Four-dimensional polymer collapse II: Pseudo-First-Order Transition in Interacting Self-avoiding Walks

In earlier work we provided the first evidence that the collapse, or coil-globule, transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical lattice model of polymer collapse, namely interacting self-avoiding walks, to show that it not only has a distinct collapse transition at finite temperature but that for any finite polymer length this collapse has many characteristics of a rounded first-order phase transition. However, we also show that there exists a `$\theta$-point' where the polymer behaves in a simple Gaussian manner (which is a critical state), to which these finite-size transition temperatures approach as the polymer length is increased. The resolution of these seemingly incompatible conclusions involves the argument that the first-order-like rounded transition is scaled away in the thermodynamic limit to leave a mean-field second-order transition. Essentially this happens because the finite-size \emph{shift} of the transition is asymptotically much larger than the \emph{width} of the pseudo-transition and the latent heat decays to zero (algebraically) with polymer length. This scenario can be inferred from the application of the theory of Lifshitz, Grosberg and Khokhlov (based upon the framework of Lifshitz) to four dimensions: the conclusions of which were written down some time ago by Khokhlov. In fact it is precisely above the upper critical dimension, which is 3 for this problem, that the theory of Lifshitz may be quantitatively applicable to polymer collapse.Comment: 30 pages, 14 figures included in tex

IUPAC-NIST solubility data series. 81. Hydrocarbons with water and seawater - Revised and updated. Part 8. C9 hydrocarbons with water

The mutual solubility and related liquid-liquid equilibria of C9 hydrocarbons with water are exhaustively and critically reviewed. Reports of the experimental determination of solubility in 18 chemically distinct binary systems that appeared in the primary literature prior to the end of 2002 are compiled. For 8 systems, sufficient data are available to allow critical evaluation. All data are expressed as mass percent and mole fraction, as well as the originally reported units. In addition to the standard evaluation criteria used throughout the Solubility Date Series, a new method based on the evaluation of the all experimental data for a given homologous series of aliphatic and aromatic hydrocarbons was used

IUPAC-NIST solubility data series. 81. Hydrocarbons with water and seawater-revised and updated. Part 5. C7 hydrocarbons with water and heavy water

The mutual solubility and related liquid-liquid equilibria of C7 hydrocarbons with water and heavy water are exhaustively and critically reviewed. Reports of experimental determination of solubility in 23 chemically distinct binary systems that appeared in the primary literature prior to end of 2002 are compiled. For 9 systems sufficient data are available to allow critical evaluation. All data are expressed as mass percent and mole fraction as well as the originally reported units. In addition to the standard evaluation criteria used throughout the Solubility Data Series, a new method based on the evaluation of the all experimental data for a given homologous series of aliphatic and aromatic hydrocarbons was used

Distribution of Salmonella enterica isolates from human cases in Italy, 1980 to 2011

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Exact Results for Hamiltonian Walks from the Solution of the Fully Packed Loop Model on the Honeycomb Lattice

We derive the nested Bethe Ansatz solution of the fully packed O($n$) loop model on the honeycomb lattice. From this solution we derive the bulk free energy per site along with the central charge and geometric scaling dimensions describing the critical behaviour. In the $n=0$ limit we obtain the exact compact exponents $\gamma=1$ and $\nu=1/2$ for Hamiltonian walks, along with the exact value $\kappa^2 = 3 \sqrt 3 /4$ for the connective constant (entropy). Although having sets of scaling dimensions in common, our results indicate that Hamiltonian walks on the honeycomb and Manhattan lattices lie in different universality classes.Comment: 12 pages, RevTeX, 3 figures supplied on request, ANU preprint MRR-050-9

