Class: Nematic Liquid Crystal

Nematic Liquid Crystal model.

class comfit.nematic_liquid_crystal.nematic_liquid_crystal.NematicLiquidCrystal(dim, **kwargs)

Bases: BaseSystem

__init__(dim, **kwargs)

Initializes a system to simulate a (active) nematic liquid crystal

Parameters

dimint: The dimension of the system.
kwargsdict, optional: Optional keyword arguments to set additional parameters. See https://comfitlib.com/ClassNematicLiquidCrystal/

Returns

NematicLiquidCrystal: The system object representing the nematic simulation.

Examples

>>> nematic = NematicLiquidCrystal(2, xRes=100, yRes = 100, alpha=-0.5)
Creates a nematic liquid crystal with 2 dimensions and a spatial resolution of 100.
The activity alpha is set to -0.5.

calc_active_force_f(Q)

Function that calculates the active force in Fourier space.

Parameters

Qnumpy.ndarray: the order parameter that we use to find the force.

Returns

numpy.ndarray: The active force in Fourier space

calc_disclination_density()

Calculates the disclination density for the nematic. Note that in three dimension the disclination density is a tensor

Returns

numpy.ndarray: The disclination density

calc_disclination_density_decoupled()

Calculates the decoupled disclination density in three dimensions.

Returns

omeganumpy.ndarray: The scalar magnitude of the disclination density tensor.
rotation_fieldnumpy.ndarray: The rotation vector field, the leading eigenvector of the disclination density tensor contracted with its transpose.
Tnumpy.ndarray: The tangent vector, the leading eigenvector of the disclination density tensor’s transpose contracted with itself.
rho_tracenumpy.ndarray: The trace of the disclination density tensor.

calc_disclination_nodes(dt_Q=None, polarization=None, charge_tolerance=0.1)

Calculates the positions and charges of disclination nodes based on the disclination density.

Parameters

dt_Qnumpy.ndarray, optional: The time derivative of the order parameter. If not provided, the velocity of the disclination nodes will not be calculated.
polarizationnumpy.ndarray, optional: The polarization field for positive defects in 2D. If provided the direction of the positive defects are shown.
charge_tolerancefloat, optional: The tolerance given to the defect finding algorithm in 3D. Default 0.1

Returns

list of dict

A list of dictionaries representing the disclination nodes. Each dictionary contains the following keys:

‘position_index’: The position index of the disclination node in the disclination density array.
‘charge’: The charge of the disclination node.
‘position’: The position of the disclination node as a list [x, y].
‘velocity’: The velocity of the disclination node as a list [vx, vy].

In 3F the charge key is removed and we instead have

-‘tangent_vector’: The tangent vector of the dislocation -‘rotation_vector’: The rotation vector of the dislocation

calc_disclination_polarization_field()

Calculates the polarization field of the disclination in two dimensions

Returns

numpy.ndarray: The polarization field

calc_disclination_velocity_field(dt_Q, tangent_vector=None, rotation_vector=None, g_matrix=None, disclination_density_magnitude=None)

Calculates the velocity field of the disclination in two dimensions

Parameters

dt_Qnumpy.ndarray: the time derivative of the order parameter
tangent_vectornumpy.ndarray, optional: the unit tangent vector to the disclination line (3D only)
rotation_vectornumpy.ndarray, optional: the unit rotation vector of the disclination line, i.e. the axis about which the director winds (3D only)
g_matrixnumpy.ndarray, optional: the auxiliary tensor coupling dt_Q to the spatial derivatives of self.Q, from calc_g_matrix (3D only)
disclination_density_magnitudenumpy.ndarray, optional: the scalar magnitude of the disclination density tensor (3D only)

Returns

numpy.ndarray: The velocity field. Note in 2D this returns a field while in 3D this is returning a vector

calc_dt_psi(Q_prev, delta_t)

Calculates the time derivative of the order parameter as a complex field

Parameters

Q_prevnumpy.ndarray: the order parameter at the previous time step
delta_tfloat: the time step

Returns

numpy.ndarray: The time derivative of the order parameter

calc_equilibrium_S()

Calculates the strength of nematic order S

Returns

numpy.ndarray: equilibrium value of S

calc_g_matrix(dt_Q)

Calculates the matrix g, that is used to find the disclination velocity in 3D

Returns

numpy.ndarray: The g matrix

calc_gradient_pressure_f(p_f)

Calculates the gradient of the pressure

Parameters

p_fnumpy.ndarray: the pressure in Fourier space

Returns

numpy.ndarray: Gradient of the pressure

calc_molecular_field(Q)

Finds the molecular field

Parameters

Qnumpy.ndarray: The nematic tensor

Returns

numpy.ndarray: The molecular field

calc_nonlinear_evolution_function_f(Q, t)

