Executive Summary : | Aggregation processes are a significant field of study due to their wide applications in physical systems, biology, astrophysics, and non-physical systems. They can be divided into diffusion limited aggregation and ballistic aggregation, depending on the dynamics followed by clusters. Analytical approaches typically focus on simple scenarios with spherical or point-like particles or homogeneous domains. However, recent advancements in experiments and numerics of physical systems reveal more complex situations. Individual properties of aggregating units, such as structure or intrinsic dynamics, can alter the nature of aggregation. Environmental factors like intermediate metastable states or traps can also affect aggregate formation timescales. Homogeneity, localized influx, traps, and other factors play a significant role in aggregation formation. This project aims to investigate dynamics and how they affect aggregation characteristics using coarse grained models. It will use biological systems where diffusion of aggregating species occurs in crowded environments to investigate how waiting time distributions at locations alter aggregation scaling laws. The project will also examine the geometry of the embedding space of aggregates, specifically the ballistic and diffusive current of particles across a wedge from the center. The research will also investigate how correlations sustain in these systems, indicating deviation from mean field analysis. Additionally, it will explore models with intrinsic long-range correlations in hopping rate and waiting times and how this is reflected in mass distributions. |