Another little update, speed issue solved for now by adding SymPy’s fortran wrappers to the derivative calculations—calculating the SVD isn’t (yet?) the bottleneck. Can now quickly get results from 1,000+ step simulations of 100s of particles.
Unfortunately, even for the pretty stable configuration below, the values are indeed exploding. I need to go back through the program and double check the logic but I don’t think it should be chaotic, if anything I would expect the values to hit zero.
It might be that there’s some kind of quasi-chaotic behaviour where the residual motion of the particles is impossibly sensitive to the initial conditions, even as the macro state is very stable, with a nicely defined derivative wrt initial conditions. Not yet sure how to deal with this.
If the wheels are bouncing off each other, then that could be chaotic in the same way as billiard balls. But at least macroscopically, there’s a crapton of damping in that simulation, so I find it more likely that the chaos is microscopic. But also my intuition agrees with yours, this system doesn’t seem like it should be chaotic...
Another little update, speed issue solved for now by adding SymPy’s fortran wrappers to the derivative calculations—calculating the SVD isn’t (yet?) the bottleneck. Can now quickly get results from 1,000+ step simulations of 100s of particles.
Unfortunately, even for the pretty stable configuration below, the values are indeed exploding. I need to go back through the program and double check the logic but I don’t think it should be chaotic, if anything I would expect the values to hit zero.
It might be that there’s some kind of quasi-chaotic behaviour where the residual motion of the particles is impossibly sensitive to the initial conditions, even as the macro state is very stable, with a nicely defined derivative wrt initial conditions. Not yet sure how to deal with this.
If the wheels are bouncing off each other, then that could be chaotic in the same way as billiard balls. But at least macroscopically, there’s a crapton of damping in that simulation, so I find it more likely that the chaos is microscopic. But also my intuition agrees with yours, this system doesn’t seem like it should be chaotic...