38. lepm.build.build_hexagonal¶
Description here
38.1. Example Usage¶
38.2. Overview¶
38.3. Classes and Functions¶
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lepm.build.build_hexagonal.add_PV(ind, want, xypts, LVUC, PV, NL, KL, BL, PVx, PVy, PVxydict, msg='', check=False)[source]¶ Parameters: ind :
want :
xypts :
LVUC :
PV :
NL :
KL :
PVx :
PVy :
PVxydict :
msg :
check :
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lepm.build.build_hexagonal.build_accordionhex(lp)[source]¶ Build hexagonal-like lattice, replacing each bond with a zigzag set of bonds
Parameters: lp : dict
lattice parameters dictionary
Returns: xy, NL, KL, BL, PVx, PVy, PVxydict, LVUC, BBox, LL, LV, UC, lattice_exten, lp :
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lepm.build.build_hexagonal.build_frame1dhex(lp)[source]¶ Generate the boundary of a hexagonal lattice, with no bulk.
Parameters: lp :
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lepm.build.build_hexagonal.build_hexagonal(lp)[source]¶ Create a hexagonal lattice using lattice parameters lp. Note that either ‘delta’ (a float, opening angle in radians) or ‘delta_lattice’ (a string, angle in units of pi) must be in lp
Parameters: lp :
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lepm.build.build_hexagonal.build_hexjunction(lp)[source]¶ Create a Y junction of gyros, with accordionized bonds going in and out
Parameters: lp :
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lepm.build.build_hexagonal.generate_flattened_honeycomb_lattice(lp)[source]¶ Generates hexagonal lattice with two different bond lengths on the sides and top of each hexagon. The ratio between the long and the short one is given by aratio, and the long one is length unity. (returns points, connectivity, name). This is the first step in making the Cairo lattice.
Parameters: lp : dict
lattice parameters with key, value pairs: shape : string or dict with keys ‘description’:string and ‘polygon’:polygon array
Global shape of the mesh, in form ‘square’, ‘hexagon’, etc or as a dictionary with keys shape[‘description’] = the string to name the custom polygon, and shape[‘polygon’] = 2d numpy array
- NH : int
Number of pts along horizontal. If shape=’hexagon’, this is the width (in cells) of the bottom side (a)
- NV : int
Number of pts along vertical, or 2x the number of rows of lattice
- aratio : float
ratio between long and short lines, with long one of length unity.
- delta : float
Deformation angle for the lattice in degrees (for undeformed hexagonal lattice, this is 0.66666*np.pi)
- phi : float
Shear angle for the lattice in radians, must be less than pi/2 (for undeformed hexagonal lattice, this is 0.000)
- eta : float
randomization of the lattice (a scaling of random jitter in units of lattice spacing)
- rot : float
angle in units of pi to rotate the lattice vectors and unit cell
- periodicBC : bool
Whether to apply periodic boundaries to the network
- check : bool
Whether to plot output at intermediate steps
Returns: xy : matrix of dimension nx2
Equilibrium lattice positions
NL : matrix of dimension n x (max number of neighbors)
Each row corresponds to a gyroscope. The entries tell the numbers of the neighboring gyroscopes
KL : matrix of dimension n x (max number of neighbors)
Correponds to Ni matrix. 1 corresponds to a true connection while 0 signifies that there is not a connection
BL : array of dimension #bonds x 2
Each row is a bond and contains indices of connected points
lattice_exten : string
description of the lattice, complete with parameters for properly saving the lattice files
LV : 3 x 2 float array
Lattice vectors for the kagome lattice with input twist angle
UC : 6 x 2 float array
(extended) unit cell vectors
PVxydict : dict
dictionary of periodic bonds (keys) to periodic vectors (values) If key = (i,j) and val = np.array([ 5.0,2.0]), then particle i sees particle j at xy[j]+val –> transforms into: ijth element of PVx is the x-component of the vector taking NL[i,j] to its image as seen by particle i
PVx : NP x NN float array
ijth element of PVx is the x-component of the vector taking NL[i,j] to its image as seen by particle i If NL and KL are remade, PVx will not be ordered properly: use dict instead
PVy : NP x NN float array
ijth element of PVy is the y-component of the vector taking NL[i,j] to its image as seen by particle i If NL and KL are remade, PVy will not be ordered properly: use dict instead
LVUC : NP x 3 array
Lattice vectors and (extended) unit cell vectors defining relative position of each point, as integer multiples of LV[0] and LV[1], and UC[LVUC[i,2]] For instance, xy[0,:] = LV[0]*LVUC[0,0] + LV[1]*LVUC[0,1] + UC[LVUC[0,2]]
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lepm.build.build_hexagonal.generate_honeycomb_lattice(lp)[source]¶ Generates hexagonal lattice (points, connectivity, name).
