What happens when the RAM is over in C#?

I'm no computer expert, so let me try to put this question a little bit more specifically:

I do some scientific computations, and the calculations sometimes requires a lot of memory to store their results. A few days ago, I'd an output file that took 4 GB in hard disk, but I have this amount of RAM. So:

• How does the CLR (or is it something else?) deals with the memory when the program you're running allocates more memory than that available in the computer? Does it create some swap in the HD? (I know that could slow down my program, but I'm only interest in the memory issue)
• Is it OS-dependent, say if I work with MONO on linux or with VS on Windows?

Thanks in advance!