Tsong-Ming Liaw

Conformation-networks of two-dimensional lattice homopolymers

The effect of different Monte Carlo move sets on the folding kinetics of lattice polymer chains is studied from the geometry of the conformation-network. The networks have the characteristics of small-world: the local connections are more clustered than that of the corresponding random lattices, and the characteristic path lengths increase logarithmically with the number of nodes. One of the elementary moves, rigid rotation, has drastic effect on the geometric properties of the network. The move increases greatly the connections and reduces significantly the shortest path lengths between conformations. Including rigid rotation to the move set results in the increase of the dimensionality of the conformation space to the value about 4.

Ferromagnetic phase transitions of inhomogeneous systems modelled by square Ising models with diamond-type bond-decorations

The two-dimensional Ising model defined on square lattices with diamond-type bond-decorations is employed to study the nature of the ferromagnetic phase transitions of inhomogeneous systems. The model is studied analytically under the bond-renormalization scheme. For an n-level decorated lattice, the long-range ordering occurs at the critical temperature given by the fitting function (kBTc/J)n=1.6410+(0.6281)exp[−(0.5857)n], and the local ordering inside n-level decorated bonds occurs at the temperature given by the fitting function (kBTm/J)n=1.6410−(0.8063)exp[−(0.7144)n]. The critical amplitude Asing(n) of the logarithmic singularity in specific heat characterizes the width of the critical region, and it varies with the decoration-level n as Asing(n)=(0.2473)exp[−(0.3018)n], obtained by fitting the numerical results. The cross over from a finite-decorated system to an infinite-decorated system is not a smooth continuation. For the case of infinite decorations, the critical specific heat becomes a cusp with the height c(n)=0.639852. The results are compared with those obtained in the cell-decorated Ising model.

Coupling-anisotropy and finite-size effects in interfacial tension of the two-dimensional Ising model

Exact expressions of the Bloch wall free energy are obtained for the Ising model on a rectangular lattice and infinitely long cylinder. The interfacial tension amplitudes are obtained for different coupling and aspect ratios. Finite-size scaling theory is used to analyse the effects of coupling anisotropy and finite size in the interfacial tension.

Master equation approach to folding kinetics of lattice polymers based on conformation networks.

Based on the master equation with the inherent structure of conformation network, the authors investigate some important issues in the folding kinetics of lattice polymers. First, the topologies of conformation networks are discussed. Moreover, a new scheme of implementing Metropolis algorithm, which fulfills the condition of detailed balance, is proposed. Then, upon incorporating this new scheme into the geometric structure of conformation network the authors provide a theorem which can be used to place an upper bound on relaxation time. To effectively identify the kinetic traps of folding, the authors also introduce a new quantity, which is employed from the continuous time Monte Carlo method, called rigidity factor. Throughout the discussions, the authors analyze the results for different move sets to demonstrate the methods and to study the features of the kinetics of folding.