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A random vibration problem
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Steady state heat flow with source
Heat flow with a constant internal heat source is governed by
$$u_t = 2u_{xx} + 8, u(0,t) = 1, u(1,t) = 7.$$
Find the steady state temperature distribution.
The steady state distribution is when $u_t = 0.$ I solved the given equation for $u_t = 0,$ which gives me the value of $u_{xx} = u''(x) = -4.$ I then antidifferentiated this expression twice to get a general solution for $u,$ and I plugged the boundary conditions into this general solution to get the steady state solution of $u(x) = -2x^2 + 8x + 1.$
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Random heat evolution problem
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Modeling 2D Heat Flow
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Eigenranking
My matrix is:
matrix = [
[0,3,4,1,3],
[4,0,1,3,4],
[4,3,0,4,4],
[4,1,4,0,2],
[2,4,3,4,0],
]
The ranking for my league is below. Team 3 is the highest ranked in the league.
Team 3: rating = 0.5176519293474793 Team 5: rating = 0.4613383888892107 Team 2: rating = 0.4237581736661745 Team 1: rating = 0.41451885767177027 Team 4: rating = 0.4096419141952378
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Modeling a steady state heat distribution in 2D