title: Survival of a static target in a gas of diffusing particles with exclusion.
abstract: Let a lattice gas of constant density, described by the symmetric simple exclusion process, be brought in contact with a "target": a spherical absorber of radius R. Employing the macroscopic fluctuation theory (MFT), we evaluate the probability P(T) that no gas particle hits the target until a long but finite time T. We also find the most likely gas density history conditional on the nonhitting. The results depend on the dimension of space d and on the rescaled parameter ℓ=R/√[D(0)T], where D(0) is the gas diffusivity. For small ℓ and d>2, P(T) is determined by an exact stationary solution of the MFT equations that we find. For large ℓ, and for any ℓ in one dimension, the relevant MFT solutions are nonstationary. In this case, lnP(T) scales differently with relevant parameters, and it also depends on whether the initial condition is random or deterministic. The latter effects also occur if the lattice gas is composed of noninteracting random walkers. Finally, we extend the formalism to a whole class of diffusive gases of interacting particles.
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Baruch
authors.initials: B
authors.lastname: Meerson
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Arkady
authors.initials: A
authors.lastname: Vilenkin
authors.affiliation: Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D005740:Gases; D008962:Models, Theoretical; D011336:Probability
chemical_list: D005740:Gases