dispel means to make disappear.
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The title of the book alludes to the ancient capital of Persia, Persepolis. At a deeper level, it alludes to a theme of tension between past and present. Persepolis had been a great historical city of Persia and now holds the burial grounds for many Persian kings. Persepolis represents a flourishing of culture. The purpose of the novel, as the author says, is partly to contrast this previous great culture with a culture of intolerance and fundamentalism found in modern day Iran. The title also alludes to the fact that within its fundamentalist exterior, a great Iranian culture and people still exist, one that the Western world is not often allowed to see.