Comments
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My matrix is: matrix = [ [0,4,2,1,4], [4,0,2,3,1], [3,1,0,3,2], [1,1,1,0,4], [4,4,1,2,0] ] Team 1: rating = 0.5079982820145703 Team 5: rating = 0.5032938392103756 Team 2: rating = 0.4485785148338271 Team 3: rating = 0.4101302319490532 Team 4: rating = 0.34525869395863085 That means Team 1 was the best but doesn't look like…
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For our conditions, $k=0$ and $f=0$, the steady-state of this polygon is shown above. The temperature in the lower right corner, at about $(31,1)$, is approximately $.96731.$
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Given my parameters, the temperature near the midpoint of the insulated side of the triangle at $t=1s$ is about $0.52492$.
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We will look at a bar of length $1$ that lies along the unit interval. Its temperature distribution is given by: $$g(x)=3x^2 - 2x.$$ At time t=0, its left end is set to temperature 3 and its right end to -2. Here is the sketch of the temperature distribution at times $t=0, t=0.01, t=0.1$, and $t=10.$
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We will look at heat flow with a constant internal heat source. This will be governed by, $$u_t=4{u_xx}+8.$$ Such that we have the initial conditions, $u(0,t)=-3$ and $u(1,t)=3.$ Given that we are looking for a steady-state distribution, we can set $u_t=0,$ such that $u(x,t)$ does not change with respect to time, $t.$…
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The displacement of the midpoint from the equilibrium at time, $t = 1.1,$ is approximately $-0.616.$