Prescribe, assign, define mean to fix arbitrarily or authoritatively for the sake of order or of a clear understanding.
Prescribe stresses dictation, especially by one in command, and usually implies that the aim is to give explicit directions or clear guidance to those who accept one’s authority or are bound to obey one’s injunctions.
Assign (sea also ALLOT ASCRIBE ) usually has some suggestion of allotment or ascription; it implies arbitrary but not despotic determination for the sake of some practical end such as harmony in operation or functioning, the proper distribution of a number of things, or the settlement of a dispute by agreement.
Define implies an intent to mark boundaries between things so as to prevent confusion, conflict, or overlapping.