I've been trying to make something like this for over 2 years now, but all websites show a double slit experiment with none of the mathematics behind simulating light waves. Keep up the useful information.
I would love to see some lecture on the electromagnetic waves. I'm working on vector wave equations and to me it's very complicated especially to treat boundaries, impedance boundaries, radiation conditions etc. But it's fascinating area for simulation. Anyway, thank you for the excellent lesson!
Great presentation, thanks for the time you took to make it! The next step in optimization to me would be multithreading, where threads each work on a patch of the lattice. Since there's no instantaneous feedback you dont have concurrent data dependencies and therefore no need for thread synchronization beyond waiting for all threads in a frame to finish. Then there are specialized SIMD instructions that provide instruction-level parallelism by lalowing you to compute several floats at once. Since most computers nowadays have 8 threads in their CPU and support 4-float SIMD instructions, there is a theoretical 32x speed improvement on the non-boundary calculations. Alternatively, you could translate the reccurence equation to an OpenCL or CUDA kernel to have it run on the GPU, which should be fairly easy for the same reasons of not having instantaneous feedback in the recurrence equations.
Have you experimented with simulating waves in the frequency domain (given the solution you showed at 16:20)? It appears that in the frequency domain, you can simulate the state of the wave at any point in time in constant time (assuming the dimensions of the wave are constant). The only problem I see with that, at least in the 1D case, is the need to perform an inverse Fourier transform for each saved image, which may be costly. However, the advantage is that you can simulate for an arbitrarily long time with no error accumulation (or so I believe). But I don't know how well or poorly these properties would translate to the 2D case.
The frequency domain is useful in many cases, and a commenter made some videos on their channel using this method. However, boundary conditions tend to be hard to implement that way, except in very special cases. That is why I have not developed the approach so far in my code.
There are 3 types of simulation: pure quantum, very heavy with few particles, semi classical with classical particles but with quantum mechanics implict like Lennard Jonnes and density for big systems but you can't track a single particle way. The simulations of this channel is density.
For the 2D case, do you get any interesting effects by modelling the displacement as a 2D value per cell? In my head, with the 2D spring model in mind, I expected the displacement to be a two dimensional value.
You would get two uncoupled wave equations, one for each direction of displacement. So it may create some nice interference patterns, depending on your initial state, but there will be no real interaction between the directions.
@@NilsBerglund I think there could still be interaction between the components. The X axis springs could affect the Y offsets via the transverse math that you hinted at in the video, and vice versa. And one way to interpret the scalar values per cell you use is as offsets in the Z direction, transverse to both X and Y. But since you say that the result after going through the math of treating the waves as transverse ends up being the same as longitudinal, I wonder if it basically all cancels out, and you'd get effectively just the same simulation, except a bit slower.
A big thank you for showing how it work !! I had to think about "Huygens Optics Channel" which mostly deals with light experiments...and some theory. Many thanks !!
In a finite difference solver for the wave equation, wouldn't you also face a constraint on the time step size (Courant Levy condition). Also purely from a wave equation perspective is it possible for a "shock front" to emerge for Electromagnetic waves ? I guess not, because Speed of light is a constant wrt all observers.
Yes, you need to satisfy a CFL condition, it is mentioned in the tutorial. Shock waves are indeed not possible with light in our relativistic universe, but they are possible with sound and water waves. See for instance th-cam.com/video/E-8P4nJqfVQ/w-d-xo.html
@@NilsBerglund Thank you - i might have been mistaken Fermi/Feynmann but i recall an image that there were many linearly connected oscillators without a nonlinearity. I remember that at least 3 degrees of freedom and a nonlinearity in contained phase space are required for the onset of chaos but maybe there was some numeric error involved or they approximated the 2D movement with that nonlinearity - 2D double pendulum is enough for the onset of chaos still i dont remember if the arms need to be stiff or can be flexible - rather rigid.
Nice. Very interesting work indeed! What about the boundary conditions for lens simulations, like the ones you shared with that other channel (Huygens optics). I tried to find such simulations in your GitHub, but could not find them. Thanks and happy new year!
Thanks, same to you! To reproduce a simulation, look up the file Parameter_**.md of the correct month, and adapt the parameter values in the specified C file. Some extra dummy values may have to be added if you use a more recent version of the code.
I've been trying to make something like this for over 2 years now, but all websites show a double slit experiment with none of the mathematics behind simulating light waves. Keep up the useful information.
It is not that hard. I hope the presentation will be useful to you.
I would love to see some lecture on the electromagnetic waves. I'm working on vector wave equations and to me it's very complicated especially to treat boundaries, impedance boundaries, radiation conditions etc. But it's fascinating area for simulation. Anyway, thank you for the excellent lesson!
Thanks Nils! At 25:31 the 1D difference equation uses C^2, but at 28:32 the 2D difference equation uses just C, not C^2. Is this correct?
That is a type, sorry for that. It should be C^2 in both cases.
Thank you so very much for giving us all that value, it's great!
Great presentation, thanks for the time you took to make it! The next step in optimization to me would be multithreading, where threads each work on a patch of the lattice. Since there's no instantaneous feedback you dont have concurrent data dependencies and therefore no need for thread synchronization beyond waiting for all threads in a frame to finish.
Then there are specialized SIMD instructions that provide instruction-level parallelism by lalowing you to compute several floats at once.
