title: Spontaneous formation of large clusters in a lattice gas above the critical point.
abstract: We consider clustering of particles in the lattice gas model above the critical point. We find the probability for large density fluctuations over scales much larger than the correlation length. This fundamental problem is of interest in various biological contexts such as quorum sensing and clustering of motile, adhesive, cancer cells. In the latter case, it may give a clue to the problem of growth of recurrent tumors. We develop a formalism for the analysis of this rare event employing a phenomenological master equation and measuring the transition rates in numerical simulations. The spontaneous clustering is treated in the framework of the eikonal approximation to the master equation.
authors.affiliation: Department of Physics, Oakland University, Rochester, Michigan 48309, USA.
authors.forename: Evgeniy
authors.initials: E
authors.lastname: Khain
authors.affiliation: Department of Physics, Oakland University, Rochester, Michigan 48309, USA and Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Khasin
authors.affiliation: Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA.
authors.forename: Leonard M
authors.initials: LM
authors.lastname: Sander