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Re:What Makes the Hardest Equations in Physics So Difficult? by openasocket on Tuesday January 16, 2018 @03:56PM (#16162475)
Well, we still don't have the computational power to do things atom-by-atom, even in small things like modeling cells, let alone something like simulating wind shear on a plane or predicting weather patterns.

It's not just computational power but memory. There's something like 1E14 atoms in a cell. Storing the x,y,z position with 4 bytes for each dimension (though you'll probably want 8 bytes) comes out to 1.2E15 bytes = 1.2 petabytes of information. Add in more fields for velocity and other pieces of state and you're talking about something that would only fit in working memory in some of our largest machines.

Re:What Makes the Hardest Equations in Physics So Difficult? by Retric on Tuesday January 16, 2018 @04:07PM (#16162595)
Here is a billion particle model (e9) which is a long way from atomic scale simulation (e14+), but not outside the realm of the possible.

https://www.youtube.com/watch?v=B8mP9E75D08

Re:What Makes the Hardest Equations in Physics So Difficult? by openasocket on Tuesday January 16, 2018 @04:44PM (#16162969)
We are definitely making progress. But another factor to consider, in additional to the number of particles, is the energy of the system. When going through one step of a simulation you have to compute the effects that every particle has on every other particle, but generally a particle only affects the other particles near it. You can take advantage of this fact to speed up computation with the right data structures.

However, as particles start moving around faster and faster, the distance they can travel in one time step increases, and the neighborhood of effect increases, limiting the speedup of this optimization. This matters less in larger scale simulations like of weather patterns, because you don't have to worry about air molecules zipping to the other side of the continent in one second. But it matters a lot in small scale simulations, especially in cells. As an example, an average glucose molecule in one of your cells is bouncing around at around 250 miles per hour! That's not 250 miles when scaled up, that's really 250 miles per hour. A molecule in your body is colliding with another billions of times every second. (Source: http://www.righto.com/2011/07/cells-are-very-fast-and-crowde...). At that scale and that level of activity it becomes much harder to simulate each time step.

Re:What Makes the Hardest Equations in Physics So Difficult? by Retric on Tuesday January 16, 2018 @06:48PM (#16164041)
The other side of this is cells are also really fast. Modeling even 0.01 seconds could be very useful.
Re:What Makes the Hardest Equations in Physics So Difficult? by SAI_Peregrinus on Tuesday January 16, 2018 @07:35PM (#16164383)
Much of the action inside cells is done via proteins. It's taken a huge amount of distributed computing power just to figure out a reasonable hypothesis for how they fold (only one part of the movement) and €1.22 billion to build the XFEL and have a way to image them on the required timescales: 1-2 femtoseconds. 0.000000000000001 seconds. 0.01 seconds is an eternity, calculating that long would take an utterly enormous amount of computer time.
Re:What Makes the Hardest Equations in Physics So Difficult? by Retric on Tuesday January 16, 2018 @09:10PM (#16164886)
You can spend similar amounts of processing power (or vastly more) modeling a single atom over much shorter time scales from quantum mechanics. Protean folding while important results on fairly stable configurations and you don't need the same granularity after that point.

PS: Also of note protean folding simulations don't even simulate the water surrounding the protean and are again very simplified.

Re:What Makes the Hardest Equations in Physics So Difficult? by clicea on Tuesday January 16, 2018 @11:31PM (#16165480)
Don't be fooled by the numbers e9 is 5 orders od magnitude less than e14
Re:What Makes the Hardest Equations in Physics So Difficult? by Retric on Wednesday January 17, 2018 @07:24AM (#16167309)
64 GPU's and 91 hours for a 12 second simulation. 64,000 CPU's for 910 hours (1 month) is 4 orders of magnitude.

Unfortunately, a useful cell simulation would be far more complex than simple particle collisions and a much shorter step size. But, that's not to say different kinds of simulations can't be useful. And ASIC's or general improvement in computing power can also boost things.

