The first Anton molecular dynamics supercomputer typically simulated a box of water that was 64 on a side. The computer itself might be approximated

The first Anton molecular dynamics supercomputer typically simulated a box of water that was 64 Å on a side. The computer itself might be approximated as a box with 1 m side length. A single simulation step represented 2.5 fs of simulation time, and took about 10 μs of wall-clock time. The physics models used in molecular dynamics act as if every particle in the system exerts a force on every other particle in the system on each (“outer”) time step, requiring what amounts to a global synchronization across the entire computer.

a. Calculate the spatial expansion factor from simulation space to hardware in real space.

b. Calculate the temporal slowdown factor from simulated time to wall-clock time.

c. These two numbers come out surprisingly close. Is this just a coincidence, or is there some other limit that constrains them in some way?

d. Given these limits, what would it take to use a warehouse-scale supercomputer to perform molecular dynamics simulations at Anton rates? That is, what’s the fastest simulation step time that might be achieved with a machine 10² or 10³ m on a side? What about simulating on a world-spanning Cloud service?