I look up the example sentences in some web dictionaries about the vocabulary "choose". It's like I have never seen a sentence like "Someone chooses A to be B." So I wonder if saying in this way is OK. For example, can one say "I choose my dissertation topic to be The tidal effect on Io." or "We choose the parameter to be of order 1/r.", and so on?
Here is an example that works:
I chose him[A] to be my partner[B]
Who did I choose? him [A].
What did I choose him for? to be my partner[B].
Now repeat those question with your sentence:
What did you choose? the tidal effect on Io [A]
What did I choose it for? to be my dissertation project. [B]
So the correct form for the first sentence in this form would be
I chose "the tidal effect on Io"[A] to be my dissertation project [B]
Looking at the second sentence:
What do you choose? "a function which is of order 1/r"[A].
What do you choose it for "a parameter" [B].
So the correct sentence is
We choose a function which is of order 1/r [A] to be the parameter [B].
As a native American English (and adapted Academic English) speaker, the examples you provided all seem fine.
"I choose my dissertation topic to be the tidal effect on Io."
"We choose the parameter to be of order 1/r."
"The vector fields Nᵃ are chosen to be the divergence-free vector fields..."
There is also a usage of the term, "n choose k" which has a very specific meaning (how many different ways are there to choose k of n elements?), but you are putting a person as the subject of the verb "choose" and have a B which is a specific instance of more general term A, so it's clear that some agent is making a selection of B to be the specific instance of A.
The grammatical question here is more about the relative sequence of the verb's direct object and indirect object. For example, if you said:
"I choose the tidal effect on Io to be my dissertation topic."
you would be saying the same thing conceptually, but it's grammatically different. Either way, you're drawing an equivalence between "the tidal effect on Io" and "my dissertation topic." You're basically putting an equals sign between them, and A=B is the same as B=A. Saying it in the original order helps the reader figure out what you are talking about progressively, to help them identify why they should care. If you or your dissertation were the topic of conversation, you would put "my dissertation topic" first in the sentence, because the listener can more easily attach that to their knowledge structure and then have a place to attach "the tidal effect on Io" when that concept comes up afterward. In an alternate example, if you are an unknown newcomer to a conversation where the main topic is the tidal effect on Io, you would put that first in the sentence and then mention your dissertation, so that the new information can be tacked on to the existing conceptual structure of the conversation. This assumes that "the tidal effect on Io" can be things which are not a "dissertation topic," which is true in this example.
"We chose divergence-free vector fields for Nᵃ" would work, but the author there wants to describe those vector fields in a lot more detail, and so is telling you what s/he is about to describe so you can create a place in your knowledge structure for what you are about to read, and then fill it in as you read the detail. This is helpful to the reader and makes the dense prose easier to understand.
Search online for "the known-new contract" for more details on this strategy that helps make writing easier to understand.