4 Answers

Read here>>http://psychology.about.com/od/aindex/g/assimilation.htm

Here>>http://sherisapp.hubpages.com/hub/whatisassimilation

It is the state of being assimilated; people of different backgrounds come to see themselves as part of a larger national family.

Simply:- Blending in.

I don't believe assimination is a word.  If you meant assimilation, or insemination, here are some definitions:

as•sim•i•la•tion (assimilation)
n.
1.
a. The act or process of assimilating.
b. The state of being assimilated.
2. Physiology The conversion of nutriments into living tissue; constructive metabolism.
3. Linguistics The process by which a sound is modified so that it becomes similar or identical to an adjacent or nearby sound. For example, the prefix in- becomes im- in impossible by assimilation to the labial p of possible.
4. The process whereby a minority group gradually adopts the customs and attitudes of the prevailing culture.
Insemination is the noun form of in•sem•i•nate ( n-s m -n t )
tr.v. in•sem•i•nat•ed, in•sem•i•nat•ing, in•sem•i•nates
1. To introduce or inject semen into the reproductive tract of (a female).
2. To sow seed in.