Ratnakaram Raghavendra and Saila Kumari Annareddy
In this extensive computational study, we investigate the dynamics of cosmic ray diffusion across three distinct spatial dimensions: one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) scenarios. Utilizing the fundamental heat equation, we explore the dispersion of cosmic ray density over time, guided by varying initial conditions and boundary constraints. Through a series of numerical simulations, we visualize and analyse the intricate interplay between cosmic ray behaviour and the spatial and dimensional contexts in which it unfolds. Our findings reveal a rich tapestry of cosmic ray diffusion patterns. The simulations highlight the pivotal role of initial conditions, boundary conditions, and spatial dimensions in shaping the distribution and propagation of cosmic rays. Gaussian-like initial conditions, centred at different points and endowed with specific standard deviations, lead to diverse diffusion profiles. Dirichlet and Neumann boundary conditions dictate how cosmic rays interact with system boundaries, further influencing their trajectories. This comprehensive exploration of cosmic ray diffusion extends our understanding of this phenomenon, offering critical insights into its behaviour across multidimensional environments. Beyond fundamental scientific inquiry, these results have implications for astrophysics, particle physics, and the broader realm of scientific research. By integrating data from nine distinct graphs, this study forms a holistic perspective on cosmic ray diffusion, providing a foundation for continued investigations into its complex dynamics and their broader scientific significance.