Scents and Scents-Ability

[Yes, it's a homophonous headline!]

We adopted Eros from the Humane Society, which had picked him up as a stray, so we know nothing about his breed and history. He reminds Marika of the beagle she grew up with though, and he has many hound-like traits, including an intense interest in smells. Often during walks he'll plant his feet for several minutes, and swing his head back and forth sniffing.

I was curious what kind of directionality he could get just by moving his head – I imagined that after a good distance, the scents would be too blended to pick out individual sources.

Smells are created by bits of a substance that are picked up by the air. Those bits then spread out according to Fick's Laws of Diffusion. The form of this equation, where the change in time depends on the Laplacian of the current state, is exactly the same as that of the heat equation, which I've discussed before. What's interesting about this case though is that heat has only one type spreading out, while we can have different smells that diffuse and mix.

I decided to adapt my cake-heating simulation to look at how much directional information Eros can get from his head movements. The setup is two sources of scents that emit particles according to Fick's laws. Eros then senses the concentration of each in a cone in front of his nose. I struggled to find a good way to display the concentrations, which drop off rapidly from the sources, but I suppose that's just a testament to the sensitivity of dogs' noses. The first case has the two sources equidistant:

Like I said, you can't see much past the central dots, but if we add up everything in the white cone,

Now we do get directionality. I was curious to see what happens when we put one source closer:

For this case the concentrations are

Because the blue scent is closer, it has a higher concentration in all directions, but comparing the left and right ends of each curve, we see we can still find a direction that gives more scent.