# What does the phrase Superlinear refer to?

1. Mar 4, 2009

### pokey

What does the phrase "Superlinear" refer to?

I've been reading a lot of physics journals lately in relation to a presentation I am to prepare, and I've come across the term "superlinear" a few times, but never an explanation of what it means, and a search of the forums here yielded a similar experience, where someone would just throw the term out as though everyone would know what it meant.
I've searched and come up with a few different results for the term, a couple being purely mathematical (e.g. a function f is sublinear if f(x + y) <= f(x) + f(y) for all x, y. Superlinear therefore means f(x + y) >= f(x) + f(y).), and been told that it merely means a slope > 1.

How does one go about figuring out such a mysterious term? I would provide the precise articles but they are APL papers, and I don't know if I'm allowed to reproduce their material.

In specific I am reading a paper on the "superlinearity" of the relationship between incident power and short circuit current in a Si nanocrystal photovoltaic cell created by a research team.

2. Mar 4, 2009

### uart

Re: What does the phrase "Superlinear" refer to?

Super-linear, f(x + y) >= f(x) + f(y), simply means that the curve departs from linear in a "concave upward" maner. Say for example like the curve y=x^2 for positive x.

Sub-linear, f(x + y) <= f(x) + f(y), means it departs from linear in a "concave downwards" manner. Say for example like the curve y=sqrt(x) for positive x.