Since most computers nowadays have 8 threads in their CPU and support 4-float SIMD instructions, there is a theoretical 32x speed improvement on the non-boundary calculations.
Alternatively, you could translate the reccurence equation to an OpenCL or CUDA kernel to have it run on the GPU, which should be fairly easy for the same reasons of not having instantaneous feedback in the recurrence equations.
Have you experimented with simulating waves in the frequency domain (given the solution you showed at 16:20)?
It appears that in the frequency domain, you can simulate the state of the wave at any point in time in constant time (assuming the dimensions of the wave are constant). The only problem I see with that, at least in the 1D case, is the need to perform an inverse Fourier transform for each saved image, which may be costly. However, the advantage is that you can simulate for an arbitrarily long time with no error accumulation (or so I believe).
But I don't know how well or poorly these properties would translate to the 2D case.
The frequency domain is useful in many cases, and a commenter made some videos on their channel using this method. However, boundary conditions tend to be hard to implement that way, except in very special cases. That is why I have not developed the approach so far in my code.
Great work keep it up!❤
Thanks 🔥
There are 3 types of simulation: pure quantum, very heavy with few particles, semi classical with classical particles but with quantum mechanics implict like Lennard Jonnes and density for big systems but you can't track a single particle way. The simulations of this channel is density.
For the 2D case, do you get any interesting effects by modelling the displacement as a 2D value per cell? In my head, with the 2D spring model in mind, I expected the displacement to be a two dimensional value.
You would get two uncoupled wave equations, one for each direction of displacement. So it may create some nice interference patterns, depending on your initial state, but there will be no real interaction between the directions.
@@NilsBerglund I think there could still be interaction between the components. The X axis springs could affect the Y offsets via the transverse math that you hinted at in the video, and vice versa. And one way to interpret the scalar values per cell you use is as offsets in the Z direction, transverse to both X and Y. But since you say that the result after going through the math of treating the waves as transverse ends up being the same as longitudinal, I wonder if it basically all cancels out, and you'd get effectively just the same simulation, except a bit slower.
What is the PowerPoint template that you use?
I'm not using PowerPoint. I'm making the slides in LateX, beamer document class, the theme is called Singapore.
Excellent! Always lots of good insight.
P.S. What the hell is all that banging noise?
@@stereomachine LOL 🙂
Thanks!
Sorry for the noise, it comes from a fire door my colleagues tend to let bang as it closes. Perhaps I should try using a better microphone.
Thank you so much for this!!!!
Any time!
A big thank you for showing how it work !! I had to think about "Huygens Optics Channel" which mostly deals with light experiments...and some theory. Many thanks !!
You are welcome! Jeroen from Huygens Optics indeed makes some nice videos, including real life experiments.
@@NilsBerglund I was fascinated by his Videos on the spatial and the temporal coherence of light waves
Yes, I contributed a simulation to one of those videos.
In a finite difference solver for the wave equation, wouldn't you also face a constraint on the time step size (Courant Levy condition). Also purely from a wave equation perspective is it possible for a "shock front" to emerge for Electromagnetic waves ?
I guess not, because Speed of light is a constant wrt all observers.
Yes, you need to satisfy a CFL condition, it is mentioned in the tutorial. Shock waves are indeed not possible with light in our relativistic universe, but they are possible with sound and water waves. See for instance th-cam.com/video/E-8P4nJqfVQ/w-d-xo.html
4:30 - the famous 1st chaotic behaviour "linear" system that was observed on Eniac (AFAIR) by Feynman and other phycisists.
You are thinking of the famous Fermi-Pasta-Ulam experiment, I assume. In their system, they added a non-linear term to the spring force.
@@NilsBerglund Thank you - i might have been mistaken Fermi/Feynmann but i recall an image that there were many linearly connected oscillators without a nonlinearity. I remember that at least 3 degrees of freedom and a nonlinearity in contained phase space are required for the onset of chaos but maybe there was some numeric error involved or they approximated the 2D movement with that nonlinearity - 2D double pendulum is enough for the onset of chaos still i dont remember if the arms need to be stiff or can be flexible - rather rigid.
Informational and helpful, thanks.
This is amazing, I could try it on interferometry.
Go for it!
Can you give an example of how much time such simulations take per minute? Like the one with finer mesh for parabolic reflectors.
The 2d one took about 12 minutes of simulation time per minute of movie. You can check the simulation time in the description of most videos.
Nice. Very interesting work indeed! What about the boundary conditions for lens simulations, like the ones you shared with that other channel (Huygens optics). I tried to find such simulations in your GitHub, but could not find them. Thanks and happy new year!
Thanks, same to you!
To reproduce a simulation, look up the file Parameter_**.md of the correct month, and adapt the parameter values in the specified C file. Some extra dummy values may have to be added if you use a more recent version of the code.
wow, FINALLY
日本語版が欲しいですね。。。
日本人の弟子はいませんかね？
Have you tried automatic translation of the subtitles to Japanese? I don't know how well this works, but it could be worth a try.
@@NilsBerglund 日本語自動翻訳、どこがやってるのか、まだ分かってないです。3blue***?は、理系の専門家が自分で手入力し、日本語翻訳しています。
そういうわけで、翻訳について、まだ開拓はされてません。
専門用語の翻訳環境の構築、何がボトルネックになっているのか解明する必要はあるかもしれません。