Scaling of Self-Avoiding Walks in High Dimensions

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results to $1/d$-expansions and to excellent rigorous bounds that exist. In particular, we obtain precise values for the connective constants, $\mu_5=8.838544(3)$, $\mu_6=10.878094(4)$, $\mu_7=12.902817(3)$, $\mu_8=14.919257(2)$ and give a revised estimate of $\mu_4=6.774043(5)$. All of these are by at least one order of magnitude more accurate than those previously given (from other approaches in $d>4$ and all approaches in $d=4$). Our results are consistent with most theoretical predictions, though in $d=5$ we find clear evidence of anomalous $N^{-1/2}$-corrections for the scaling of the geometric size of the walks, which we understand as a non-analytic correction to scaling of the general form $N^{(4-d)/2}$ (not present in pure Gaussian random walks).Comment: 14 pages, 2 figure

CAR Co-Operates With Integrins to Promote Lung Cancer Cell Adhesion and Invasion.

The coxsackie and adenovirus receptor (CAR) is a member of the junctional adhesion molecule (JAM) family of adhesion receptors and is localised to epithelial cell tight and adherens junctions. CAR has been shown to be highly expressed in lung cancer where it is proposed to promote tumor growth and regulate epithelial mesenchymal transition (EMT), however the potential role of CAR in lung cancer metastasis remains poorly understood. To better understand the role of this receptor in tumor progression, we manipulated CAR expression in both epithelial-like and mesenchymal-like lung cancer cells. In both cases, CAR overexpression promoted tumor growth in vivo in immunocompetent mice and increased cell adhesion in the lung after intravenous injection without altering the EMT properties of each cell line. Overexpression of WTCAR resulted in increased invasion in 3D models and enhanced β1 integrin activity in both cell lines, and this was dependent on phosphorylation of the CAR cytoplasmic tail. Furthermore, phosphorylation of CAR was enhanced by substrate stiffness in vitro, and CAR expression increased at the boundary of solid tumors in vivo. Moreover, CAR formed a complex with the focal adhesion proteins Src, Focal Adhesion Kinase (FAK) and paxillin and promoted activation of the Guanine Triphosphate (GTP)-ase Ras-related Protein 1 (Rap1), which in turn mediated enhanced integrin activation. Taken together, our data demonstrate that CAR contributes to lung cancer metastasis via promotion of cell-matrix adhesion, providing new insight into co-operation between cell-cell and cell-matrix proteins that regulate different steps of tumorigenesis

A note on graded Yang-Baxter solutions as braid-monoid invariants

We construct two $Osp(n|2m)$ solutions of the graded Yang-Baxter equation by using the algebraic braid-monoid approach. The factorizable S-matrix interpretation of these solutions is also discussed.Comment: 7 pages, UFSCARF-TH-94-1

Stretched Polymers in a Poor Solvent

Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first and last monomers. We show that both in $d=2$ and $d=3$ a phase transition occurs as this force is increased beyond a critical value, where the polymer changes from a collapsed globule to a stretched configuration. This transition is second order in $d=2$ and first order in $d=3$. For $d=2$ we predict the transition point quantitatively from properties of the unstretched polymer. This is not possible in $d=3$, but even there we can estimate the transition point precisely, and we can study the scaling at temperatures slightly below the collapse temperature of the unstretched polymer. We find very large finite size corrections which would make very difficult the estimate of the transition point from straightforward simulations.Comment: 10 pages, 16 figure

Anomalous polymer collapse winding angle distributions

In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of winding angle distributions, where simulations of interacting self-avoiding walks show that the winding angle distribution for N-step walks is compatible with the theoretical prediction of a Gaussian with a variance growing asymptotically as C log N . Here we extend this work by considering interacting self-avoiding trails which are believed to be a model representative of some of the more complex behaviour. We provide robust evidence that, while the high temperature swollen state of this model has a winding angle distribution that is also Gaussian, this breaks down at the polymer collapse point and at low temperatures. Moreover, we provide some evidence that the distributions are well modelled by stretched/compressed exponentials, in contradistinction to the behaviour found in interacting self-avoiding walks.Comment: 9 pages, 7 figure