🧠Simulating Multi-Dimensional Physical Processes with Cloud-Based Numerical Analysis-5/12

Higher-dimensional transport and diffusion equations, encompassing rigorous diffusion limits, multidimensional diffusion theory, advanced numerical and particle-based simulation methods, and fractional/telegraphic generalizations, provide powerful tools for modeling, analyzing, and simulating complex transport phenomena across a wide range of scientific and engineering fields.

Cloud computing environments provide a powerful platform for the analysis and dynamic visualization (through animation, including isosurface plots for 3D) of complex higher-dimensional partial differential equations, effectively modeling phenomena like 2D transport, 2D ink diffusion, 3D heat distribution, and multi-dimensional population dispersion using numerical techniques such as the explicit finite difference scheme.

🎬Animated result

2D Transport Equation

Ink Diffusion (2D Heat Equation)

3D heat diffusion

3D heat diffusion-isosurface

2D-individuals in a population tending to disperse from crowded areas to less dense ones

3D- individuals in a population tending to disperse from crowded areas to less dense ones