Honeycomb lattice polygons and walks as a test of series analysis techniques

We have calculated long series expansions for self-avoiding walks and polygons on the honeycomb lattice, including series for metric properties such as mean-squared radius of gyration as well as series for moments of the area-distribution for polygons. Analysis of the series yields accurate estimates for the connective constant, critical exponents and amplitudes of honeycomb self-avoiding walks and polygons. The results from the numerical analysis agree to a high degree of accuracy with theoretical predictions for these quantities.Comment: 16 pages, 9 figures, jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda

Strongly interacting Fermi gases with density imbalance

We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e. unitarity, regime. The Bogoliubov-deGennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as give rise to both phase separation and FFLO type oscillations in the order parameter. We show how radio-frequency spectroscopy reflects the phase separation, and can provide direct evidence of the FFLO-type oscillations via observing the nodes of the order parameter.Comment: Added one reference. Published in PR

Coupled ferro-antiferromagnetic Heisenberg bilayers investigated by many-body Green's function theory

A theory of coupled ferro- and antiferromagnetic Heisenberg layers is developed within the framework of many-body Green's function theory (GFT) that allows non-collinear magnetic arrangements by introducing sublattice structures. As an example, the coupled ferro- antiferromagnetic (FM-AFM) bilayer is investigated. We compare the results with those of bilayers with purely ferromagnetic or antiferromagnetic couplings. In each case we also show the corresponding results of mean field theory (MFT), in which magnon excitations are completely neglected. There are significant differences between GFT and MFT. A remarkable finding is that for the coupled FM-AFM bilayer the critical temperature decreases with increasing interlayer coupling strength for a simple cubic lattice, whereas the opposite is true for an fcc lattice as well as for MFT for both lattice types.Comment: 17 pages, 6 figures, accepted for publication in J. Phys. Condens. Matter, missing fig.5 adde

Social Learning and Course Choice

We use a broad sample of students to examine the course selection process and find evidence of social learning from peers. We also find that as the number of times students solve the course selection problem increases, they rely less on social learning and more on their own experience, limiting the potential for herd behaviour. Our results give insight to instructors about the reasons why students may be in their classes and suggest that information about courses and help in evaluating this information is especially important for students early in their college careers.

An analytical and experimental investigation of a 1.8 by 3.7 meter Fresnel lens solar concentrator

Line-focusing acrylic Fresnel lenses with application potential in the 200 to 370 C range are being analytically and experimentally evaluated. Investigations previously conducted with a 56 cm wide lens have been extended by the present study to experimentation/analyses with a 1.8 by 3.7 m lens. A measured peak concentration ratio of 64 with 90 percent of the transmitted energy focused into a 5.0 cm width was achieved. A peak concentration of 61 and a 90 percent target width of 4.5 cm were analytically computed. The experimental and analytical lens transmittance was 81 percent and 86 percent, respectively. The lens also was interfaced with a receiver assembly and operated in the collection mode. The collection efficiency ranged from 42 percent at 100 C to 26 percent at 300 C

Self-avoiding walks and polygons on the triangular lattice

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, $\mu=4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure

Role of conformational entropy in force-induced bio-polymer unfolding

A statistical mechanical description of flexible and semi-flexible polymer chains in a poor solvent is developed in the constant force and constant distance ensembles. We predict the existence of many intermediate states at low temperatures stabilized by the force. A unified response to pulling and compressing forces has been obtained in the constant distance ensemble. We show the signature of a cross-over length which increases linearly with the chain length. Below this cross-over length, the critical force of unfolding decreases with temperature, while above, it increases with temperature. For stiff chains, we report for the first time "saw-tooth" like behavior in the force-extension curves which has been seen earlier in the case of protein unfolding.Comment: 4 pages, 5 figures, ReVTeX4 style. Accepted in Phys. Rev. Let

Reaction-diffusion processes and non-perturbative renormalisation group

This paper is devoted to investigating non-equilibrium phase transitions to an absorbing state, which are generically encountered in reaction-diffusion processes. It is a review, based on [Phys. Rev. Lett. 92, 195703; Phys. Rev. Lett. 92, 255703; Phys. Rev. Lett. 95, 100601], of recent progress in this field that has been allowed by a non-perturbative renormalisation group approach. We mainly focus on branching and annihilating random walks and show that their critical properties strongly rely on non-perturbative features and that hence the use of a non-perturbative method turns out to be crucial to get a correct picture of the physics of these models.Comment: 14 pages, submitted to J. Phys. A for the proceedings of the conference 'Renormalization Group 2005', Helsink