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A random vibration problem
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Steady state heat flow with source
Looking for the temperature distribution in a steady state problem (i.e. the time derivative is not relevant once the system reaches steady state)
My given equation and boundary values were
$$ u_t = 3u_{xx} + 8, u(0, t) = -4, u(1, t) = 6 $$
when $ u_t = 0 $ the sytem is steady state, then solving for $u_{xx} $gives $ u_{xx} = \frac{8}{3} $
anti-differentiating twice gives the general solution $ u(x) = \frac{8}{3}x^2 + ax + b $
Then, using the boundary values:
$$ u(x) = \frac{4}{3}x^2 + \frac{26}{3}x - 4 $$
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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 = [
[0,1,3,2,4],
[2,0,2,2,2],
[3,1,0,1,3],
[4,4,3,0,3],
[2,4,4,4,0]
]
Team 5: rating = 0.5369571232846212 Team 4: rating = 0.5349109263288253 Team 1: rating = 0.4288594144453331 Team 3: rating = 0.35096444755792117 Team 2: rating = 0.34416697668415475
Team 5 was the best, followed very closely by team 4.