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3h
comment Moving certain variables to one side of the equation
You can modify my answer to the question I linked above, to get the desired result: eqn = x1 + x2 + x3 == 4; Map[Subtract[#, First[eqn] - (x1 + x2)] &, eqn]. Alternatively, Distribute[eqn - (First[eqn] - (x1 + x2)), Equal]. Also, I think the other linked question, Arrange equation in normal form, is a duplicate of the earlier one.
3h
comment Moving certain variables to one side of the equation
related: Is it possible to have Mathematica move all terms to one side of an equation?
17h
comment Why is ListPlot so slow here?
In version 10.1, I get a reduction in the timing by a factor of 2 simply by adding Joined->True to ListPlot. In version 8, the same change reduces the timing almost ten-fold! Apparently, it's harder to make points than to draw lines. Who would have thought... Same thing happens when I use ListLinePlot instead of ListPlot.
23h
comment Numerically solving Helmholtz equation in 3D for arbitrary shapes
Yes, that's correct. And you can always symmetrize the degenerate solutions after the computation.
1d
comment Numerically solving Helmholtz equation in 3D for arbitrary shapes
So the clever way to approach such symmetric boundaries is to first reduce them to a fundamental domain with no remaining symmetries using the properties of the group. Essentially, the reflection axes then turn into boundaries with Dirichlet or Neumann conditions and you solve the wave problem only on a wedge-shaped segment of the hexagon.
1d
comment Numerically solving Helmholtz equation in 3D for arbitrary shapes
@chris Absolutely. It's the same effect: the FEM solver has no knowledge about the discrete symmetry group of the boundary, which in this case is that of a hexagon, $D_{6h}$. Therefore, it cannot know how to label the eigenmodes by the irreducible representations of that group, and instead produces arbitrary linear combinations of them whenever there are degeneracies - which happens a lot here because $D_{6h}$ has two-dimensional irreducible representations (i.e., there are linearly independent, degenerate eigenfunctions related by symmetry operations).
1d
comment Numerically solving Helmholtz equation in 3D for arbitrary shapes
Regarding the spherically symmetric case: You're not going to get solutions that look like spherical harmonics, because solving the Dirichlet problem with FEM won't simultaneously solve the angular-momentum eigenvalue problem. Due to the degeneracies in a spherically symmetric system, the numerical solutions will be arbitrary linear combinations of spherical harmonics. You can see something analogous in the isotropic harmonic oscillator when solving with finite differences. One more reason not to use (Cartesian) FEM with spherical symmetry.
2d
comment Defining quantum-mechanical Bra and Ket operations
@Sid The additional linear algebra you're asking for would be easier to implement by not using the built-in Dot. I'll update the answer with an approach that works. But ultimately, one has to ask when it stops being worthwhile trying to re-implement all linear-algebra functionality with special notation. Then it may be better to leverage the existing conventional vector algebra and use special notation only for input and output. That's e.g. what I did in this answer.
2d
comment Defining quantum-mechanical Bra and Ket operations
@LLlAMnYP Yes, it's true - that notation is so useful and has been around forever, but is impossible to find in the documentation.
2d
comment Eigenfunctions of the Laplacian on an arbitrary mesh
I guess what you need is NeumannValue
2d
comment Eigenfunctions of the Laplacian on an arbitrary mesh
Have you seen this: Numerically solving Helmholtz equation in 2D for arbitrary shapes? Not saying it's a duplicate, just pointing out the close relation.
2d
comment How to read off coefficients of tensor-like expression in a speedy way?
Indeed, I noticed similar timing differences with the original example by just repeating it many times.
2d
comment How to read off coefficients of tensor-like expression in a speedy way?
@Mr.Wizard Yes, my initial timing included the duration of the keystrokes...
May
26
comment Asymptotic forms of Bessel function
Since this is one of the examples in the docs for Series under Scope, I would say this question can be closed.
May
26
comment Solve PDE with DiracDelta function
I don't think using the delta function is practical here. It's probably better to use the general solution in each domain (left and right half) and match them according to the compatibility conditions implied by the delta function. That should reduce the problem to a set of simultaneous (algebraic, not differential) equations for the integration constants in each interval once you know the general solution as derived in my answer to the linked question.
May
25
comment How can I customize the tooltips on a ContourPlot?
@episanty I added an answer to explain what I believe is going on.
May
25
comment Solve wave equation using DSolve?
(+1) Indeed, Laplace transforms also helped overcome the inability to solve an integro-differential equation here. For more complex boundary conditions it may be necessary to use superpositions of the general solution I obtained from separation of variables.
May
24
comment Animation of double pendulum
@shrx Sure, go ahead and add an answer - and thanks for the suggestion regarding frame rate.
May
23
comment Animation of double pendulum
@Mr.Wizard Thanks - and you're right about the tag, of course.
May
23
comment Swing of the pendulum
Another pointer: How to draw a spring?