Collisions¶

Particula-beta Index / Particula Beta / Lagrangian / Collisions

Auto-generated documentation for particula_beta.lagrangian.collisions module.

coalescence¶

Update mass and velocity of particles based on collision pairs, conserving mass and momentum.

This function processes collision pairs, sorts them to avoid duplicate handling, and then updates the mass and velocity of colliding particles according to the conservation of mass and momentum.

Arguments¶

position torch.Tensor - A 2D tensor of shape [n_dimensions, n_particles] representing the positions of particles.
velocity torch.Tensor - A 2D tensor of shape [n_dimensions, n_particles] representing the velocities of particles.
mass torch.Tensor - A 1D tensor containing the mass of each particle.
radius torch.Tensor - A 1D tensor containing the radius of each particle.
collision_indices_pairs torch.Tensor - A 2D tensor containing pairs of indices representing colliding particles.
remove_duplicates_func function - A function to remove duplicate entries from a tensor of index pairs.

Returns¶

- torch.Tensor - A 2D tensor of shape [n_dimensions, n_particles] representing the updated velocities of particles.

Notes¶

This function modifies the velocity and mass tensors in-place.
It assumes that the mass and momentum are transferred from the right particle to the left in each collision pair.
The subtraction approach for the right-side particles ensures no mass is lost in multi-particle collisions (e.g., A<-B and B<-D).

Signature¶

def coalescence(
    position: torch.Tensor,
    velocity: torch.Tensor,
    mass: torch.Tensor,
    radius: torch.Tensor,
    collision_indices_pairs: torch.Tensor,
) -> Tuple[torch.Tensor, torch.Tensor]: ...

elastic_collision¶

Show source in collisions.py:139

Update velocities of particles based on elastic collision pairs using matrix operations, conserving kinetic energy and momentum.

Arguments¶

velocity torch.Tensor - A 2D tensor of shape [n_dimensions, n_particles] representing the velocities of particles.
mass torch.Tensor - A 1D tensor containing the mass of each particle.
collision_indices_pairs torch.Tensor - A 2D tensor containing pairs of indices representing colliding particles.
remove_duplicates_func function - A function to remove duplicate entries from a tensor of index pairs.

Returns¶

torch.Tensor - A 2D tensor of shape [n_dimensions, n_particles] representing the updated velocities of particles.

Notes¶

This function modifies the velocity tensor in-place.
Mass remains unchanged in elastic collisions.

Examples¶

2d - https://www.wolframalpha.com/input?i=elastic+collision&assumption=%7B%22F%22%2C+%22ElasticCollision%22%2C+%22m2%22%7D+-%3E%221+kg%22&assumption=%7B%22F%22%2C+%22ElasticCollision%22%2C+%22m1%22%7D+-%3E%221+kg%22&assumption=%22FSelect%22+-%3E+%7B%7B%22ElasticCollision2D%22%7D%7D&assumption=%7B%22F%22%2C+%22ElasticCollision%22%2C+%22v1i%22%7D+-%3E%221+m%2Fs%22&assumption=%7B%22F%22%2C+%22ElasticCollision%22%2C+%22v2i%22%7D+-%3E%22-0.5+m%2Fs%22
3d fortran - https://www.plasmaphysics.org.uk/programs/coll3d_for.htm https://www.plasmaphysics.org.uk/collision3d.htm

I think the approach is take a pair, and rotate the coordinate system so that the collision is in the x-y plane. Then, the z component of the velocity is a 1d problem, and the x-y component is a 2d problem. Then, rotate back to the original coordinate system.

Signature¶

def elastic_collision(
    velocity: torch.Tensor, mass: torch.Tensor, collision_indices_pairs: torch.Tensor
) -> torch.Tensor: ...

find_collisions¶

Show source in collisions.py:9

Find the collision pairs from a distance matrix, given the mass and indices of particles.

This function identifies pairs of particles that are within a certain distance threshold (<0), indicating a collision. It filters out pairs involving particles with zero mass.

Arguments¶

distance_matrix torch.Tensor - A 2D tensor containing the pairwise distances between particles.
indices torch.Tensor - A 1D tensor containing the indices of the particles.
mass torch.Tensor - A 1D tensor containing the mass of each particle.
k int, optional - The number of closest neighbors to consider for each particle. Defaults to 1.

Returns¶

torch.Tensor - A 2D tensor of shape [n_collisions, 2] containing the indices of colliding pairs of particles.

Notes¶

The function assumes that the diagonal elements of the distance matrix (distances of particles to themselves) are less than zero.
Particles with zero mass are excluded from the collision pairs.

Signature¶

def find_collisions(
    distance_matrix: torch.Tensor, indices: torch.Tensor, mass: torch.Tensor, k: int = 1
) -> torch.Tensor: ...