Motivated by recent models of Bak, Tang, and Wiesenfeld we study dissipative transport in open systems. A simple continuum equation is constructed to describe fluctuations around a steady state in a flowing ‘‘sandpile.’’ The principle of scale invariance and self-similarity is understood in terms of a conservation law in dynamics. A dynamic renormalization-group calculation allows us to determine various critical exponents exactly in all dimensions.

• Received 23 January 1989

DOI:https://doi.org/10.1103/PhysRevLett.62.1813