Recently it has been shown that a two-dimensional model of self-attracting polymers based on attracting segments with the addition of stiffness displays three phases: a swollen phase, a globular, liquid-like phase, and an anisotropic crystal-like phase. Here, we consider the attracting segment...

Recently it has been shown that a two-dimensional model of self-attracting polymers based on attracting segments displays two phase transitions, a θ-like collapse between swollen polymers and a globular state and another between the globular state and a polymer crystal. On the other hand, the...

We present the results of simulations of kinetic growth trails (KGT) (bond-avoiding walks) in four dimensions. We use a mapping from a kinetic growth model to a static model of self-interacting trails (ISAT) at a particular temperature to argue that this temperature is precisely the collapse...

We have simulated four-dimensional interacting self-avoiding trails (ISAT) on the hypercubic lattice with standard interactions at a wide range of temperatures up to length 4096 and at some temperatures up to length 16384. The results confirm the earlier prediction (using data from a...

Gene Stanley's early contribution to the n-vector model is briefly reviewed. Also discussed is a problem solved by McCrea and Whipple in 1940; namely random walks with absorbing boundaries. We have found the exact solution of the analogous problem on the triangular lattice with a true finite...

When DNA molecules are heated they undergo a denaturation transition by which the two strands of the molecule are separated and become unbound. Experimental studies strongly indicate that the denaturation transition is first order. The main theoretical approach to study this transition,...

We have calculated exactly the mean-square end-to-end distance, the mean-square radius of gyration, and the mean-square distance of a monomer from the origin, for n-step self-avoiding walks on the honeycomb lattice up to 46 steps. We also calculated the mean-square radius of gyration and moments...

We will utilise the self-avoiding walk (SAW) mapping of the vortex line conformations in turbulence to get the Kolmogorov scale dependence of energy dispersion from SAW statistics, and the knowledge of the effects of disordered fractal geometries on the SAW statistics. These will give us the...

We study the critical behavior of surface-interacting self-avoiding random walks on a class of truncated simplex lattices, which can be labeled by an integer n ⩾ 3. Using the exact renormalization group method we have been able to obtain the exact values of various critical exponents for all...

Double-tethered polymers are a kind of linear polymer with a peculiar topological constraint; that is, both of its end-points are attached to a plane which the polymer segments cannot penetrate. The effects of the constraint on the polymer's configurational and entropic properties were...