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 “\sigma = 1” of the Lennard-Jones potential may be interpreted as \sigma = 1\,\text{m}, \sigma =
1\,\text{pm}, or even \sigma = 3.4\,\AA (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