  Burdzy, Pal, and Swanson considered solid spheres of small radius moving in
the unit interval, reflecting instantaneously from each other and at x=0, and
killed at x=1, with mass being added to the system from the left at constant
rate. By transforming to a system with zero-width particles moving as
independent Brownian motion, they derived a limiting stationary distribution
for a particular initial distribution, as the width of a particle decreases to
zero and the number of particles increases to infinity. This space-removing
transformation has a direct analogy in the isomorphism between a new
unbounded-range exclusion process and a superimposition of random walks with
random boundary. We derive the hydrodynamic limit for these isomorphic
processes, demonstrating that this elastic exclusion is an appropriate model
for the reflecting Brownian spheres in one dimension.
