No abstract

The ring structure of certain polymers in nature, like proteins and DNA indicates a benefit compared with the linear form. Transcriptional regulation in higher eukaryotes is maintained among others by the formation of chromatin loops. Experimental studies revealed that different chromosomes as well as chromatin regions on one single chromosome tend to be segregated into distinct territories. Here we study a system of two rings in both catenane and bonded topology as a toy model for the influence of loops and topological constraints on the polymers' conformational properties. Athermal Monte Carlo simulations reveal that the mean square radius of gyration AER gyr 2 ae of catenated or bonded rings follows a similar scaling exponent as isolated rings, which in turn is close to the value of ν ≈ 0.588 for a self-avoiding walk. However, the effective segment length is larger for catenated rings, reflecting the swelling of the polymers. The shape of catenated and bonded rings, in contrast, shows pronounced differences even in the limit of infinite chain length. We observe a strong tendency toward segregation for the bonded topology in comparison with a similar ring-linear and linear-linear system. The orientation of the rings' gyration ellipsoids is slightly perpendicular, trying to minimize the overlap area. These findings indicate that loops might play an important role in the entropy-driven segregation of chromatin.

Effective quantum field theoretical continuum models for graphene are investigated. The models include a complex scalar field and a vector gauge field. Different gauge theories are considered and their gap patterns for the scalar, vector, and fermion excitations are investigated. Different gauge groups lead to different relations between the gaps, which can be used to experimentally distinguish the gauge theories. In this class of models the fermionic gap is a dynamic quantity. The finite-energy vortex solutions of the gauge models have the flux of the "magnetic field" quantized, making the Bohm-Aharonov effect active even when external electromagnetic fields are absent. The flux comes proportional to the scalar field angular momentum quantum number. The zero modes of the Dirac equation show that the gauge models considered here are compatible with fractionalization

We show that the assumption of a nontrivial zero band gap for a graphene sheet within an effective relativistic field theoretical model description of interacting Dirac electrons on the surface of graphene describes the experimental band gap of graphene nanoribbons for a wide range of widths. The graphene band gap is dynamically generated, corresponding to a nontrivial gapless solution, found in the limit of an infinitely wide graphene ribbon. The nanoribbon band gap is determined by the experimental graphene work function.

We study the time evolution of the one-dimensional random-bond transverse Ising model with four-spin interactions. We calculate the time-dependent correlation function as well as the longitudinal rclaxation 'function of the infinite chain. We analyze how the presence of disordeT affect the dynamical behavior of the~ system in comparison with the pure model. We find that the main effect of disorder is to produce a crossover from a central mode to a collective-mode type of dynamics, as the concentration of weaker bonds is enhanced: Such crossover is also present in the case of an increase in bond dilution.