Julia aims to be better than R and Python at statistics and data analysis. It's not there yet, but I could easily see it replacing a great deal of academic use of Numpy and Python in Jupyter notebooks (the 'ju' is Julia).
On the other hand, Rust seems like it's aiming at being a safer alternative to C for low-level systems programming.
I'm sure there's things Julia could learn from Rust, but the design decisions are going to differ wildly because they just aren't trying to do similar things.