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Mathematical Physics Seminar

Facilitated, Cooperative, and Obstructed Exclusion

Sid Redner, Santa Fe Institute

Location:  Zoom
Date & time: Wednesday, 28 September 2022 at 10:45AM - 11:45PM

Abstract:  In the famous exclusion process, each lattice site contains either zero or one particle.  A particle is randomly selected and moves to a neighboring empty site. The transport properties of this simple model are surprisingly rich.  In this talk, we investigate the roles of facilitation, cooperativity, and geometric obstruction on this exclusion process.  In facilitation, a particle hops to its vacant right neighbor only if "pushed" by an occupied left neighbor.  Surprisingly, an initial density downstep develops into a rarefaction wave with a jump discontinuity at the leading edge.  In cooperativity, an inflection point exists in the current-density relation and the group velocity has opposite density dependences on either side of the inflection.  Thus within a hydrodynamic theory, initial density upsteps and downsteps can evolve into: (a) shock waves, (b) continuous compression or rarefaction waves, or (c) a mixture of shocks and continuous waves.  Finally, we present some intriguing aspects of asymmetric exclusion in junction geometries.