WordNet sense 1 (the social process of absorbing one cultural group into harmony with another):

assimilation

WordNet sense 2 ((chemistry) a process in which one substance permeates another; a fluid permeates or is dissolved by a liquid or solid):

soaking up

WordNet sense 3 (complete attention; intense mental effort):

concentration, engrossment, immersion

WordNet sense 4 (the mental state of being preoccupied by something):

preoccupation, preoccupancy