ARMSによる化学反応のシミュレーション
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- さや みやのじょう
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1 Brusselator BrusselatorMulti Multi-set ARMSAbstruct Rewriting Multiset System BZ BrusselatorARMS Belousov-Zhabotinsky BZ Belousov-Zhabotinsky BZ B.P.Belousov 1951 A.M.Zhabotinsky Belousov 2 Belousov-Zhabotinsky 1
2 Fe Prigogine Brusselator Brusselator k1 A X k2 B + X Y + D k3 2X + Y 3X k4 X E AB XY DE AB AB CSTR dx = k1 A k 2 BX + k3 X dt dy 2 = k 2 BX k3 X Y dt 2 Y k 4 X ARMS 2
3 ARMS(Abstract Rewriting Multiset System) ARMS Abstract Rewriting System(ARS) Abstract Rewriting System ARS a Sa [Abstract Rewriting System] ARS ( A, R) A R A b A a A A a b a b Abstract Rewriting System normal form() [Normal Form] a b b a A normal form() abstract rewriting model Ru = { 2 2 4,4 2 8} Ru Ru
4 normal form normal form normal form ARMS ARS ARMSabstract rewriting system on multi-setsarms A k = { a, b, L, } φ Multi-set S S [Multi-set] k Multi-set n t A ( 1 k n) A k k A 1 K Ak A = A 1 A 2 L Ak Multi-set n Multi-set Multi-set Multi-set ARMS [] lrr( l, r ) l, r Multiset, n lrr l r a akb heating rule r < 0 4
5 akc b cooling rule r > 0 ARMS] Abstract Rewriting System on Multi-sets Multi-setT Ru ARMS ] ( T, Ru) ARMS l s t = ( s l) r l r Ru Ru s t ARMS φ a [Normal Form in ARMS] Ru Multi-set Multi-set Multi-set Normal Form Normal Form ARMS ARMS aaa b : r 1 b a : r2 b c : r3 a bb : r4 { r4 r1 r3 r2 } {aaa} Multi-set 5
6 {aaa} a bb : r4 Multi-set {aaa} aaa b : r1 Multi-set {b} Multi-set Brusselator ARMS ARMS Brusselator Brusselator k1 A X k2 B + X Y + D k3 2X + Y 3X k4 X E ARMS A X : r B + X Y + D : r 2X 1 + Y 3X X E : r 4 : r 3 2 6
7 k1k4 Multi-set AB CSTR(continuously-fed stirred tank reactor) CSTR Brusselator Brusselator Brusselator Y Y X,Y X Y 'CX10-4.dat' 'CY10-4.dat'
8 'CX20-19.dat' 'CY20-19.dat' 'CX15-20.dat' 'CY15-20.dat' Y X Y ARMS Brusselator r1 が r2 より非常に大きい r1 が r2 よりわずかに大きい r1 が r2 よりわずかに小さい r1 が r2 より非常に小さい 収束安定振動不安定振動発散 8
9 2 1 r X r 'CX30-10.dat' 'CY30-10.dat' X Y B X Y A AB X Y X Y Y r 3 X Y X 4 r 4 X 3 Brusselator ARMS ARMS ARMS 9
10 ARMS ARMS ARMS CD AB XYC 1 ARMS CSTR 10
11 ARMS ARMS Y Y Y XXY X Y 'CX34.dat' 'CY34.dat' 'CX34.dat' 'CY34.dat' X Y X Y XY Y X 150 'CX61.dat' 'CY61.dat'
12 X Y X Y 'CX53.dat' 'CY53.dat' X Y 'CX52.dat' 'CY52.dat' 'CX52.dat' 'CY52.dat' Y 12
13 Suzuki,Y. and H.Tanaka 1997.Chemical oscillation on cymbolic chemical system and its behavioral patern. In Proceedings of the International Conference on Complex System,Nashua,NH,21-26 Sept Suzuki,Y and H.Tanaka Order Parameter for a Symbolic Chemical System,Alife,MIT press(in press) (2000) 13
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