Abstract
In this work, we consider the question of whether a simple diffusive model can explain the scent tracking behaviors found in nature. For such tracking to occur, both the concentration of a scent and its gradient must be above some threshold. Applying these conditions to the solutions of various diffusion equations, we find that the steady state of a purely diffusive model cannot simultaneously satisfy the tracking conditions when parameters are in the experimentally observed range. This demonstrates the necessity of modeling odor dispersal with full fluid dynamics, where nonlinear phenomena such as turbulence play a critical role.
Highlights
We live in a universe that obeys mathematical laws but at a fundamental level appears determined to keep those laws comprehensible.[1]
For such tracking to occur, both the concentration of a scent and its gradient must be above some threshold. Applying these conditions to the solutions of various diffusion equations, we find that the steady state of a purely diffusive model cannot simultaneously satisfy the tracking conditions when parameters are in the experimentally observed range
Even in this idealized scenario, the possibility of the shark being able to distinguish and act on a 4% increase in the concentration is remote. This suggests that the diffusion model is doing a poor job capturing the real physics of the blood dispersion, and/or the shark’s ability to sense a gradient is somehow improved when odorants are at homeopathically low concentrations
Summary
We live in a universe that obeys mathematical laws but at a fundamental level appears determined to keep those laws comprehensible.[1]. We wish to understand whether such simple models can account for the capacity of organisms to detect odors and track them to their origin. The behavior described by the diffusion equation is the random spread of substances,[36,37] with its principal virtue being that it is described by wellunderstood partial differential equations whose solutions can often be obtained analytically It is, a natural candidate for modeling random-motion transport such as (appropriately in 2020) the spread of viral infections[38] or the dispersal of a gaseous substance such as an odorant. Scitation.org/journal/phf diffusion, which applies in scenarios such as a drop of blood diffusing in water The processes that enable our sense of smell cannot be captured by a simple phenomenological description of time-independent spatial distributions, and models for the olfactory sense must account for the nonlinear[39] dispersal of odor caused by secondary phenomena such as turbulence
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