Re:What Makes the Hardest Equations in Physics So Difficult? by ctdonath on Tuesday January 16, 2018 @07:02PM (#16164127)
we still don't have the computational power to do things atom-by-atom

That's what puzzles me about this discussion.

Of course we don't. The goal here is to model more atoms than we have atoms to model with. Until we get to quantum computers that can represent more information per atom, than information per atom we want to represent, it's simply a matter of objectively & obviously inadequate resources. You can't simulate wind shear on a plane when there's more atoms in that wind & plane than there are in the computer simulating them: every single atom being simulated contains the complete information about its state (information independent of any other atom), so simulating it will require at least one atom per atom simulated - if you don't have at least as many atoms to simulate as you are simulating, you can't achieve a complete simulation.

Re:What Makes the Hardest Equations in Physics So Difficult? by evandijk70 on Tuesday January 16, 2018 @07:12PM (#16164212)
It is not necessarily the goal to model more atoms than we have atoms to model with. The goal can be, for example, to model a folding protein, which has fewer atoms than a CPU.
Re:What Makes the Hardest Equations in Physics So Difficult? by njarboe on Wednesday January 17, 2018 @12:34AM (#16165714)
And one might be happy to spend a month computing the folding while in the cell it takes a few seconds.
Re:What Makes the Hardest Equations in Physics So Difficult? by pcvarmint on Wednesday January 17, 2018 @05:43PM (#16172775)
That may be true of digital computers, but it's not necessarily true of analog ones.
Re:What Makes the Hardest Equations in Physics So Difficult? by RhysU on Tuesday January 16, 2018 @09:43PM (#16165053)
> Well, we still don't have the computational power to do things atom-by-atom...

We still don't have the computational power to do certain classes of continuous Navier--Stokes calculations (i.e. not atom based).

Re:What Makes the Hardest Equations in Physics So Difficult? by tw1010 on Tuesday January 16, 2018 @04:02PM (#16162545)
Sure, but you'd think we would shift our focus to using models explicitly tailored with that aim in mind. Using something that explicitly approximates a desired, precise, foundation. Perhaps parameterized by model accuracy. I would think taking inspiration from approximation algorithms would be a much more appropriate lens with which to model physics.
Re:What Makes the Hardest Equations in Physics So Difficult? by btilly on Tuesday January 16, 2018 @05:37PM (#16163416)
The mental model of a bunch of hard little atoms flying around, colliding, rebounding, etc is actually NOT the desired, precise, foundation for understanding how gases behave.

The better foundation is quantum mechanics. An example of a macroscopically visible difference between these foundations are the van der Waals forces.

Re:What Makes the Hardest Equations in Physics So Difficult? by auntienomen on Tuesday January 16, 2018 @04:12PM (#16162658)
In the case of Navier-Stokes, this was done in 1934 by Jean Leray, who showed that the so-called 'weak' solutions always exist. (A weak solution is not a function, but a more general object called a distribution which can be fuzzed out on very short distance scales.)

It's a very reasonable idea, and useful enough for computations, but it lacks the essential tension that makes Navier-Stokes a mathematical Everest.

Re:What Makes the Hardest Equations in Physics So Difficult? by electricslpnsld on Tuesday January 16, 2018 @04:19PM (#16162714)
> Well, we still don't have the computational power to do things atom-by-atom

People do atom-by-atom molecular dynamics simulations of proteins and such.

Re:What Makes the Hardest Equations in Physics So Difficult? by effie on Wednesday January 17, 2018 @05:36PM (#16172715)
Yes, but those are simulations of classical mechanics models of molecules which are known to be very limited when it comes to atom-scale objects. We have another model that was much more useful there (Schroedinger's equation) but it is only computationally tractable for systems of few atoms. We do not have the computational power to work out the consequences of the model for proteins.
Re:What Makes the Hardest Equations in Physics So Difficult? by openasocket on Tuesday January 16, 2018 @04:44PM (#16162980)
Certainly, but not at the level of an entire cell