How to work communication between different physical servers?

[eluser]jedd[/eluser]
Well, I think we need a bit more info too.

Do these applications have to run as the user that launches them - for either permission reasons or to track/audit usage?

If they do, then it gets a bit more complex - you need to authenticate the users at the web server, and (securely) onward authenticate to the cluster. You can start doing passwords here, but that'll get painful real quick (and you also need to look at https, self-signed certificates, etc).

If there's a small number of users involved you could perhaps keep copies of their ssh keys - but this introduces security risks of its own.

If you just need to connect to the remote host and run applications, and you don't care as who - then this is (relatively) easy.

How much data are you sending across, too - and in what format (lots of small files, very large binary lumps, just a few parameters on a commandline?)