Dust Coagulation and Spatial Memory Coupling in Protoplanetary Disks via K-Kernel Dynamics

The early stages of planet formation rely on the coagulation of dust grains in protoplanetary disks. Understanding the spatial distribution of these grains is crucial for modeling planetesimals. In this study, we apply the Adaptive Memory-Decay Control Framework (AMDCF) to model dust column density, introducing a non-Markovian spatial memory kernel that couples to grain size. We demonstrate that larger grains exhibit stronger coupling to the spacetime memory, resulting in faster spatial decay of column density. The simulation reproduces the expected radial density profiles for grain sizes ranging from 0.04 μm to 36.0 μm, providing a novel geometric interpretation for dust settling and radial drift in protoplanetary environments.