External Quartic Potential Fix

Overview

Applies an external potential to a group of atoms to mimic confinement in a quartic/double well potential.

\[U_{\text{ext}} = \sum_{i=1}^4 \mathbf{k}_i\cdot(\Delta \mathbf{r})^i,\]

where \(\mathbf{k}_i=(k_{ix},k_{iy},k_{iz}) \text{for} i = 1,\dots,4, \Delta \mathbf{r} = (\mathbf{r} - \mathbf{r}_0)\) for \(\mathbf{r}_0=(r_{x0},r_{y0},r_{z0})\). Here, each of the \(\mathbf{k}_i\) and \(\mathbf{r}_0\) are Vector parameters that must be set to define the external potential. As the parameters are vectors, one- and two-dimensional potentials may be created by setting some of the spring coefficients to zero.

Quartic potentials are defined directly within the python input script as a Fix using its constructor.

Constructor

FixExternalQuartic(state,handle,groupHandle,k1,k2,k3,k4,r0)

Arguments

state

Simulation state to apply the fix.

handle

A name for the object. Named argument.

groupHandle

Group of atoms to which the fix is applied. Named argument. Defaults to all.

k1

Vector of spring constant coefficient for \(k_{1x},k_{1y},k_{1z}\) for strength of linear portion of confining potential in each dimension. These are specified as Vector(k1x,k1y,k1z).

k2

Vector of spring constant coefficient for \(k_{2x},k_{2y},k_{2z}\) for strength of quadratic portion of confining potential in each dimension. These are specified as Vector(k2x,k2y,k2z).

k3

Vector of spring constant coefficient for \(k_{3x},k_{3y},k_{3z}\) for strength of cubic portion of confining potential in each dimension. These are specified as Vector(k3x,k3y,k3z).

k4

Vector of spring constant coefficient for \(k_{4x},k_{4y},k_{4z}\) for strength of quartic portion of confining potential in each dimension. These are specified as Vector(k4x,k4y,k4z).

r0

Vector of minima \(r_{x0},r_{y0},k_{z0}\) in each dimension for the harmonic potential. These are specified as Vector(rx,ry,rz).

Examples

Adding and activating the fix

#Add Fix for external quartic potential
UextDblWell = FixExternalQuartic(state,handle='Udbl',groupHandle='all',
  k1 = Vector(0.0,0.0,0.0),
  k2 = Vector(-1.,-1.,-1.),
  k3 = Vector(0.0,0.0,0.0),
  k4 = Vector(0.015,0.015,0.015),
  r0 = Vector(0.0,0.0,1.0))
#Activate fix
state.activateFix(UextDblWell)