The Saguaro Seminar, under the leadership of Robert D. Putnam, has been conducting research on the inter-relation of diversity, immigration and social capital since 2001. They have also been examining the relationship between inequality and both diversity and social capital. The first publication from this research, called 'E Pluribus Unum: Diversity and Community in the 21st Century. The 2006 Johan Skytte Lecture' by Robert D. Putnam appears in the June 2007 Scandinavian Political Studies Journal. The Journal is making this paper available free online.
There are three key elements of this research:
1) Increased diversity and immigration are essential, inevitable and generally strengthen advanced nations;
2) But in the short-term, diversity and immigration challenges community cohesion; and
3) Longer-term, successful immigrant societies overcome these challenges by building a broader sense of "we".
America has successfully done this with the wave of immigration from the late 1800s to the early 1900s. This integration can be done through popular culture, education, national symbols, or common experiences (like national service). The page linked to below also supplies a variety of other resources, such as commentaries and responses, relating to the research.