶ࡿࠋ⌧ᅾࠊ௨ୗࡢ◊✲ࣉࣟࢪ࢙ࢡࢺ࡟ཧ⏬ࡋ࡚࠸ࡿࠋ᫬㛫࡟ไ⣙ࡀ࡞ࡃࠊ㈨※ೃ⿵せ⣲ࡢ㡰఩࡟ࡋ࠿╔(1) ᩥ 㒊 ⛉ Ꮫ ┬  ⛉ Ꮫ ◊ ✲ ㈝ ⿵ ຓ 㔠 ᇶ ┙ ◊ ✲┠ࡋ࡞࠸ࡶࡗ࡜ࡶ⣲ᮔ࡞ၥ㢟౛࡞࡝࡟ࡘ࠸࡚ࡣከࡃ(B)“࢚ࢿࣝࢠ࣮ᩓ㐓ⓗ㠀⥺ᙧಖᏑ๎ࡢゎࡢ᫬㛫ࡢ◊✲࡟ࡼࡾᩘᏛⓗ࡟᫂ᛌ࡞⤖ㄽࡀ࠸ࡃࡘ࠿ᚓࡽࢀ

኱ᇦᵓ㐀”㸦ᖹᡂ 23㹼26 ᖺᗘ㸧㐃ᦠ࡚࠸ࡿࡀࠊ᥇⏝ࡲ࡛ࡢ᫬㛫࡟ไ⣙ࡀ࠶ࡾࠊ㈨※ࡢᛶ㸦௨ୖ ᑠ⏣୰㸧㉁ࠊホ౯್ࡀ㐃⥆ⓗ࡛☜⋡ⓗ࡟ศᕸࡍࡿ≧ែ࡛ࠊ࠿(2) ᩥ㒊⛉Ꮫ┬ ⛉Ꮫ◊✲㈝⿵ຓ㔠ᣮᡓⓗⴌⱆ “㠀― 35 ―ᵓ㐀໬࣓ࢵࢩࣗୖࡢ࣎ࣟࣀ࢖᱁Ꮚᕪศ࡟ࡼࡿᵓ

schemes with weak nonlinearity based on discrete㐀ಖᏑᩘ್ゎἲ” (ᖹᡂ 23㹼25 ᖺᗘ) ௦⾲variational derivative method", International(3) ᩥ 㒊 ⛉ Ꮫ ┬  ⛉ Ꮫ ◊ ✲ ㈝ ⿵ ຓ 㔠 ᇶ ┙ ◊ ✲conference of numerical analysis and appliedmathematcs, Kos, 2012.

(B)“᭷㝈య✚ἲࡢᩘᏛⓗᇶ┙⌮ㄽࡢ☜❧” (ᖹᡂ(4) D.Furihata, "Design to construct weakly nonlinear

23㹼26 ᖺᗘ)ศᢸ

schemes in structure preserving context", 2013(4) ᩥ㒊⛉Ꮫ┬ ⛉Ꮫ◊✲㈝⿵ຓ㔠 ᣮᡓⓗⴌⱆ "࣋ࢡࢺ್ࣝⓎᒎ᪉⛬ᘧ࡟ᑐࡍࡿᗄఱᵓ㐀ᆺᩘ್ゎ

Tokyo Workshop on Structure-Preserving Methods,ἲ" (ᖹᡂ 24㹼26 ᖺᗘ)ศᢸ

Tokyo, 2013.

(5) ᩥ㒊⛉Ꮫ┬ ⛉Ꮫ◊✲㈝⿵ຓ㔠 ᇶ┙◊✲(B)“ᖹᆒሙ᪉⛬ᘧ࡛グ㏙ࡉࢀࡿ㠀⥺ᙧ⮫⏺⌧㇟ࡢゎᯒⓗ◊✲” (ᖹᡂ 20㹼24 ᖺᗘ) 㐃ᦠཱྀ㢌Ⓨ⾲㸦ᅜෆ◊✲఍࡞࡝㸧(௨ୖ 㝆᪝)(1) 㙂 ⳡᘅ, ᑠ⏣୰ ⤀஧, “༙ᑟయ࡟࠾ࡅࡿ㔞Ꮚ࢚ࢿࣝࢠ࣮㍺㏦ࣔࢹࣝࡢࡓࡵࡢᩘ್ࢫ࣮࣒࢟࡜཯

