I was able to perform a valid laser-beam fragmentation. Writing the code took me few days, but I improved some parts and made better model of my system. Below is some another ill-prepared video with the effect.
Also – I have the voice actor for Singularity! 🙂
Not much, because I spent last few days learning from tutorials on particles effects. Effect is great – I have finally a laser beam I am not ashamed of! Probably I’ll edit it anyway, but it’s something I can show.
After few months I came back to my grant project in quantum simulations. For now the main goal is to simulate the following equation in three dimensions:
The biggest issue is the singularity in 1/R. There is something more – I have never simulated such complicated equation, so I started from something much much easier – the equations for free quantum particle in space.
After this (having very simple evolution) I checked if version with separated variables ( psi = f + i g) gives the same solution:
Now I’m trying again to obtain same results with another change of coordinate system: psi = R exp(i Theta). There are some problems, unfortunately…
Because of desperation, I changed the system into one dimensional space, where I have bigger control. Still, the last pair of equations are difficult to simulate. I suspect that it can be partially of troublesome behaviour of theta variable – it is something I call periodical variable, which is given with the error of 2 pi. That generates wrong behaviour in getting the derivative – sometimes small change of argument generates great change of function value. I have a method to get rid of it, in changing a definition of theta derivative:
This way I can remove a discontinuity in theta.