title: Heat conduction in two-dimensional disk models.
abstract: We study the heat conduction problem in two-dimensional (2D) lattice models of disk shape consisting of two circular heat baths with radius r1 and r2 (r1<r2) , located concentrically at the center and the edge of the disk. Compared with the lattice models of rectangle shape adopted in previous studies, the main advantage of the disk models is that they have an unambiguous 2D dimensionality. The Fermi-Pasta-Ulam interaction of β type and the ϕ4 system are considered, respectively, as momentum conserving and nonconserving prototypes. In the former we find that in the range of the system size investigated, the heat conductivity κ depends on the system size L=r2-r1 as κ∼(ln L)α with α being a function of r1/r2. In particular, in the limit of r1/r2→1 we have α→1 , i.e., a logarithmic dependence of κ on L , which is in agreement with the prediction of existing theories. In the momentum nonconserving ϕ4 system the heat conductivity converges to a finite value as the system size is increased.
authors.affiliation: Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, People's Republic of China.
authors.forename: Daxing
authors.initials: D
authors.lastname: Xiong
authors.forename: Jiao
authors.initials: J
authors.lastname: Wang
authors.forename: Yong
authors.initials: Y
authors.lastname: Zhang
authors.forename: Hong
authors.initials: H
authors.lastname: Zhao