Questions on the sorting/ordering functions of Mathematica (Sort, SortBy, Ordering, etc.).

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Sorting Data by Differences between Columns

In Band Structure calculations one gets rather extensive data of Energy Values (Eigenvalues) and the associated Eigenvectors out of the solution of an Eigenequation of e.g. the form H.$\psi$=E.$\psi$. ...
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How to customize the order of leaf labels in a dendrogram plot?

Take the following simple case as an example: Needs["HierarchicalClustering`"] SeedRandom[99]; Sort@RandomInteger[99, {10}] gives {2, 7, 22, 34, 42, 58, 60, ...
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Finding correct combination of functions

I am trying to write code where I have an array $S$ or numbers in any order [5,4,2,1,....] Then I have a specific set of functions that I can write. ...
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Collision detection algorithm (discrete) with sweep and prune algorithm for periodic boundary conditions

EDIT: Question Updated with solution approach, but solution much slower than original implementation. Any ideas to speed up implementation? In the discussion on collision detection (see here) I asked ...
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How do I reassign canonical ordering of special expressions?

1. Default behavior of Sort Note: this peculiarity is described in a comment to a related question at StackOverflow but I think it's worth restating here at mma.sx. It is estabilished in ...
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How To Sort BarChart Data Based On the Selected Column

This sample code works fine for the category of StarData selected. What I would like to do is sort the data based on which BarChart is selected. ...