Version 1 (modified by 7 years ago) ( diff ) | ,
---|
Beginning with the continuity equation for settled systems
where the source term is due to probe launches as opposed to diffusion - and follows the logistic equation
Here
can be thought of as the average thermal velocity and is a constant, so we can pull it out of the derivative…We then normalize the density of settled systems by the density of total systems
which gives us
We then look for self-similar solutions of the form
where
Upon substituting that in to the continuity equation we arrive at
or
which gives a front thickness of
where is the average speed and is the speed of the front (maximum speed from maxwellian).Note - I also tried
where
Substituting that form for the solution into the continuity equation we get
but that is no longer self-similar
Attachments (5)
- Screen Shot 2017-10-17 at 11.48.19 PM.png (76.5 KB ) - added by 7 years ago.
- settled.gif (1.7 MB ) - added by 7 years ago.
- settled0099.png (36.0 KB ) - added by 7 years ago.
- settled.2.gif (1.7 MB ) - added by 7 years ago.
- settled0099.2.png (29.9 KB ) - added by 7 years ago.
Note:
See TracWiki
for help on using the wiki.