title: Extending the Transport Theorem to Rough Domains of Integration.
abstract: Transport theorems, such as that named after Reynolds, are an important tool in the field of continuum physics. Recently, Seguin and Fried used Harrison's theory of differential chains to establish a transport theorem valid for evolving domains that may become irregular. Evolving irregular domains occur in many different physical settings, such as phase transitions or fracture. Here, emphasizing concepts over technicalities, we present Harrison's theory of differential chains and the results of Seguin and Fried in a way meant to be accessible to researchers in continuum physics. We also show how the transport theorem applies to three concrete examples and approximate the resulting terms numerically. Furthermore, we discuss how the transport theorem might be used to weaken certain basic assumptions underlying the description of continua and the challenges associated with doing so.
authors.affiliation: Postdoctoral Fellow Division of Mathematics, University of Dundee , Dundee DD1 4HN, Scotland , UK e-mail:  bseguin@maths.dundee.ac.uk.
authors.forename: Brian
authors.initials: B
authors.lastname: Seguin
authors.affiliation: Graduate Student Department of Mechanical Engineering, McGill University , Montréal, PQ H3A 0C3 , Canada e-mail:  denis.hinz@mail.mcgill.ca.
authors.forename: Denis F
authors.initials: DF
authors.lastname: Hinz
authors.affiliation: Professor Mathematical Soft Matter Unit, Okinawa Institute of Science and Technology , 1919-1 Tancha, Onna-son, Kunigami-gun , Okinawa, Japan 904-0495 e-mail:  eliot.fried@oist.jp.
authors.forename: Eliot
authors.initials: E
authors.lastname: Fried
keywords: chains; fractals; geometric integration