Pages with math

Math investigating (in)validity of common concerns

Energy, force, and stiffness
Some investigations useful for asserting in how far results of macroscale robotic prototyping
will be transferable to nanoscale diamondoid systems.
See also: Applicability of macro 3D printing for nanomachine prototyping
See also: Intuitive feel

Nanomechanics is barely mechanical quantummechanics and
Estimation of nanomechanical quantisation:
Some simple math to show that concerns about quantum mechanics making
macroscale style machinery at the nanoscale infeasibly are very much not valid.

Atom placement frequency
Some investigations on whether with reachable reasonable numbers of

• temporal placement frequency and
• spacial parallelity

useful levels of throughpur (product output rate) can be reached without

• needing excessive amounts of volume
• causing excessive amount of waste heat

And that despite the outrageously high necessary effective atom placement frequencies
due to to less than 6.022*10^23 particles per mol (very roughly sugar cube volume quantity of atoms)

Power density & Mechanical energy transmission
Some math further investigating the outrageous results for
possible powerdensities that were found in Nanosystems

Analysis for gem-gum on chip factories

Higher throughput of smaller machinery:
A very important little known scaling law that:

• allows to reduce friction by a large factor
• has major influence on design choices (e.g. why gem-gum factories are a better target than molecular assemblers)

Limits to lower friction despite higher bearing area:
This pages covers math determining the optimal number of sub layers for minimal frictive losses.
As it turns out this coincides with where the scaling law of higher throughput of smaller machinery breaks down.

Math of convergent assembly:
Level throughput balancing
TODO

Nanofactory design parameters

See: Gem-gum factory design parameters

• Compenslow: This is a parameter quantifying increase of internal bearing are for reducing friction.
• B … Branching factor
• F … Chamber to part size ratio
• C … Scaling factor (near one) for average distance traveled per one-part-placed
• D … Scaling factor (slightly above one) for chip-area per chamber-area

(wiki-TODO: revolve conflict with D on page …)

Math on the basics

• Friction – Main goal: getting a reasonable (and better confirmed) quantitative estimate on levels of
  dynamic friction in atomically precise sliding bearings
• Scaling law – corroborating that while physics change when going down to the nanoscale
  it's not necessarily for the worse for macroscale style machinery, but rather often surprisingly much for the better.

Related

• Exotic math

For more complete list of pages with math go to the category page:.