Fractional Diffusion to a Cantor Set in 2D

A random walk on a two dimensional square in R2 space with a hidden absorbing fractal set Fμ is considered. This search-like problem is treated in the framework of a diffusion–reaction equation, when an absorbing term is included inside a Fokker–Planck equation as a reaction term. This macroscopic approach for the 2D transport in the R2 space corresponds to the comb geometry, when the random walk consists of 1D movements in the x and y directions, respectively, as a direct-Cartesian product of the 1D movements. The main value in task is the first arrival time distribution (FATD) to sink points of the fractal set, where travelling particles are absorbed. Analytical expression for the FATD is obtained in the subdiffusive regime for both the fractal set of sinks and for a single sink.

Moth Mating: Modeling Female Pheromone Calling and Male Navigational Strategies to Optimize Reproductive Success

Male and female moths communicate in complex ways to search for and to select a mate. In a process termed calling, females emit small quantities of pheromones, generating plumes that spread in the environment. Males detect the plume through their antennae and navigate toward the female. The reproductive process is marked by female choice and male–male competition, since multiple males aim to reach the female but only the first can mate with her. This provides an opportunity for female selection on male traits such as chemosensitivity to pheromone molecules and mobility. We develop a mathematical framework to investigate the overall mating likelihood, the mean first arrival time, and the quality of the first male to reach the female for four experimentally observed female calling strategies unfolding over a typical one-week mating period. We present both analytical solutions of a simplified model as well as results from agent-based numerical simulations. Our findings suggest that, by adjusting call times and the amount of released pheromone, females can optimize the mating process. In particular, shorter calling times and lower pheromone titers at onset of the mating period that gradually increase over time allow females to aim for higher-quality males while still ensuring that mating occurs by the end of the mating period.