The universal Turing machine is the standard theoretical model of a stored-program computer. While in one sense as general as possible (Turing completeness), it doesn't explicitly contain many of the more advanced features of real-world/practical stored-program computers and their operating systems that have been developed since the 1950's. I am referring to basic features such as,
the fact that there is an "operating system" at all that can control execution of other stored-programs.
that there is a distinction between kernel and user mode, that the kernel mode can allocate and remove privileges to programs, and that this is hardcoded into the CPU,
That programs can execute "system calls" and that this causes a switch to kernel mode and to the OS,
the notion of "interactive programs", such as a shell with a command line where the input and output strings interact with some non-deterministic entity such as a human,
the notion of CPU "interrupts" that can stop the execution of programs based on events,
I know this is a general question, but I am wondering whether there are mathematical models of computation that capture more advanced features such as these. I'm hoping someone could point me in the right direction.