Aging continuous time random walks in fluids

The subject of aging continuous time random walks (CTRWs) has attracted increasing attention in recent years. To describe the aging behaviors of random particles whose jumps are biased by a nonhomogeneous velocity field, we propose herein a generalized scheme of aging CTRWs in flows and obtain the corresponding generalized master equation in Fourier–Laplace space for probability density functions. Moreover, we derive the generalized aging advection diffusion equation for particles with a power law waiting time and Gaussian jump length densities, investigate the corresponding ensemble and time mean square displacements, and show how anomalous diffusion depends on the age of the process and on the moving fluids.The subject of aging continuous time random walks (CTRWs) has attracted increasing attention in recent years. To describe the aging behaviors of random particles whose jumps are biased by a nonhomogeneous velocity field, we propose herein a generalized scheme of aging CTRWs in flows and obtain the corresponding generalized master equation in Fourier–Laplace space for probability density functions. Moreover, we derive the generalized aging advection diffusion equation for particles with a power law waiting time and Gaussian jump length densities, investigate the corresponding ensemble and time mean square displacements, and show how anomalous diffusion depends on the age of the process and on the moving fluids.