The term assimilate or assimilation refers to a new person or group of people entering into a new group and being absorbed into the culture of that new group.
Assimilation is crucial in order to maintain the stability and unity of a nation of immigrants from a number of different countries. (See Melting Pot)
When an immigrant comes to the United States to become a naturalized citizen it may take many years for him/her to assimilate.
When members of the Tea Party joined the Republican Party, in such large numbers, in such a short period of time, and with so little prior knowledge of politics and the Republican Party, it was difficult for them to assimilate.