2.9. Order Parameters¶
2.9.1. Order parameter initialisations¶
2.9.1.1. Composition \(\phi\)¶
The following initialisations are available.
phi_initialisation spinodal # spinodal
phi0 0.0 # mean
noise 0.05 # noise amplitude
random_seed 102839 # +ve integer
Suitable for initialising isothermal spinodal decomposition, the order parameter may be set at random at each position via \(\phi = \phi_0 + A(\phi_r - 1/2)\) with the random variate \(\phi_r\) selected uniformly on the interval \([0,1)\). For symmetric quenches (mean order parameter \(\phi_0 = 0\) and \(\phi^\star = \pm 1\)), a value of \(A\) in the range 0.05-0.1 is usually appropriate.
For off-symmetric quenches, larger patches of fluid may be required to initiate decomposition:
phi_initialisation patches # patches of phi = +/- 1
phi_init_patch_size 2 # patch size
phi_init_patch_vol 0.1 # volume fraction phi = -1 phase
random_seed 13 # +ve integer
The initialises cubics patches of fluid of given size with \(\phi= \pm 1\) at random. The requested overall volume fractions may be met approximately.
A uniform value of the order parameter may be apprpropriate for some situations. This is arranged using a single value \(\phi_0\):
phi_initialisation uniform # same everywhere
phi0 0.2 # the uniform value
A spherical drop can be initialised at the centre of the system.
phi_initialisation drop # spherical droplet
phi_init_drop_radius 16.0 # radius
phi_init_drop_amplitude -1.0 # phi value inside
The drop is initialised with a \(\tanh(r/\xi)\) profile where the interfacial width \(\xi\) is computed via the current free energy parameters.
A pair of plane interfaces at \(z = L_z/4\) and \(z=3L_z/4\) may be initialised via
phi_initialisation block
The interfacial width is again set via the current free energy parameters. The centre of the system has order parameter \(\phi = +\phi^\star\).
For restarted simulations, the default position is to read order parameter information from file
phi_initialisation from_file
in which case a file or files for the appropriate time step should be present in the working directory.
2.9.2. Tensor order parameter¶
A number of different initialisations are available for the liquid crystal order parameter \(Q_{\alpha\beta}\). Some care may be required to ensure consistency between the choice and the free energy parameters, the system size, and so on (particularly for the blue phases).
A summary of choices is:
lc_q_initialisation nematic # uniform nematic...
lc_init_nematic 1.0_0.0_0.0 # ...with given director
lc_q_initialisation cholesteric_x # cholesteric with helical axis x
lc_q_initialisation cholesteric_y # cholesteric with helical axis y
lc_q_initialisation cholesteric_z # cholesteric with helical axis z
lc_q_initialisation o8m # BPI high chirality limit
lc_q_initialisation o2 # BPII high chirality limit
lc_q_initialisation o5
lc_q_initialisation h2d # 2d hexagonal
lc_q_initialisation h3da # 3d hexagonal BP A
lc_q_initialisation h3db # 3d hexagonal BP B
lc_q_initialisation dtc # double twist cylinders
lc_q_initialisation bp3
lc_q_initialisation cf1_x # cholesteric ``finger'' axis x
lc_q_initialisation cf1_y # cholesteric ``finger'' axis y
lc_q_initialisation cf1_z # cholesteric ``finger'' axis z
lc_q_initialisation cf1_fluc_x # as cf1_x with random perterbations
lc_q_initialisation cf1_fluc_y # as cf1_y with random perturbations
lc_q_initialisation cf1_flux_z # as cf1_z with random perturbations
lc_q_initialisation random # with randomly chosen unit director
lc_q_initialisation random_xy # random nematic in (x,y) plane
Note many of the initialiations require an initial amplitude of order, which should be set via
lc_q_init_amplitude 0.01 # initial amplitude of order A
For example, if an initial uniform nematic is requested with unit director \(n_\alpha\), the corresponding initial tensor will be