Notation

The hoomd-rs documentation uses the following mathematical notation.

General notation:

Symbol	Definition
$x$	Scalar.
$a$	Vector.
$a$	Magnitude of the vector $a$ .
$\overset{a}{^}$	Unit vector in the direction of $a$ .
$A$	Matrix.
$b$	Quaternion.
$∣ b ∣$	Magnitude of a quaternion.
$i$ , $j$ , $k$	Indices.
$i$	$- 1$ in some contexts.
$function$	A mathematical function.
a $[length]^{2}$	The quantity "a" has dimensions of $length^{2}$ .

Symbol definitions:

Symbol	Definition
$v_{ij}$	$v_{j} - v_{j}$
$r$	Position.
$v$	Velocity.
$q$	Orientation.
$m$	Mass.
$p$	Momentum.
$I$	Moment of inertia.
$q$	Charge.
$N$	Number.
$L$	Length.
$V$	Volume.
$P$	Pressure.
$ρ$	Number density.
$a_{1}$ , $a_{2}$ , $a_{3}$	Box unit cell vectors.
$F$	Force.
$τ$	Torque.
$U$	Potential energy.
$K$	Kinetic energy.
$E$	Total energy.
$T$	Temperature.
$k$	Boltzmann's constant in some contexts. Typically appears multiplying temperature: $k T$ .
$k$	Spring constant in some contexts.
$β$	$\frac{1}{k T}$
$t$	Time.

Development of hoomd-rs is led by the Glotzer Group at the University of Michigan.

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