Simulation units

Most physical quantities carry a dimension, and their numeric values are meaningful only in conjuction with a suitable unit. A computer, on the other hand, processes just plain numbers. The interpretation of such a numeric value as physical quantity depends on the—completely arbitrary—specification of the associated unit. Within a given simulation, the only constraint is that all units are derived from the same set of base units, e.g., for length, time, mass, temperature, and current/charge.

For example, an interaction range specified as “\(\sigma = 1\)” of the Lennard-Jones potential may be interpreted as \(\sigma = 1\,\text{m}\), \(\sigma = 1\,\text{pm}\), or even \(\sigma = 3.4\,Å\) (for argon). Another more abstract interpretation of “\(\sigma = 1\)” is that all lengths are measured relative to \(\sigma\).

Typical choices for base units along with some derived units are given in the table:

physical dimension	symbol	SI base units	cgs system	abstract units (Lennard-Jones potential)
length	L	metre	centimetre	\(\sigma\)
time	T	second	second	\(\tau=\sqrt{m\sigma^2/\epsilon}\)
mass	M	kilogram	gram	\(m\)
temperature	Θ	kelvin		\(\epsilon/k_\text{B}\)
current	I	ampère	franklin / second	\(q / \tau\)
energy	M×L²×T⁻²	joule	erg	\(\epsilon\)
force	M×L×T⁻²	newton	dyne	\(\epsilon/\sigma = m \sigma / \tau^2\)
pressure	M×L⁻¹×T⁻²	pascal	barye	\(\epsilon/\sigma^3\)
dynamic viscosity	M×L⁻¹×T⁻¹	pascal × second	poise	\(\sqrt{m \epsilon} / \sigma^2 = m/\sigma\tau\)
charge	I×T	ampère × second	franklin	\(q\)