pfc-util 0.4.4

package for PFC (phase field crystal) simulations

PFC simulation in python

created by michael in 2022/04

pfc_util is a python package for PFC (phase field crystal) simulations.

Dependencies

• numpy

• scipy

• matplotlib

• pyfftw

• torusgrid

• rich

Installation

Install via pip:

pip install pfc-util

Modules

pfc_util.core - Core module; definitions of PFC free energy functional, state functions, as well as minimizers

pfc_util.extra - Extensions to vanilla PFC. Currently includes pfc6, which is a 6th-order generalization to the PFC functional

pfc_util.toolkit - Static preminimized solid/liquid profiles & utility functions.

Minimizers

The package provides three main means of minimizing/evolving a PFC system:

• Constant chemical potential - The grand potential \(\Omega \equiv F - \mu \int d\mathbf{r} \psi\) is minimized with fixed \(\mu\)

• Stress relaxer - The grand potential density \(\omega \equiv \Omega / V\) is minimized with respect to the density field and system size with fixed \(\mu\)

• Conserved dynamics - The free energy \(F\) is minimized with fixed \(\bar\psi\)

Example Code Snippet

The following code snippet will retrieve a preminimized solid unit cell, evolve it under \(\epsilon=0.05\) and \(\mu=0.08\) until \(\bar\psi\) barely changes, and save the newly minimized unit cell to solid_eps0.05_mu0.08.field

import pfc_util as pfc
import torusgrid as tg

'''Get a preminimized solid profile at epsilon = 0.1'''
solid = pfc.toolkit.get_unit_cell(eps='0.1')


'''Minimize this profile at epsilon = 0.2 and mu = 0.26'''
pfc.ConstantMuMinimizer(solid, dt=0.001, eps=0.05, mu=0.08).run(
        n_steps=31, # n_steps means the number of evolution steps between hook calls
                    # hooks are invoked to update display, monitor values, etc
        hooks= (
            tg.dynamics.Display() # add display capability
            + tg.dynamics.Panel() # add a panel to live display
            + tg.dynamics.MonitorValues(
                {'psibar': lambda e: e.field.psi.mean()},
                period=8
            ) # tell the minimizer that psi.mean() should be monitored and stored as "psibar"
              # here e refers to the minimizer instance
              # period = 8 means that the values are logged every 8 hook calls
              # so in this case we would be calculating the values every 31*8 = 248 time steps
            + tg.dynamics.Text('psibar={psibar:.8f}')
            + tg.dynamics.DetectSlow(
                'psibar', rtol=1e-9, atol=0, period=8, patience=200
            ) # make the minimizer stop if psibar varies sufficiently slowly
        )
    )

tg.save(solid, './solid_eps0.05_mu0.08.field') # save the minimized field