pcatut 5472 presentation
TRANSCRIPT
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Pyroclastic flows Montserrat
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dAdt
=A
t+ v
A = F(A,A)
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= (1 r2)
m = (x)2
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AI(r) =
A(r)W(r r, h)dr
A(r) =
A(r)(r r)dr
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limh0
W(r, h) = (r)
W(r, h)dr = 1
W(r, h) =er
2/h2
h33/2
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A(r)
(r
)
W(r r, h)(r)dr b
mbAb
b
W(r rb)
A(r) =
b
mbAb
b
W(r rb)
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(r
) =b
mbW(r rb, h
)
(r)dr =
b
mb
W(r, h)dr =b
mb
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As(r)
b
mbAb
b
W(r rb)
As(r)
b
mbAb
b
W(r rb)
A = 1((A)A)
(A)a =1
a
mbb
b(Ab Aa)W(ra rb, h)
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d
dt= v
d
dt=
( (v) v )
d
dt
=
a
a
b
mbb
b
(vb va) Wab
d
dt
a
= a
b
mb
b
vab aWab
= 1
aWab = rabFab
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mbvab
rabFab
ddta
=b
mbvab aWab
=
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AI(x) =
A(x)W(x x, h)dx
AI(x) =
A(x) + (x x)dA/dx +
1
2(x x)2d2A/dx2 + ......
W(xx)dx
O(h2)d2A/dx2
AI(x) = A(x) +1
2h2d2A/dx2 + ...
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M1(q) = 1
M1(q) = 0
M2(q) = 1 q
M2(q) = 0
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M4(q) =2
3 q2 +
1
2q3
M4(q) =1
6(2 q)
3
M4(q) = 0
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A =
hK(W(0, h) + 2W(, h) + 2W(2, h) + ....)
h =
h = 1.2
h = 1.5
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0 1 2-2
-1
0
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