typeset reduced units

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   units metal

   units lj

For style *lj*\ , all quantities are unitless.  Without loss of

generality, LAMMPS sets the fundamental quantities mass, sigma,

epsilon, and the Boltzmann constant = 1.  The masses, distances,

generality, LAMMPS sets the fundamental quantities mass, :math:`\sigma`,

:math:`\epsilon`, and the Boltzmann constant :math:`k_B = 1`.

The masses, distances,

energies you specify are multiples of these fundamental values.  The

formulas relating the reduced or unitless quantity (with an asterisk)

to the same quantity with units is also given.  Thus you can use the

mass & sigma & epsilon values for a specific material and convert the

results from a unitless LJ simulation into physical quantities.

* mass = mass or m

* distance = sigma, where x\* = x / sigma

* time = tau, where t\* = t (epsilon / m / sigma\^2)\^1/2

* energy = epsilon, where E\* = E / epsilon

* velocity = sigma/tau, where v\* = v tau / sigma

* force = epsilon/sigma, where f\* = f sigma / epsilon

* torque = epsilon, where t\* = t / epsilon

* temperature = reduced LJ temperature, where T\* = T Kb / epsilon

* pressure = reduced LJ pressure, where P\* = P sigma\^3 / epsilon

* dynamic viscosity = reduced LJ viscosity, where eta\* = eta sigma\^3 / epsilon / tau

* charge = reduced LJ charge, where q\* = q / (4 pi perm0 sigma epsilon)\^1/2

* dipole = reduced LJ dipole, moment where \*mu = mu / (4 pi perm0 sigma\^3 epsilon)\^1/2

* electric field = force/charge, where E\* = E (4 pi perm0 sigma epsilon)\^1/2 sigma / epsilon

* density = mass/volume, where rho\* = rho sigma\^dim

* mass = mass or *m*

* distance = :math:`\sigma`, where :math:`x^* = \frac{x}{\sigma}`

* time = :math:`\tau`, where :math:`\tau^* = \tau \sqrt{\frac{\epsilon}{m \sigma^2}}`

* energy = :math:`\epsilon`, where :math:`E^* = \frac{E}{\epsilon}`

* velocity = :math:`\frac{\sigma}{\tau}`, where :math:`v^* = v \frac{\tau}{\sigma}`

* force = :math:`\frac{\epsilon}{\sigma}`, where :math:`f^* = f \frac{\sigma}{\epsilon}`

* torque = :math:`\epsilon`, where :math:`t^* = \frac{t}{\epsilon}`

* temperature = reduced LJ temperature, where :math:`T^* = \frac{T k_B}{\epsilon}`

* pressure = reduced LJ pressure, where :math:`p^* = p \frac{\sigma^3}{\epsilon}`

* dynamic viscosity = reduced LJ viscosity, where :math:`\eta^* = \eta \frac{\sigma^3}{\epsilon\tau}`

* charge = reduced LJ charge, where :math:`q^* = q \frac{1}{\sqrt{4 \pi \varepsilon_0 \sigma \epsilon}}`

* dipole = reduced LJ dipole, moment where :math:`\mu^* = \mu \frac{1}{\sqrt{4 \pi \varepsilon_0 \sigma^3 \epsilon}}`

* electric field = force/charge, where :math:`E^* = E \frac{\sqrt{4 \pi \varepsilon_0 \sigma \epsilon} \sigma}{\epsilon}`

* density = mass/volume, where :math:`\rho^* = \rho \sigma^{dim}`

Note that for LJ units, the default mode of thermodynamic output via

the :doc:`thermo_style <thermo_style>` command is to normalize all

"""""""

.. parsed-literal::

.. code-block:: LAMMPS

   units lj