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The olfactory system of male moths is exquisitely sensitive to pheromones emitted by females and transported in the environment by atmospheric turbulence. Moths respond to minute amounts of pheromones and their behavior is sensitive to the fine-scale structure of turbulent plumes where pheromone concentration is detectible. Pheromone whiffs are qualitatively known to be intermittent, yet quantitative characterization of their statistical properties is lacking. This challenging fluid dynamics problem is also relevant for entomology, neurobiology and the technological design of olfactory stimulators aimed at reproducing physiological odor signals in well-controlled laboratory conditions. Here, we develop a Lagrangian approach to the transport of pheromones by turbulent flows and exploit it to predict the statistics of odor detection during olfactory searches. The theory yields explicit probability distributions for the intensity and the duration of pheromone detections, as well as their spacing in time. Predictions are favorably tested by using numerical simulations, laboratory experiments and field data for the atmospheric surface layer. The resulting signal of odor detections lends to implementation with state-of-the-art technologies and quantifies the amount and the type of information that male moths can exploit during olfactory searches.
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