Exact Solution of the Discrete (1+1)-dimensional RSOS Model in a Slit with Field and Wall Interactions

We present the solution of a linear Restricted Solid--on--Solid (RSOS) model confined to a slit. We include a field-like energy, which equivalently weights the area under the interface, and also include independent interaction terms with both walls. This model can also be mapped to a lattice polymer model of Motzkin paths in a slit interacting with both walls and including an osmotic pressure. This work generalises previous work on the RSOS model in the half-plane which has a solution that was shown recently to exhibit a novel mathematical structure involving basic hypergeometric functions ${}_3\phi_2$. Because of the mathematical relationship between half-plane and slit this work hence effectively explores the underlying $q$-orthogonal polynomial structure to that solution. It also generalises two other recent works: one on Dyck paths weighted with an osmotic pressure in a slit and another concerning Motzkin paths without an osmotic pressure term in a slit

The role of three-body interactions in two-dimensional polymer collapse

Various interacting lattice path models of polymer collapse in two dimensions demonstrate different critical behaviours. This difference has been without a clear explanation. The collapse transition has been variously seen to be in the Duplantier-Saleur $\theta$-point university class (specific heat cusp), the interacting trail class (specific heat divergence) or even first-order. Here we study via Monte Carlo simulation a generalisation of the Duplantier-Saleur model on the honeycomb lattice and also a generalisation of the so-called vertex-interacting self-avoiding walk model (configurations are actually restricted trails known as grooves) on the triangular lattice. Crucially for both models we have three and two body interactions explicitly and differentially weighted. We show that both models have similar phase diagrams when considered in these larger two-parameter spaces. They demonstrate regions for which the collapse transition is first-order for high three body interactions and regions where the collapse is in the Duplantier-Saleur $\theta$-point university class. We conjecture a higher order multiple critical point separating these two types of collapse.Comment: 17 pages, 20 figure

Identification and characterization of polymorphisms at the HSA alpha1-acid glycoprotein (ORM*) gene locus in Caucasians

Human a1-acid glycoprotein (AGP) or orosomucoid (ORM) is a major acute phase protein that is thought to play a crucial role in maintaining homeostasis. Human AGP is the product of a cluster of at least two adjacent genes located on HSA chromosome 9. Using a range of restriction endonucleases we have investigated DNA variation at the locus encoding the AGP genes in a panel of healthy Caucasians. Polymorphisms were identified using BamHI, EcoRI, BglII, PvuII, HindIII, TaqI and MspI. Non-random associations were found between the BamHI, EcoRI, BglII RFLPs. The RFLPs detected with PvuII, TaqI and MspI were all located in exon 6 of both AGP genes. The duplication of an AGP gene was observed in 11% of the indiviuals studied and was in linkage disequilibrium with the TaqI RFLP. The identification and characterization of these polymorphisms will prove useful for other population and forensic studies

Stretching of a chain polymer adsorbed at a surface

In this paper we present simulations of a surface-adsorbed polymer subject to an elongation force. The polymer is modelled by a self-avoiding walk on a regular lattice. It is confined to a half-space by an adsorbing surface with attractions for every vertex of the walk visiting the surface, and the last vertex is pulled perpendicular to the surface by a force. Using the recently proposed flatPERM algorithm, we calculate the phase diagram for a vast range of temperatures and forces. The strength of this algorithm is that it computes the complete density of states from one single simulation. We simulate systems of sizes up to 256 steps.Comment: 13 pages, 7 figure