3 ms·
Speaking as someone whose PhD was simulating the nuclear structure of nuclei like this... yes, we probably could, now. Back then (like, 30 years ago, and I sto
by bazzargh 3y ago
Speaking as someone whose PhD was simulating the nuclear structure of nuclei like this... yes, we probably could, now.
Back then (like, 30 years ago, and I stopped doing physics after this so my memory of this is fuzzy) we were looking at simulations of nuclei like O16. I say 'we' - nuclear theorists were _very_ thin on the ground, we were the only remaining group in the UK. Most particle physicists are of the kind looking at subatomic particles, not nuclei. Anyway, we were attempting to port the code to run on parallel processors (a 96 transputer rack at the time), and then diagonalise the matrices of the interactions to get out a spectrum of energy levels. IIRC the matrices worked out as ~20m x 20m, and the technique used was the https://en.wikipedia.org/wiki/Lanczos_algorithm https://en.wikipedia.org/wiki/Lanczos_algorithm ... the problem we had was that the state space explodes combinatorically with increasing numbers of nucleons; and the computation time scaled something like n^1.1 for n states, due to inter-processor communication.
In the end that was what killed the project - it became clear that with moores law we were about 10 years from having affordable access to a computer that could do the calculation for larger shells (including O28, which was well out of our range).
That was the state for _exact_ calculations, but there were alternative approaches - I recall VAMPYR being a German Monte-Carlo simulator for shell models that performed really well, and could extract properties even for quite heavy nuclei.
Looking back a lot of the problems were just a lack of memory, even more so than compute. The matrix elements weren't stored explicitly but recalculated on the fly because we lacked memory, this led to us not using off-the-shelf matrix code and the whole thing had numerical stability issues and used lanczos because we could fit that into the memory on board the processors. These days I use servers in AWS with ungodly amounts of memory and extremely fast cpus, I'm pretty sure they could simulate this for a couple of hundred bucks.
- sjtgraham 3y agoThis is the kind of HN comment I live for.
- jacquesm 3y agoCan you give an indication of the amount of precision required for the initial conditions to be able to perform such a simulation? Fascinating stuff this, thank you for your comment.
- bazzargh 3y agoAs one of the other commentators mentioned, it's not that kind of simulation. It's similar to looking at electron shells in an atom, where you don't simulate the motion of an electron from a start point to an end point, but can predict bulk properties of energy states, eg that radiation of a particular wavelength will excite the system to another state, and we should see absorbtion an emission spectra from those effects (and this is how you get lasers, and detect the composition of stars, and so on). Analogously in nuclei you get gamma radiation spectra, and statistical predictions about other phenomena. The numerical stability issues I complained about are inherent due to the accumulation of floating point errors in the Lanczos algorithm. You just end up with completely junk results. (so, you work with double precision all the time, chewing more memory). We do have some "initial conditions" in the calculation, in that the lanczos algorithm is repeatedly applying a matrix to a vector that represents state occupancies; but if this was numerically stable it wouldn't much matter what initial vector you chose (I can't remember if ours used (1,0,0...0) or 1/root(N)*(1,1,...,1))
- ftxbro 3y agoIs there a code that i can run to check the stability, if i have a lot of time to spare and a fast computer with a lot of memory? Do the codes use GPU for their Lanczos things yet?
- bazzargh 3y agoGPU? I was writing this stuff _30 years ago_. You were lucky to have a soundblaster. Everyone I knew who worked on this is long retired or passed away. AFAIK the code isn't available, that just wasn't how things worked back then, there were some ftp sites but open source was still nascent (Linux didn't exist yet). The architecture I was writing for was a Parsytec Supercluster https://en.wikipedia.org/wiki/Parsytec https://en.wikipedia.org/wiki/Parsytec which doesn't exist as a thing any more, it was mostly straight K&R C tho with a harness written in Occam, controlled from a workstation running SunOS (not even Solaris). If you happened to find the code it'd be completely worthless. Like I said above, we weren't able to use off the shelf, optimised matrix libraries because of the way we were generating coefficients on the fly, for what was a very sparse matrix. It's just not how you'd do it on modern hardware.
- pfdietz 3y agoHow accurate are the empirical internucleon potentials, though? According to the wikipedia page on "Nuclear force", one major obstacle is: "There is evidence that three-nucleon forces (and possibly higher multi-particle interactions) play a significant role. This means that three-nucleon potentials must be included into the model."