What does the phrase Superlinear refer to?

[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.

 

[uart]

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.

 

[sir-pinski]

The term "superlinear" refers to a relationship or function that exhibits a greater than linear growth or increase. In other words, when there is a superlinear relationship, the output or result increases at a faster rate than the input or cause. This can be seen in various fields such as mathematics, physics, and economics.

In the context of your research on Si nanocrystal photovoltaic cells, the term "superlinearity" is used to describe the relationship between incident power (input) and short circuit current (output). In this case, it means that the increase in short circuit current is greater than the increase in incident power. This could be due to the unique properties of the Si nanocrystals used in the photovoltaic cell.

To understand the meaning of a term like "superlinear," it is important to look at the context in which it is used and the specific field or discipline it relates to. In your case, it is helpful to consult with experts in the field or refer to other sources such as textbooks or articles to gain a better understanding.