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by The universe operates on many different size scales, from intra-particle to inter-galactic. Most phenomena do not require more than one scale to be fuly understood. But, some phenomena operate along multiple scales. For example, the particles in a coronal mass ejection interact with each other (short scale) while they travel from the Sun to the Earth (long scale). In order to be correctly simulated, both length scales must be accounted for; making multi-scale problems difficult and computationally expensive to model.
Dr. Vay, a physicist from Lawrence Berkeley National Laboratory, has shown (PRL abstract, Physical Review Focus) that special relativity can be used to reduce the time required to simulate systems that have multiple scales in both time and distance. According to relativity, both time and distance change based upon the speed of the observer. Dr. Vay showed that ratio between the sizes of the multiple scales also changes with the speed of the observer. In other words, a speed can be found that reduces the differences between the scales, thus decreasing the number of steps required to simulate the system. To test this hypothesis, Dr. Vay simulated the interaction of a pulse of protons (length ~10 cm) travelling down a particle accelerator beam line (length ~1 km) and interacting with a cloud of electrons. On an 8 processor cluster, this simulation normally requires a week. With these improvements, the simulation only required 30 minutes giving the same results.
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Scale vs length by scottb :: NR7 :: Show
The abstract and article don't really give enough information to entirely judge what they're saying here.
If I'm following it, they've got this simulation in which the individual elements are smallish - around 10cm - and the overall system is fairly large - around 5km. So we've got roughly a million-to-one scale. Simulating a tens or hundreds of millions of elements as they evolve is where all the workload comes from.
The paper proposes to reduce this workload by simulating instead what it looks like to an observer passing by at near relativistic speed, presumably to harness something like the ladder paradox.
So the total 5km length of the system is shortened by the Lorentz contraction by a factor of γ = 1/√(1 - v2/c2) - if v is 90% of c, then the system is a little over 2km. At 99%, it's only about 700m.
The only way that seems relevant is if the "fine" scale (10cm) measurement doesn't change, or at least changes less than the coarse scale. But at least one dimension of its length will be contracted by the exact same amount.
The other thing that seems confusing about the descriptions is that they suggest there's a sort of "sweet spot" in the velocity. I assume that below this "optimal" velocity, you haven't squeezed out the maximum benefit. What might happen above it? The Lorentz equations are all linear in both time and space, I can't imagine how you might start losing the benefits by running it too "fast". To me, this suggests that part of the effect of the relativistic simulation is to discard some of the detail in the simulation. So the "sweet" spot represents a compromise between getting answers quickly and getting an accurate simulation.
These "pay us to see our results" journals are annoying. :(