Science/Engineering/Technical forums

Interesting!!..


[attachment]total_binding_energy2s.jpg[/attachment]

VERY interesting. The last time I saw something like this I was investigating various schemes for pseudo-random vector generation, and plotting the results of a few vector components against one another. It turns out that most of the vector random number generators have accidental correlations when shown that way that look a lot like this (including the generator used for Black-Scholes analysis of market risks for option pricing). I was looking for a good generator for MLFN neural net training and perturbation, and I got pretty excited when most of the "best" algorithms had "these problems" of accidental correlations in various hyperplanes.

Of course, the reason I saw what I saw was that there was underlying structure in the PRN generators that only showed up under further analysis, and this did show up even in the ones from Knuth, Numerical recipes and others -- even some of the crypto PRN generators.

I would suppose the same would apply here, due to the underlying structure, or sub-structures in nuclei. This plot will bear some more analysis to tie that together.

Isn't the human ability to find patterns in things amazing? All the PRN's I found things like this in were highly "vetted" as producing completely uncorrelated numbers by the conventional techniques. But plot say, V1, V5, V11 as a 3d scatter plot (out of a longer vector) and here's these patterns and blobs....and most attempts to "fix" that and get a truly random, flat distribution by further shuffling simply changed the way it looked -- but not the non-random nature. I didn't get as far as trying a diode noise generator or a radioactive source, and probably I should -- we may be looking at a number theoretical issue there with the PRN's. With nuclei, it's probably due to underlying sub-structures, like the semi-classical idea that alphas are preformed in a larger nucleus before decay, or that ??? shell/magic number junk -- there's only so many ways to combine with a few integer (quantum number eigenvalues) or binary (say, spin) properties.

This deserves more looking at than I can do on a Sunday morning over the first cup of tea....

This is what the 'lines' look like to me;



I generally think each of the lines represents elements with a lot of stable isotopes, so that each nucleon 'added to' the lower 'A' isotope bumps up its total binding energy for each nucleon addition, so we see these little lines. What I find interesting - and it may just be me seeing things in the dots, is that around 100 we get elements where the isotopes 'cross' with elements the other side of that 'divide', whereas elsewhere they tend to [generally] run side-by-side to the next one along.

Still thinking on this and trying not to say anything too stupid about it - it really does bear some examination. Dan DT's comment on fusor.net came to mind here too. It's relevant as once the total binding energy reaches that of a nuclear particle -- 931 MeV or so for a proton, one might expect to see "funny" things happening, but we don't because due to the short range saturation of the strong force, it's not all available to say, create another nucleon as the nucleus flies apart -- we'd have no real heavy elements otherwise. Some others don't seem to "get" the skewed axes, but that's no sweat for me - I get that one fine. Your "cross" is near tin, right? That's the element with the most stable isotopes I believe. Maybe we should make a line plot like your last, but use one color for all the stable ones, and another for the unstable (but existing with reasonable half life, else there'd be too many), it might show something more obvious?

I don't really have the software to do this well, but here is a re-plot of the points, in the same 'grid-space' as above, with the line showing the points that are potassium - rubidium - tin and then osmium

...I guess we are looking at a series of 'humps' (on these axes) for each isotope, and the ones with the most isotopes stand out. Maybe I should look to see where the stable isotopes sit on each element-curve, but too much computer work done for today now.... another day, perhaps...

Yes, you've come across something that I look at as "long term study" here - There's something to see, but I'm not yet sure what it is, it's going to take a little percolation on the back burner.