23 lines
848 B
Markdown
23 lines
848 B
Markdown
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# Appendix A
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## Laplace Operator[^khan-1]
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It is defined as $\nabla \cdot \nabla f \in \R$ and is equivalent to the
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**divergence of the function**. Technically speaking it gives us the
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**magnitude of a local maximum or minimum**.
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Positive values mean that we are around a local maximum and vice-versa. The
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higher the magnitude, the higher (or lower) is the local maximum (or minimum).
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Another way to see this is as the divergence of the function that tells us whether
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that is a point of attraction or divergence.
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It can also be used to compute the net flow of particles in that region of space
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> [!CAUTION]
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> This is not a **discrete laplace operator**, which is instead a **matrix** here,
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> as there are many other formulations.
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[^khan-1]: [Khan Academy | Laplace Intuition | 9th November 2025](https://www.youtube.com/watch?v=EW08rD-GFh0)
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