Why MD simulations can't simulate proposed speeds fro diamondoid nanomachinery.
The limitation
In molecular dynamics (MD) simulations the time-steps for the motions of atoms
need to be small enough to subdivide a single vibration oscillation of the fastest oscillating atoms
(usually the lightest ones thus hydrogen atoms) into several sub-steps.
If there are not enough sub-steps then the simulation (often Verlet integration) becomes unstable.
At the proposed speeds for advanced productive nanosystems (of a few mm/s)
to see any motion of nanomachinery at all within the length of a simulation run
there would need to be an enormous (too great to be practical) amount of time-steps.
And it would be highly wasteful as most of these computed frames would be disposed for the final video.
Even for making averaged nuclear position blur clouds it is much more information than needed.
For classical MD simulations there is no way around it.
One can not avoid running all the steps in the simulation.
Consequences on nanomachie simualtions videos present on the web (2026)
This restriction naturally leads to simulations of diamondoid nanomachinery
being run at 10s to 100s of m/s and frequencies in the several GHz range
rather than proposed speeds of mm/s and MHz frequencies.
Which gives a severely misleading impression on the typical mechanical behavior of these machines
showing them wobbling like jelly.
Macroscale machines out of steel also start wobbling like crazy when run at ludacris speeds.
The difference being that in thecase of macroscale machinery the fiction would be to much
even for a single machine running in isolation leading to a swift self-destruction event,
whereas a single diamondoid nanomachine in isolation,
and coupled to a cool diamondoid bulk martix/frame,
while massively lossy and damped, handles such speeds just fine.
See page: A better intuition for diamondoid nanomachinery than jelly
Other nanomachinery simulation methods averting delivering a misleading intuition
Thee are other methods for simulating nanomachinery that do allow for slower speeds
without exploding the need for compute, but these do not fall under the category of MD simulations.
Proposed method "sparse mainframes quasistatic push-only-walls nanmoachine simulation"
One method that should be possible and good is
doing a sequence of quasi-static relax/minimization frames.
It is a bit like using animation frames as starting points for relax minimizations
under certain not too strong constraints.
(wiki-TODO: Find better name for the proposed method.)
Smarter than an animation; Catching snap ahead instabilities
It is smarter than literally starting from animation frames though.
In particular (and of great interest for nanomachine behavior)
this method can even catch forward snap instabilities
(snap to the next commensurate interdigitating corrugation position) if
diamondoid nanoparts are avoided to be too strongly constrained/anchored.
See: Intercrystolecular snapping modes => notch-snapping
Driving motion: Constant speed push-only virtual wall
For driving translation at constant speed
(as would be the natural operation mode avoiding freewheeling snaps)
what advances across frames is a constant-speed virtual push-only-wall.
For setting up the next starting configuration based on the result of the former
(i.e. for the frame advancing set up)
one can use high speed minimization under the gradually advancing pusher constraint
several pushing steps to the next actual serious local minimization main-frame.
Driving rotations poses the challenge of most parts having no angular start and end.
So a rotating virtual push-only wall would need to cut through the driven axle.
That might pose some complications.
Anchoring atoms and driving them is also an option but
there is high risk to add too strong constraints.
n case of proposed pusher all atoms are free to move sideways unconstrained and also move ahead.
No pull back attraction to the wall.
The wall may simulate Pauli repulsion lie characteristic for
numeric stability during discrete steps of advance.
Getting from the result of one frame to starting point of the next
The pushing process between the major frames is close to fast MD simulation at 100s of m/s speed
but it can be a sequence of 0K minimizations.
This does not get into the final result, it is just needed for frame setup.
The steps between major frames are still small compared to the size of atoms but
much larger than the the effective step size during a single time-step in classical MD at mm/s speeds)
Optional: Pushing may have a few not seriously minimized subdivision sub-frames.
Only necessary in case of taking larger steps for the actual frames.
One may miss the aforementioned forward snap jumps when going too crude though.
Effect of jump ahead instabilities (if present) on the main frame setup process
If the pushed part jumps forward ahead of the virtual push-only wall then
Then the pusher will just catch up and push against nothing for a few of the major frames.
See: Intercrystolecular snapping modes => notch-snapping
Actual quasistatic minimization (the main process, most compute goes there)
At each major frame a serious minimization is taken and a MD sim run to gain position averages at operating temperature.
Putting in as much compute as one is willing to afford.
Compiling the resulting atomic positions frame sequence (& video)
At the end the (usually temporarily equidistant) main frame minimizations are sequenced together
to make the final result of the simulation.
Intention that should be fulfilled
With this process the final result of the simulation should be as faithful as possible
to the real (FAPP quasi-static) behavior of the nanomachinery parts simulated at proposed speeds of few mm/s.
Versus classical MD sims: Why is this faster / practical-at-all for mm/s level speeds?
Unlike classical MD this method can simulate slow speeds without taking excessive amounts of timesteps because:
- large spacial steps between the major frames
- the high quality quasi-static minimization during a main frame happens/operates entirely withing a single molecular oszillation,
all the efforts during of a main-frame minimization goes into what in MD would be one single very crudly passed oscillation cycle. - the motion between main frames can be done at high speed and even more crude than conventional MD
- (most likely no and if so just a few sub frames for push-only wall advance)
- an adapted multi-grid method (further below) should be able to give further massive speedup
Side-note: The steps between major frames are still small compared to the size of atoms but
much larger than the the effective step size during a single time-step in classical MD at mm/s speeds)
Related novel(?) atomistic multi-grid method for further massive speedup that should be possible
Adapting multi-grid simulation methods to get a massive simulation speedup.
It seems this is not done for proteins due to small local changes being able to have
large global structural reconfiguration consequences there.
Crystolecules do not have that constraint for there is a huge speedup opportunity present.
Nontrivial challenge is linking up well known bulk continuous matter multi-grid methods
known from finite element methods with atomistic crystal lattice minimization.
This would be applicable to minimizations like present in the here described method.
Related
- Lower stiffness of smaller machinery
- Misleading aspects in animations of diamondoid molecular machine elements
- A better intuition for diamondoid nanomachinery than jelly