A scale-free network hidden in the collapsing polymer

We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent $\gamma = 1/(2-c)$ up to a cut-off degree $d_c \propto L^{2-c}$, where $c$ is the loop exponent for dense polymers ($c=11/8$ in two dimensions) and $L$ is the length of the polymer. Our results exemplify how a scale-free network (SFN) can emerge from standard criticality.Comment: 4 pages, 3 figures, address correcte

The role of electron-hole recombination in organic magnetoresistance

Magneto-electrical measurements were performed on diodes and bulk heterojunction solar cells (BHSCs) to clarify the role of formation of coulombically bound electron-hole (e-h) pairs on the magnetoresistance (MR) response in organic thin film devices. BHSCs are suitable model systems because they effectively quench excitons but the probability of forming e-h pairs in them can be tuned over orders of magnitude by the choice of material and solvent in the blend. We have systematically varied the e-h recombination coefficients, which are directly proportional to the probability for the charge carriers to meet in space, and found that a reduced probability of electrons and holes meeting in space lead to disappearance of the MR. Our results clearly show that MR is a direct consequence of e-h pair formation. We also found that the MR line shape follows a power law-dependence of B0.5 at higher fields

Universality of collapsing two-dimensional self-avoiding trails

Results of a numerically exact transfer matrix calculation for the model of Interacting Self-Avoiding Trails are presented. The results lead to the conclusion that, at the collapse transition, Self-Avoiding Trails are in the same universality class as the O(n=0) model of Blote and Nienhuis (or vertex-interacting self-avoiding walk), which has thermal exponent $\nu=12/23$, contrary to previous conjectures.Comment: Final version, accepted for publication in Journal of Physics A; 9 pages; 3 figure

On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures

We study the interaction problem of a linear polymer chain, floating in fractal containers that belong to the three-dimensional Sierpinski gasket (3D SG) family of fractals, with a surface-adsorbed linear polymer chain. Each member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing surface, which appears to be 2D SG fractal. The two-polymer system is modelled by two mutually crossing self-avoiding walks. By applying the Monte Carlo Renormalization Group (MCRG) method, we calculate the critical exponents $\phi$, associated with the number of contacts of the 3D SG floating polymer chain, and the 2D SG adsorbed polymer chain, for a sequence of SG fractals with $2\le b\le 40$. Besides, we propose the codimension additivity (CA) argument formula for $\phi$, and compare its predictions with our reliable set of the MCRG data. We find that $\phi$ monotonically decreases with increasing $b$, that is, with increase of the container fractal dimension. Finally, we discuss the relations between different contact exponents, and analyze their possible behaviour in the fractal-to-Euclidean crossover region $b\to\infty$.Comment: 15 pages, 3 figure

Vertex Models and Random Labyrinths: Phase Diagrams for Ice-type Vertex Models

We propose a simple geometric recipe for constructing phase diagrams for a general class of vertex models obeying the ice rule. The disordered phase maps onto the intersecting loop model which is interesting in its own right and is related to several other statistical mechanical models. This mapping is also useful in understanding some ordered phases of these vertex models as they correspond to the polymer loop models with cross-links in their vulcanised phase.Comment: 8 pages, 6 figure

Sequence randomness and polymer collapse transitions

Contrary to expectations based on Harris' criterion, chain disorder with frustration can modify the universality class of scaling at the theta transition of heteropolymers. This is shown for a model with random two-body potentials in 2D on the basis of exact enumeration and accurate Monte Carlo results. When frustration grows beyond a certain finite threshold, the temperature below which disorder becomes relevant coincides with the theta one and scaling exponents definitely start deviating from those valid for homopolymers.Comment: 4 pages, 4 eps figure

Polymer desorption under pulling: a novel dichotomic phase transition

We show that the structural properties and phase behavior of a self-avoiding polymer chain on adhesive substrate, subject to pulling at the chain end, can be obtained by means of a Grand Canonical Ensemble (GCE) approach. We derive analytical expressions for the mean length of the basic structural units of adsorbed polymer, such as loops and tails, in terms of the adhesive potential and detachment force, and determine values of the universal exponents which govern their probability distributions. Most notably, the hitherto controversial value of the critical adsorption exponent $\phi$ is found to depend essentially on the interaction between different loops. The chain detachment transition turns out to be of the first order, albeit dichotomic, i.e., no coexistence of different phase states exists. These novel theoretical predictions and the suggested phase diagram of the adsorption-desorption transformation under external pulling force are verified by means of extensive Monte Carlo simulations.Comment: 10 pages, 4 figure

Finite size scaling of current fluctuations in the totally asymmetric exclusion process

We study the fluctuations of the current J(t) of the totally asymmetric exclusion process with open boundaries. Using a density matrix renormalization group approach, we calculate the cumulant generating function of the current. This function can be interpreted as a free energy for an ensemble in which histories are weighted by exp(-sJ(t)). We show that in this ensemble the model has a first order space-time phase transition at s=0. We numerically determine the finite size scaling of the cumulant generating function near this phase transition, both in the non-equilibrium steady state and for large times.Comment: 18 pages, 11 figure

RNA denaturation: excluded volume, pseudoknots and transition scenarios

A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous transition. Otherwise a smooth crossover occurs from the swollen linear polymer behavior to highly ramified, almost compact conformations with secondary structures. In the latter scenario, which is appropriate when these structures are much more stable than pseudoknot links, probability distributions for the lengths of both loops and main branches obey scaling with nonclassical exponents.Comment: 4 pages 3 figure

Hamiltonian dynamics of homopolymer chain models

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the theta-transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.Comment: 11 pages, 8 figures, accepted for publication in Physical Review