Intuition for distribution differences
Let's look at and compare cumulative distribution functions, and think about in which direction the divergence operator measures flux.
Intuition for distribution differences
In which we plot the cumulative distribution function of a population, and the empirical distribution of a subset of that population, and try to divine differences between them. This serves as an introduction for a later article where we'll figure out if the subset is special or drawn from the same population.
Full article (3–7 minute read): Intuition for distribution differences
Flashcard of the week
From Numerical Computation of Flows (Hirsch):
What is the intuitive interpretation of ∫ ∇·F_U dV, integrated across a volume V?
In the conventions of the book, F_U is the flux of some quantity U. The flux, in turn, is the number of units of U passing through a unit surface in the direction of flow. This means F_U is a vector field.
This means the integral represents
The net flux of U out of the volume V.
Once familiar with the conventions (integrating across a volume sums up contributions from everywhere in the volume; the divergence operator ∇· stands for flux out of an infinitessimal point in any direction) this interpretation becomes fairly easy.
The reason I still have it in as a flashcard is that I forget in which direction it measures: is it flux out of or into the volume? One would think you can tell from the name ("divergence" sort of says it is flux out of a point) yet I keep forgetting, probably because flux into a volume is usually the more interesting number, to the point where this integral often shows up as a negative term in equations.
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