Mean exit time in irregularly-shaped annular and composite disc domains

Abstract Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications biophysics, economics and heat mass transfer. While many exact results MET are known simple geometries involving homogeneous materials, calculating realistic heterogeneous materials typically limited to repeated stochastic simulations or numerical solutions associated boundary value (BVP). In this work we derive irregular annular domains, including some where occurs heterogenous media. These obtained by taking an annulus, then constructing perturbation account involved. solutions, range conditions, implemented symbolically compare very well averaged data from BVP. Software implement available on \href{https://github.com/ProfMJSimpson/Exit_time}{GitHub}.