Parameters: lp : dict
lattice parameters dictionary, with keys:
shape : string or dict with keys ‘description’:string and ‘polygon’:polygon array
Global shape of the mesh, in form ‘square’, ‘hexagon’, etc or as a dictionary with keys shape[‘description’] = the string to name the custom polygon, and shape[‘polygon’] = 2d numpy array
NH : int
Number of pts along horizontal. If shape=’hexagon’, this is the width (in cells) of the bottom side (a)
NV : int
Number of pts along vertical, or 2x the number of rows of lattice
delta : float
Deformation angle for the lattice in degrees (for undeformed hexagonal lattice, this is 0.66666*np.pi)
phi : float
Shear angle for the lattice in radians, must be less than pi/2 (for undeformed hexagonal lattice, this is 0.000)
eta : float
randomization of the lattice (a scaling of random jitter in units of lattice spacing)
rot : float
angle in units of pi to rotate the lattice vectors and unit cell
periodicBC : bool
Wether to apply periodic boundaries to the network
check : bool
Wehter to plot output at intermediate steps
Returns: xy : matrix of dimension nx2
Equilibrium lattice positions
NL : matrix of dimension n x (max number of neighbors)
Each row corresponds to a gyroscope. The entries tell the numbers of the neighboring gyroscopes
KL : matrix of dimension n x (max number of neighbors)
Correponds to Ni matrix. 1 corresponds to a true connection while 0 signifies that there is not a connection
BL : array of dimension #bonds x 2
Each row is a bond and contains indices of connected points
lattice_exten : string
description of the lattice, complete with parameters for properly saving the lattice files
LV : 3 x 2 float array
Lattice vectors for the kagome lattice with input twist angle
UC : 6 x 2 float array
(extended) unit cell vectors
PVxydict : dict
dictionary of periodic bonds (keys) to periodic vectors (values) If key = (i,j) and val = np.array([ 5.0,2.0]), then particle i sees particle j at xy[j]+val –> transforms into: ijth element of PVx is the x-component of the vector taking NL[i,j] to its image as seen by particle i
PVx : NP x NN float array
ijth element of PVx is the x-component of the vector taking NL[i,j] to its image as seen by particle i If NL and KL are remade, PVx will not be ordered properly: use dict instead
PVy : NP x NN float array
ijth element of PVy is the y-component of the vector taking NL[i,j] to its image as seen by particle i If NL and KL are remade, PVy will not be ordered properly: use dict instead
LVUC : NP x 3 array
Lattice vectors and (extended) unit cell vectors defining relative position of each point, as integer multiples of LV[0] and LV[1], and UC[LVUC[i,2]] For instance, xy[0,:] = LV[0]*LVUC[0,0] + LV[1]*LVUC[0,1] + UC[LVUC[0,2]]
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lepm.build.build_hexagonal.generate_honeycomb_strip(lp)[source]¶ Generates hexagonal strip that is only one cell wide in at least one of the dimensions. Note that this also handles creating the honeycomb unitcell.
Parameters: lp : dict
lattice parameters dictionary, with keys: shape : string
Global shape of the mesh, in form ‘square’, ‘hexagon’, etc or as a dictionary with keys shape[‘description’] = the string to name the custom polygon, and shape[‘polygon’] = 2d numpy array However, since this is a strip, it really only makes sense to use ‘square’
- NH : int
Number of pts along horizontal. If shape=’hexagon’, this is the width (in cells) of the bottom side (a)
- NV : int
Number of pts along vertical, or 2x the number of rows of lattice
- delta : float
Deformation angle for the lattice in degrees (for undeformed hexagonal lattice, this is 0.66666*np.pi)
- phi : float
Shear angle for the lattice in radians, must be less than pi/2 (for undeformed hexagonal lattice, this is 0.000)
- eta : float
randomization of the lattice (a scaling of random jitter in units of lattice spacing)
- rot : float
angle in units of pi to rotate the lattice vectors and unit cell
- periodicBC : bool
Wether to apply periodic boundaries to the network
- check : bool
Wehter to plot output at intermediate steps
Returns: xy : matrix of dimension nx2
Equilibrium lattice positions
NL : matrix of dimension n x (max number of neighbors)
Each row corresponds to a gyroscope. The entries tell the numbers of the neighboring gyroscopes
KL : matrix of dimension n x (max number of neighbors)
Correponds to Ni matrix. 1 corresponds to a true connection while 0 signifies that there is not a connection
BL : array of dimension #bonds x 2
Each row is a bond and contains indices of connected points
lattice_exten : string
description of the lattice, complete with parameters for properly saving the lattice files
LV : 3 x 2 float array
Lattice vectors for the kagome lattice with input twist angle
UC : 6 x 2 float array
(extended) unit cell vectors
PVxydict : dict
dictionary of periodic bonds (keys) to periodic vectors (values) If key = (i,j) and val = np.array([ 5.0,2.0]), then particle i sees particle j at xy[j]+val –> transforms into: ijth element of PVx is the x-component of the vector taking NL[i,j] to its image as seen by particle i
PVx : NP x NN float array
ijth element of PVx is the x-component of the vector taking NL[i,j] to its image as seen by particle i If NL and KL are remade, PVx will not be ordered properly: use dict instead
PVy : NP x NN float array
ijth element of PVy is the y-component of the vector taking NL[i,j] to its image as seen by particle i If NL and KL are remade, PVy will not be ordered properly: use dict instead
LVUC : NP x 3 array
Lattice vectors and (extended) unit cell vectors defining relative position of each point, as integer multiples of LV[0] and LV[1], and UC[LVUC[i,2]] For instance, xy[0,:] = LV[0] * LVUC[0,0] + LV[1] * LVUC[0,1] + UC[LVUC[0,2]]
