Graduate What is the packet speed in the discrete case?

[intervoxel]

I've been struggling with the problem below for some time. It is not a homework.

A simple bubble S is a spherical surface that expands with constant speed c. A vector bubble V also expands with the same constant speed c. There is a 3d vector associated with a V.

If two S bubbles touch, they are both reissued at the contact point, while two V bubbles never interact.

If an S and a V touch, they are reissued at the point where the line defined by the vector of V, passing through the origins, pierces the respective spherical surface.

Initially, a number of NS of simple bubbles and NV vectorial ones are randomly distributed in a given volume. The vectors are also random but biased in a preferred direction.

As the system evolves, it is supposed that the bubbles move as a packet with constant speed v at the direction of the resultant vector of all the V's vectors.

The space is either continuous or discrete, that is, we have two distinct cases.

What is the packet speed v in the discrete case?

Thanks for any help.

 

[pbuk]

I've been struggling with the problem below for some time. It is not a homework.

A simple bubble S is a spherical surface that expands with constant speed c.

What is it that increases at c: radius, area, volume or something else?

A vector bubble V also expands with the same constant speed c. There is a 3d vector associated with a V.

Presumably this means the length of the vector increases at c.

If two S bubbles touch, they are both reissued at the contact point, while two V bubbles never interact.

What does 'reissued' mean? What happens if the 'reissued' bubbles touch or intersect with each other or some other bubbles?

If an S and a V touch, they are reissued at the point where the line defined by the vector of V, passing through
the origins, pierces the respective spherical surface.

What does 'reissued' mean? What does 'passing through the origins' mean?

Initially, a number of NS of simple bubbles and NV vectorial ones are randomly distributed in a given volume. The vectors are also random but biased in a preferred direction.

What are the initial sizes of the 'bubbles'? How are intersections dealt with?

As the system evolves, it is supposed that the bubbles move as a packet with constant speed v at the direction of the resultant vector of all the V's vectors.

Why do you suppose that the random interactions you have (partially) described would result in a constant (average) velocity?

The space is either continuous or discrete, that is, we have two distinct cases.

What does a 'discrete' space mean?

What is the packet speed v in the discrete case?

You need to go away and think about the answers to the questions I have asked, then you can build a model of your system and investigate how it evolves yourself.

 

[berkeman]

A problematic post by the OP has been deleted, and they are on a temporary time-out from PF. Thread is closed.