Calculates the non-linear evolution function for the nematic

Parameters

Qnumpy.ndarray: the nematic order parameter

Returns

numpy.ndarray: The non-linear evolution function evaluated in Fourier space

calc_nonlinear_evolution_term_no_flow_f(Q, t)

Calculates the non-linear evolution function for the nematic without the flow field

Parameters

Qnumpy.ndarray: the nematic order parameter

Returns

numpy.ndarray: The non-linear evolution function evaluated in Fourier space

calc_order_and_director()

Calculates the amount of order (S) and the director field (n)

Returns

tuple

Tuple consisting of

Amount of order (scalar field)
the director field (vector field)

calc_passive_force_f(Q)

Calculates the passive force in Fourier space

Parameters

Qnumpy.ndarray: the order parameter that we use to find the force.

Returns

numpy.ndarray: The passive force in Fourier space

calc_passive_stress_f(Q)

Calculates the passive stress in Fourier space

Parameters

Qnumpy.ndarray: the order parameter that we use to find the stress.

Returns

numpy.ndarray: The passive stress in Fourier space

calc_pressure_f(F_af, F_pf)

Calculates the pressure in Fourier space. The zero mode is set to zero

Parameters

F_afnumpy.ndarray: the active force in Fourier space
F_pfnumpy.ndarray: the passive force in Fourier space

Returns

numpy.ndarray: The pressure

calc_strain_rate_tensor_f()

Calculates the strainrate tensor

Returns

numpy.ndarray: The strainrate

calc_trace_Q2(Q)

calc_vorticity_tensor()

Calculates the vorticity tensor

Returns

numpy.ndarray: The vorticity tensor

conf_active_channel(width=None, interface_width=7)

Configures the activity to zero everywhere except for inside a channel of width “width”

Parameters

widthfloat: width of the channel
interface_widthfloat, optional: width of interface

Returns

None: Updates the activity to the channel configuration.

conf_initial_condition_ordered(noise_strength=0.01)

Configures the system with the nematogens pointing in the x-direction in 2D and in the z-direction in 3D with some random noise in the angle.

Parameters

noise_strengthfloat: A measure for how much noise to put in the angle

Returns

None: Initialises self.Q and self.Q_f

Raises

Exception: If the dimension is not 2 or 3

conf_initial_disclination_lines(position1=None, position2=None)

Sets the initial condition for a disclination line in a 3-dimensional system.

The dislocation is parallel to the z-axis

Parameters

position1list: the position of the first dislocation. Only the position in the xy plane is used

Returns

None: Sets the value of self.Q and self.Q_f

conf_insert_disclination_dipole(dipole_vector=None, dipole_position=None)

Sets the initial condition for a disclination dipole configuration in a 2-dimensional system.

Returns

None: Configures self.Q and self.Q_f with a disclination dipole configuration.

Raises

Exception: If the dimension of the system is not 2.

conf_velocity(Q)

Updates the velocity and its fourier transform given a nematic field Q.

Parameters

Qnumpy.ndarray: the Q tensor

Returns

None: Updates self.u and self.u_f.

evolve_nematic(number_of_steps, method='ETD2RK')

Evolves the nematic system

Parameters

number_of_stepsint: the number of time steps that we are evolving the equation
methodstring: the integration method we want to use. ETD2RK is sett as default

Returns

None: Updates the fields self.Q and self.Q_f

evolve_nematic_no_flow(number_of_steps, method='ETD2RK')

Evolves the nematic system without the flow field

Parameters

number_of_stepsint: the number of time steps that we are evolving the equation
methodstring: the integration method we want to use. ETD2RK is sett as default

Returns

None: Updates the fields self.Q and self.Q_f

plot_field_velocity_and_director(field, velocity, director, **kwargs)

comfit.nematic_liquid_crystal.plot_field_velocity_and_director_matplotlib.plot_field_velocity_and_director_matplotlib(self, field, velocity, director, **kwargs)

Plot the fields, velocity, and director field in 2 dimensions

Parameters

fieldndarray: The field to be plotted.
velocityndarray: The velocity to be plotted.
directorndarray: The director to be plotted.
**kwargsAny: Keyword arguments for the plot. See https://comfitlib.com/ClassBaseSystem/ for a full list of keyword arguments.

Returns

tuple

A tuple consisting of

The figure
The axes with the plotted field, velocity, and director.

Raises

Exception: If the dimension is other than 2.

comfit.nematic_liquid_crystal.plot_field_velocity_and_director_plotly.plot_field_velocity_and_director_plotly(self, field, velocity, director, **kwargs)

Plot the fields, velocity, and director field in 2 dimensions using Plotly.

Parameters

fieldndarray: The field to be plotted.
velocityndarray: The velocity to be plotted.
directorndarray: The director to be plotted.
**kwargsAny: Keyword arguments for the plot.

Returns

go.Figure: The plotly figure.