I am modeling the collective behavior of random walkers (using CTRW) on a 2d lattice and I am having trouble finding a "correct" rule that won't eventually violate the uniformly random motion of my agents. Any ideas?
What about reflecting boundaries? That's what I used in case of the confined CTRW,
Article Subdiffusion in time-averaged, confined random walks
Thinking about boundaries as inverse "affordances" and applying a decoding rule:
Preprint Role of affordance in perception Decoding the sensory input
Thanks Thomas Neusius for the suggestion and your informative article. I'll check it out for sure.
I am thinking of something like neutron transport theory. Reflective boundary is indeed an option. A ""white" boundary condition might be another one, that is, reflection direction is uniformly distributed over a half unit sphere going in.
For cases where someone needs some loss I cannot think of a good solution, but there might one, maybe a partial reflection of a grey condition. Proving it might be more complicated, if transport theory is any guide.
This is one possible approach, it might be wrong though.
in neutron transport, we do often use reflective boundary conditions, for example, in monte carlo lattice physics calculations like Vinicius says. Additionally, you could look at the interface "albedo" or exiting current divided by entrant current. This could give you an idea of how to handle the losses, perhaps. You could possibly implement this by assigning a new weight to the particle based on the physics at the interface you are looking at. These were just my initial thoughts without having a deeper understanding of the problem you are trying to solve. For example, the bottom paragraph of this webpage may give you further ideas. https://www.nuclear-power.net/nuclear-power/reactor-physics/neutron-diffusion-theory/albedo-boundary-condition/