Blob Shapes

We can choose between four different blob shapes that are specified with the blob_shape argument of the Model class.

The blob shape consists of two parts, the blob shape in the propagation direction and the blob shape in the perpendicular direction thereof. The propagation direction is calculated from vx and vy of each individual blob (see Blob Alignment for further details).

You can choose one of the following blob shapes for the propagation and perpendicular direction:

“exp”	“gauss”	“lorentz”	“secant”	“dipole”
Exponential Pulse	Gaussian Pulse	Lorentz Pulse	Secant Pulse	Dipole Pulse
`np.exp(theta) * np.heaviside(-1.0 * t, 1)`	`1 / np.sqrt(2np.pi) np.exp(-(t**2)/2)`	`1 / (np.pi * (1 + t**2))`	`2 / np.pi / (np.exp(t) + np.exp(-t))`	`-2 * theta / np.sqrt(np.pi) * np.exp(-(theta**2))`

Propagation direction

If you specify the blob_shape as a string such as blob_shape = "exp", the specified blob shape will be used in the propagation direction. The perpendicular blob shape will be set to gauss.

Perpendicular direction

In order to specify the blob shape in the perpendicular direction we need to specify the blob shapes with the BlobShapeImpl class. The first argument refers to the propagation direction and the second one refers to the perpendicular direction. An example would look like this:

from blobmodel import Model, BlobShapeImpl

bm = Model(
    Nx=100,
    Ny=100,
    Lx=10,
    Ly=10,
    dt=0.1,
    T=10,
    num_blobs=10,
    blob_shape=BlobShapeImpl("exp", "lorentz"),
    periodic_y=True,
    t_drain=1e10,
)

Two-sided exponential blob shape

The last blob shape we discuss is the two-sided exponential blob shape. In contrast to the shapes above, it requires an asymmetry parameter lam to specify the exact shape. The shape is implemented as follows:

shape[t < 0] = np.exp(t[t < 0] / lam)
shape[t >= 0] = np.exp(-t[t >= 0] / (1 - lam))

We specify the asymmetry parameter when defining the blob_factory. An example would look like this:

bf = DefaultBlobFactory(
    A_dist="deg",
    wx_dist="deg",
    spx_dist="deg",
    spy_dist="deg",
    shape_param_x_parameter=0.5,
    shape_param_y_parameter=0.5,
)

bm = Model(
    Nx=100,
    Ny=100,
    Lx=10,
    Ly=10,
    dt=0.1,
    T=10,
    num_blobs=10,
    blob_shape=BlobShapeImpl("2-exp", "2-exp"),
    t_drain=1e10,
    blob_factory=bf,
)

Take a look at examples/2_sided_exp_pulse.py for a fully implemented example.