did you apply bc's on the complementary solution at the 32:22? Cause Ycompl= c1+c2e^(-s), where s is your strange X. The bc's can only be applied to the whole solution of Y=Ycompl+Yparticular
Asymptotic boundary matching is very useful in plasma physics, e.g. fusion, to understand evolution of instabilities. The outer region can be governed by a set of equations different from the inner region. Richard Fitzpatrick (UT Austin) has some helpful literature about this.
I suspect the poorly simplified function at 49:30 is partly because Mathematica is assuming that epsilon could still be negative or complex. I don't have the program, but I suspect if you tried FullSimplify[f[x], Assumptions -> {epsilon > 0}] You'll get something cleaner?
when you try to determine B, do you use that the boundary layer is of order epsilon, i.e. if it were of order epsilon^{1/2}, would I look for O(x^2, epsilon) terms?
It's 3:00 am and I am here learning perturbation theory. This course is amazing. Thanks for sharing.
So important to share when an expert reaches an unfamiliar or mysterious feeling area. Vital for less experienced folks to see.
did you apply bc's on the complementary solution at the 32:22? Cause Ycompl= c1+c2e^(-s), where s is your strange X. The bc's can only be applied to the whole solution of Y=Ycompl+Yparticular
Asymptotic boundary matching is very useful in plasma physics, e.g. fusion, to understand evolution of instabilities. The outer region can be governed by a set of equations different from the inner region. Richard Fitzpatrick (UT Austin) has some helpful literature about this.
working on tearing modes right now actually!
I suspect the poorly simplified function at 49:30 is partly because Mathematica is assuming that epsilon could still be negative or complex. I don't have the program, but I suspect if you tried
FullSimplify[f[x], Assumptions -> {epsilon > 0}]
You'll get something cleaner?
The other part is that Mathematica is still limited in its ability to present things usefully.
I tried but the result was the same.
when you try to determine B, do you use that the boundary layer is of order epsilon, i.e. if it were of order epsilon^{1/2}, would I look for O(x^2, epsilon) terms?
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