This is somewhat universal. (Some physical insights)

Naively, to achieve optimal access time, you can pack your memory within a sphere of radius R, and R=O(N^(1/3)).

But, for large R you start having cooling problems. If each memory element needs some power P to operate, then the total power consumption is P×N = O(R^3). But your area is only 4pi R^2, so the power flow per unit area is O(R)=O(N^(1/3)). So if it has large radius, and it has limited thermal conductivity, your memory will melt (since temperature ~ power flow^(1/3) (Plank's law)).

The threshold for stable temperatures at any radius is memory access as O(N^(1/2)).

This analysis is valid for general computing and circuits, but since computers are usually modeled as memory machines I think that's sufficient (?).

Obs: Why, or how, is the human brain roughly spherical then? Because we have a very effective (water based) cooling system. Still, if it got large enough, and you admit limited flow rates of water and such, cooling eventually would be limiting. If you immediately thought of elephants, so did I, and this may be linked to their fantastic large ears:

https://asknature.org/strategy/large-ears-aid-cooling/

I love how everything is connected.

Obs2: Yes this is related to the Bekenstein bound, but much more relevant of course (because existing RAM is almost thermally limited and you need black hole densities to achieve bekenstein bound). The memories we use are organized in (mostly) flat packages.

Well the problem with that is "this is a curve that roughly fits the data" is a bad way to go about constructing a model. It's a useful and neat observation, but that doesn't make it a good model. It might model random accesses to memory reasonably well (such as traversing a linked list, the example used there), but it doesn't model a scan over an array well. That doesn't make for a useful model. In contrast, the external memory model assumes a fast internal memory of size M (e.g., cache), which can be accessed in constant time, and a slow external memory of infinite size (e.g., RAM) which can only be accessed in blocks of size B (e.g., a cache line). Then you count how many blocks the algorithm needs to read or write. Now, scanning an array of size N takes O(N/B) I/Os, whereas scanning a linked list of the same size takes O(N) I/Os. The complexity of sorting is O(N/B log(N/B)/log(M/B)) I/Os. This models the same behaviour in a much cleaner way, applies equally to all levels of the memory hierarchy (you can also view RAM as the internal memory and a hard disk/SSD as the external memory), and is widely used in what you called "serious academic work" :) See also https://en.wikipedia.org/wiki/External_memory_algorithm

Furthermore, the introduction in the article you linked misunderstands Big-O notation so incredibly fundamentally that I don't think the author has done their background reading on machine models and Big-O notation.

> I am not sure if any serious academic work has been built on this model, but it's a nice short hand.

Not that nmodel specifically, but cache-oblivious data structures are specifically designed to scale well in a hierarchical cache model, no matter the cache block size. So they scale excellently across L1 cache all the way down to hard disk.