6. 6
方法
モデル:曲面上の進行波
• 反応拡散方程式による進行波
[Nishiura et al. 2005]
u
t = u(1 u)(u a) v
+ d u
v
t = u v
ut = Du u
uv2
1 + f2w
+ f0(1 u)
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<latexit sha1_base64="SA7s6ep9iKDOvb1duLdOG0V9290=">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</latexit>
<latexit sha1_base64="SA7s6ep9iKDOvb1duLdOG0V9290=">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</latexit>
vt = Dv v
uv2
1 + f2w
+ (f0 + f1)v
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<latexit sha1_base64="0WqknVjBpeJpC1HA2mtH3R++UuY=">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</latexit>
<latexit sha1_base64="0WqknVjBpeJpC1HA2mtH3R++UuY=">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</latexit>
⌧wt = Dw w + f3(v w)
<latexit sha1_base64="PCqLYI4GLg7yTcZwNV0p9s5w7tk=">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</latexit>
<latexit sha1_base64="PCqLYI4GLg7yTcZwNV0p9s5w7tk=">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</latexit>
<latexit sha1_base64="PCqLYI4GLg7yTcZwNV0p9s5w7tk=">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</latexit>
<latexit sha1_base64="PCqLYI4GLg7yTcZwNV0p9s5w7tk=">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</latexit>
d2
xi
dt2
+ i
jk
dxj
dt
dxk
dt
= 0
i
jk =
1
2
gil glj
xk
+
glk
xj
gjk
xl
:Position(i=1,2)
xi
gil
• 測地線方程式(曲面上の最短経路)
:Metric tensor
Christoffel symbols of the second kind
Geodesic equation
3変数のGray-Scott型
ガウス関数