# 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](https://viadean.notion.site/Simulating-Multi-Dimensional-Physical-Processes-with-Cloud-Based-Numerical-Analysis-21d1ae7b9a3280b1abb1d6ba27d77b9c?source=copy_link), 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.

### :clapper:Animated result

{% embed url="<https://youtu.be/So4j5THXhxQ>" %}
2D Transport Equation
{% endembed %}

{% embed url="<https://youtu.be/8Tf6QCG5g24>" %}
Ink Diffusion (2D Heat Equation)
{% endembed %}

{% embed url="<https://youtu.be/JKdQ5D6KUMk>" %}
3D heat diffusion
{% endembed %}

{% embed url="<https://youtu.be/B4jR9KgeFR4>" %}
3D heat diffusion-isosurface
{% endembed %}

{% embed url="<https://youtu.be/gaIIE9mqvW4>" %}
2D-individuals in a population tending to disperse from crowded areas to less dense ones
{% endembed %}

{% embed url="<https://youtu.be/YHpBplhARQU>" %}
3D- individuals in a population tending to disperse from crowded areas to less dense ones
{% endembed %}