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Jan
23
answered Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?
Jan
22
comment Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?
@Narasimham: Sounds like a good idea. And with ybeltukov's code, you can now try it! Let me know if you find anything interesting :)
Jan
22
comment How do I add custom deviation when using LinearModelFit?
LinearModelFit doesn't support NormFunction, but maybe you can get what you want using the Weights option. From the documentation: "With the setting Weights -> {w1, w2, ...}, the error variance for $y_i$ is assumed to be $\sigma^2/w_i$. By default, unit weights are used."
Jan
22
comment Long running ToElementMesh with very “large” domains
That should be x^2 + y^2 <= r^2 in your ImplicitRegion. But also, see my comment on the question.
Jan
22
comment Long running ToElementMesh with very “large” domains
I get all timings between 0.1 and 0.2 seconds on your code. Maybe a system-dependent issue? I have Mathematica 10.0.1.0 on Mac OS X Yosemite. (Also your copy-pasted result seems to be missing the first timing.)
Jan
22
revised Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?
fixed some errors
Jan
22
comment ListPlot3D. Only plots about half of the data in a 3D matrix
That's really odd. I can't find the problem, but here's a workaround for the time being: ListPlot3D[Transpose@Partition[Last /@ data, 15], DataRange -> {{100, 2000}, {0.01, 0.08}}, PlotRange -> All, ColorFunction -> "Rainbow"] i.stack.imgur.com/mwQmc.png
Jan
22
revised ListPlot3D. Only plots about half of the data in a 3D matrix
formatted code
Jan
22
comment CPU usage ~18%, but Mathematica is fully running
If your CPU has multiple cores but your code is not parallel, then you will generally only use one core. (Unless you use some of the built-in functions that are already parallelized.)
Jan
22
comment Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?
Fantastic! I for one am perfectly happy to provide an initial surface. @halirutan: For your curve one could simply form a "cone" by connecting all the points to the origin. I think that works for arbitrary curves, but I don't know if self-intersections will cause the result to get stuck in local minima.
Jan
21
awarded  Nice Question
Jan
21
comment Initial Value Problem with initial conditions as closed region
Another way to see all the solutions at once: ParametricPlot[{t, sol[p][t]}, {p, 0, 1}, {t, 0, 10}, Mesh -> {9, 0}] i.stack.imgur.com/YQ8EF.png
Jan
21
revised Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?
incorrect definition of Scherk's first surface
Jan
21
asked Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?
Jan
20
comment How can I make an linear breakdown chart similar to those seen on iCloud?
Have you tried reading the BarChart documentation? (See under Scope > Data and Layouts.)
Jan
20
comment Least effort to handle a point source inside the domain of PDE(s)
@user21: Sorry, I misread the documentation; I was looking for "IncludePoints" in the ToElementMesh documentation, but it's mentioned in ToBoundaryMesh instead. So that's my mistake. But there's another thing: If I just use mesh = ToElementMesh[Rectangle[{-1, -1}, {1, 1}], "IncludePoints" -> {{0, 0}}], it does place a node at {0,0} but it doesn't make it a boundary, so the node can't be used in DirichletSolve. It works if I set "MeshElementType" -> TriangleElement though.
Jan
19
awarded  Nice Answer
Jan
19
answered Discretizing regions with pointy boundaries
Jan
19
comment Least effort to handle a point source inside the domain of PDE(s)
@xzczd: Well, the Laplace equation approximates the displacement of an elastic membrane only when the gradient of the displacement is small. What you could argue is that in the limit as the displacement of the rod goes to zero, so does the relative size of the region it affects. The Laplace equation is a better model for heat distribution: if you stick an infinitely thin pin held at a constant warm temperature on a colder membrane, it won't heat up the membrane at all.
Jan
17
comment Creating a right hand in graphics3d to illustrate the right hand rule
Pick a format on this page and see the examples.