the energy per vertex problem for lattice systems. In general for a type of lattice in statistical physics, to compute the …

is developed from the algebraic approach: the concept of lattice (a type of partially ordered set) is applied to the … patterns. We concluded that the minimum units of fracture patterns can be expressed as three kinds of lattice. Our model is …, the symmetropy of lattice decreases with the evolution of fracture process. We find that the pre-nucleation process of …

dramatic changes in the embedded networks, in comparison to their off-lattice counterparts, and call into question the … applicability of off-lattice scale-free models to realistic, everyday-life networks. …

. We propose a simple square lattice model to explain the observed empirical behaviour. …

In this paper we propose a lattice analog of phase-space fractional Liouville equation. The Liouville equation for … phase-space lattice with long-range jumps of power-law types is suggested. We prove that the continuum limit transforms this … lattice equation into Liouville equation with conjugate Riesz fractional derivatives of non-integer orders with respect to …

results by Yan and Zhang (2009), we propose the incidence energy per vertex problem for lattice systems, and present the … closed-form formulae expressing the incidence energy of the hexagonal lattice, triangular lattice, and 33.42 lattice …