5.5 ࡑࡢ௚ࡢάື᚟ ゎ ἲ ”, ᪥ ᮏ ᛂ ⏝ ᩘ ⌮ Ꮫ ఍ ᖺ ఍ ㅮ ₇ ண ✏ 㞟 ,5.5.1 ఍㆟㐠Ⴀ(1)InternationalConference

onSimulation

pp.357-358, 2012 ᖺ 9 ᭶.

ofSemiconductor Processes and Devicesࠊ2011 ᖺ 9 ᭶ 8(2) 㙂 ⳡᘅ, ᑠ⏣୰ ⤀஧, “༙ᑟయ࡟࠾ࡅࡿ㔞Ꮚ࢚ࢿࣝࢠ࣮㍺㏦ࣔࢹࣝࡢᩘ್ࢩ࣑࣮ࣗࣞࢩࣙࣥ”,᪥-10 ᪥᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍ᖺ఍, 2012 ᖺ 9 ᭶.

(2) 2013 Tokyo Workshop on Structure-Preserving(3) 㙂 ⳡᘅ, ᑠ⏣୰ ⤀஧, “ᚤ⣽ MOSFET ࡢ㟁ᏊMethods, Tokyo University, 2013 ᖺ 1 ᭶ 8 ᪥㍺㏦ࢩ࣑࣮ࣗࣞࢩࣙࣥࡢࡓࡵࡢ㔞Ꮚὶయࣔࢹࣝ,ᛂ⏝≀⌮Ꮫ఍ 2013 ᖺᗘᖺ఍, 2013 ᖺ 3 ᭶.
 ᖺᗘ◊✲Ⓨ⾲ㄽᩥ୍ぴ(4) 㝆᪝ ኱௓, "ၥ㢟ࡢ㠀⥺ᙧᛶࢆᙅࡵࡿ㞳ᩓኚศࢫᏛ⾡ㄽᩥㄅ࣮࣒࢟ࡢᵓᡂ", ᪥ᮏᛂ⏝ᩘ⌮Ꮫ఍ᖺ఍, ⛶ෆ,(1) 66KR DQG 62GDQDND ͆$ TXDQWXP HQHUJ\2012 ᖺ 8 ᭶.

WUDQVSRUW PRGHO IRU VHPLFRQGXFWRU GHYLFH

ゎㄝࡑࡢ௚VLPXODWLRQV͇ -RXUQDO RI &RPSXWDWLRQDO

(1) ᑠ⏣୰ ⤀஧, “ࢫ࣮ࣃ࣮ࢥࣥࣆ࣮ࣗࢱ࡜༙ᑟయ”,3K\VLFV, 235(2013), 486-496.

Cybermedia HPC Journal, No.2, pp.3-6, 2012.

ᅜ㝿఍㆟఍㆟㘓 D. Furihata and T. Matsuo, “Weakly nonlinear ᖺᗘ≉ู◊✲ሗ࿌࣭ಟኈㄽᩥ࣭༤ኈㄽᩥ

structure preserving schemes for strongly nonlinear
partialdifferentialCongressonequations”,

ComputationalInternationalandApplied༤ኈㄽᩥ㸦࡞ࡋ㸧Mathematics, Gent, 2012.
(2) T. Matsuo and D. Furihata, "A note on thestabilization of multistep linearly-implicit schemesಟኈㄽᩥ ᯘ ර㤿 ᐃᖖ࡞༙ᑟయ᪉⛬ᘧ⣔࡟࠾ࡅࡿ⦰ᑠ

for dissipative systems", International Congress on෗ീࡢᵓᡂ࡜ホ౯

Computational and Applied Mathematics, Gent, 㔝ᮧ࿴ྐ⛎᭩ၥ㢟ࡢ୍ࡘࡢุ᩿ᇶ‽ࡢᥦ᱌2012.

 ⚟ᮏ㝧඾▱ぬ᝟ሗࡢ⢒ど໬࡟ࡼࡿຠ⋡ⓗ࡞ᙉ(3) D. Furihata, "A new technique to design numerical໬Ꮫ⩦― 36 ―