Notation

The HOOMD-blue documentation uses the following mathematical notation.

General notation:

\(x\)

Scalar.

\(\vec{a}\)

Vector.

\(a\)

Magnitude of the vector \(\vec{a}\).

\(\hat{a}\)

Unit vector in the direction of \(\vec{a}\).

\(\mathbf{A}\)

Matrix.

\(\mathbf{b}\)

Quaternion.

\(\vert \mathbf{b} \vert\)

Magnitude of a quaternion.

\(i\), \(j\), \(k\)

Indices.

\(i\)

\(\sqrt{-1}\) in some contexts.

\(\mathrm{function}\)

A mathematical function.

a \([\mathrm{length}]^2\)

The quantity “a” has dimensions of \(\mathrm{length}^2\).

Symbol definitions:

\(\vec{v}_{ij}\)

\(\vec{v}_j - \vec{v}_j\)

\(\vec{r}\)

Position.

\(\vec{v}\)

Velocity.

\(\mathbf{q}\)

Orientation.

\(m\)

Mass.

\(\vec{p}\)

Momentum.

\(I\)

Moment of inertia.

\(q\)

Charge.

\(N\)

Number.

\(L\)

Length.

\(V\)

Volume.

\(P\)

Pressure.

\(\rho\)

Number density.

\(\vec{a}_1\), \(\vec{a}_2\), \(\vec{a}_3\)

Box unit cell vectors.

\(\vec{F}\)

Force.

\(\vec{\tau}\)

Torque.

\(U\)

Potential energy.

\(K\)

Kinetic energy.

\(E\)

Total energy.

\(T\)

Temperature.

\(k\)

Boltzmann’s constant in some contexts. Typically appears multiplying temperature: \(kT\).

\(k\)

Spring constant in some contexts.

\(\beta\)

\(\frac{1}{kT}\)

\(t\)

Time.