Jens
Reputation
1551/1000 score
 Mar 23 comment Frontend flickering Is this version 10.4? What OS? Looks like a case for Wolfram support. Mar 22 comment How to use BezierCurve or BSplineCurve to define a quarter of a circle? Also worth pointing out a bug that still exists in version 10.3: Where is the other half of my fourth degree Bézier curve? Mar 22 comment How to implement Feynman function notation? How would he have written $\sin\sigma$? Or $\sqrt{\cos\gamma}$? Mar 21 comment How to use BezierCurve or BSplineCurve to define a quarter of a circle? I think you'll have to explain what more complex shape designs you are looking for, otherwise the answer may end up being too narrow for your purpose. Mar 21 comment How to use BezierCurve or BSplineCurve to define a quarter of a circle? Why not use something like this? Graphics[{Black, Thickness[.1], CapForm["Round"], Circle[{0, 0}, ArmRadius + WireRadius, {0, -90 Degree}]}] If you only want one end to be round, you can make two halves, one of which has CapForm["Butt"]. Mar 20 comment periodic boundary conditions and NDEigensystem @user21 Sure, you can use the visualization - I'd of course be curious to find out where exactly. If anything needs clarification, just let me know. Mar 20 comment Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square I don't understand exactly what you're asking, because I don't see where I said anything about problems. Not all accidental degeneracies can be explained by geometric symmetries, and the square is an example for that because its spectrum is so regular. The explanation for its higher degeneracies is essentially number-theoretical, relying on square numbers being decomposable into sums of different squares. Mar 19 comment periodic boundary conditions and NDEigensystem I posted an answer using Bloch's theorem and finite difference. Mar 19 comment periodic boundary conditions and NDEigensystem Sorry, can't think of anything better... anyway, the Q only wanted periodic bc, so the projectors aren't strictly needed here (although it's nice to know how it can be done, of course). But I noticed that you should probably delete the line vd = ndstate["VariableData"] in PDEtoMatrix because it throws an error in version 10.3 (no method for VariableData). Since those data aren't needed anywhere, cutting that line is OK, I think. For other bc, one might also think about using Bloch's theorem (but that's a separate answer). Mar 18 comment Teaching Mathematica more about DiracDelta and KroneckerDelta I don't think so, because you're looking for generalized functions as output, and neither Integrate nor Sum are intended for those kinds of output. Regularizations don't give you generalized functions. The desired delta function output has ambiguities, depending on what is identified as the intended integration variable in the result. In my definitions for h, this is made explicit. But in Integrate or Sum, the first argument is just an expression and there's not enough information to easily identify the intended variables that should appear in DiracDelta. Mar 18 comment periodic boundary conditions and NDEigensystem Just a quick observation: Comparing to the ParametricNDSolveValue solution by @bbgodfrey, one difference is that this answer finds the degeneracies for the symmetric Cos[x]-derived potential automatically, whereas they are obtained in separate calculations when using ParametricNDSolveValue. But in this symmetric case it looks like the numerical accuracy of this answer is not as good as the previous approach, e.g., if I compare the ground state, which should come out to be zero and is 0.0000220456 in this answer. Mar 17 comment How to see phase difference of two pendulum @JasonB Thanks for the info! In this case, the original was over 20MB, so I think it was worth reducing the size just for the sake of page load times... Mar 17 comment How to see phase difference of two pendulum @JasonB Indeed, I had something prepared already in both this and the double-pendulum answer. The hard part was remembering where I kept it... and then making the movies to upload here. For this answer, I definitely wanted to show a movie, of course. As they say: two thousand pictures say more than a thousand words. Or something like that. Mar 17 comment How to see phase difference of two pendulum @LLlAMnYP Thanks - it's about 2400 frames (from a ListAnimate), and I had to shrink the GIF down quite a lot because the upload limit on this site is just 2MB... Mar 17 comment Creating 3D dice You can find all you need in the documentation for Texture Mar 17 comment Teaching Mathematica more about DiracDelta and KroneckerDelta The outcomes containing KroneckerDelta can't be valid in general because Mathematica doesn't know that the arguments in those results are supposed to be integers. It generically assumes complex variables, but adds some reality assumptions in FourierTransform. So for point 3, you would in general expect something involving DiracComb instead of KroneckerDelta. Mar 17 comment Teaching Mathematica more about DiracDelta and KroneckerDelta For numbers 1 and 2, you can use Fourier transforms instead of integrals, and the result comes out correctly. Specifically, for 1: InverseFourierTransform[ Limit[ FourierTransform[a/(x^2+a^2),x,y], a->0], y,x] yields $\pi \delta(x)$. See Laplacian and DiracDelta. This also works with additional relations, not in your list, e.g., InverseFourierTransform[ Limit[ FourierTransform[Sin[ω t]^2/(π t ω^2),ω,τ], t->∞], τ,ω] Mar 17 comment Color of figure keeps changing Could be a problem with the PDF viewer. What OS are you on, what Mathematica version, how do you invoke latex to create the PDF (pdflatex, xetex, via dvips, ...)? Mar 16 comment General techniques for creating complex animations Then I would strongly recommend this approach. I think it can be adapted to a very broad range of animations. Mar 16 comment General techniques for creating complex animations Is the goal that you want to export the animation, or does it stay inside a Mathematica notebook? A simple approach would be to export a suitable Manipulate autorun sequence.