On ephemeral continua

Among the fundamentals of continuum mechanics, a cardinal tenet is the perfect identifiability of material elements. Consequently, the key mathematical tools one summons are bijections, of various degree of regularity, between sets in Euclidean space. Here we explore how one can manage without that tenet and what might ensue from the attendant want. The image one evokes directly is that of a loose shifting throng of minute pebbles, a numerous assembly of streaming motes. Thus, directly, the issues are relevant to fast granular flows; however, most results bear also on the study of complex media generally, even on a deeper analysis of response of standard continua.