Numerical Method for Accessing the Universal Scaling Function for a Multi-Particle Discrete Time Asymmetric Exclusion Process

In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz's original publication [PRL 80 209 (1998)] this universality has been verified for a variety of continuous time, periodic boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large system size limit (N-->infty) of a single particle discrete time system, even in the case of very small system sizes (N <= 22). This fact allows us to not only verify that the DLSF properly characterizes multiple particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open boundary ASEP

A rural agricultural-sustainable energy community model and its application to Felton Valley, Australia

Energy and food security require a delicate balance which should not threaten or undermine community prosperity. Where it is proposed to derive energy from conventional fossil fuel resources (such as coal, shale oil, natural gas, coal seam gas) located in established rural areas, and particularly where these areas are used for productive agricultural purposes, there are often both intense community concern as well as broader questions regarding the relative social, economic and environmental costs and benefits of different land uses and, increasingly, different energy sources. The advent of mainstream renewable energy technologies means that alternative energy options may provide a viable alternative, allowing energy demand to be met without compromising existing land uses. We demonstrate how such a Sustainable Energy Rural Model can be designed to achieve a balance between the competing social goals of energy supply, agricultural production, environmental integrity and social well-being, and apply it to the Felton Valley, a highly productive and resilient farming community in eastern Australia. Research into available wind and solar resources found that Felton Valley has a number of attributes that indicate its suitability for the development of an integrated renewable energy precinct which would complement, rather than displace, existing agricultural enterprises. Modelling results suggest a potential combined annual renewable energy output from integrated wind and solar resources of 1,287 GWh/yr from peak installed capacity of 713 MW, sufficient to supply the electrical energy needs of about 160,000 homes, in combination with total biomass food production of 31,000 tonnes per annum or 146 GWh/yr of human food energy. The portfolio of renewable energy options will not only provide energy source diversity but also ensures long-term food security and regional stability. The Felton Valley model provides an example of community-led energy transformation and has potential as a pilot project for the development of smart distributed grids that would negate the need for further expansion of coal mining and coal fired power stations

Statistical mechanics of RNA folding: a lattice approach

We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA consists of just one hairpin. Using exact arguments and Monte Carlo simulations we determine the phase diagram for this case. We show that the denaturation transition is first order and can either occur directly or through an intermediate molten phase.Comment: 8 pages, 9 figure

Quasiparticle density of states in dirty high-T_c superconductors

We study the density of quasiparticle states of dirty d-wave superconductors. We show the existence of singular corrections to the density of states due to quantum interference effects. We then argue that the density of states actually vanishes in the localized phase as $|E|$ or $E^2$ depending on whether time reversal is a good symmetry or not. We verify this result for systems without time reversal symmetry in one dimension using supersymmetry techniques. This simple, instructive calculation also provides the exact universal scaling function for the density of states for the crossover from ballistic to localized behaviour in one dimension. Above two dimensions, we argue that in contrast to the conventional Anderson localization transition, the density of states has critical singularities which we calculate in a $2+\epsilon$ expansion. We discuss consequences of our results for various experiments on dirty high-$T_c$ materials

An elementary proof of the irrationality of Tschakaloff series

We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $T_q(z)$.Comment: 5 pages, AMSTe

Statistical mechanics of RNA folding: importance of alphabet size

We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two kinds of bases, there are many alternate folding configurations, yielding thermodynamically stable ground-states only for a small set of structures of high designability, i.e., total number of associated sequences. In contrast, sequences made from four bases, as found in nature, or six bases have far fewer competing folding configurations, resulting in a much greater average stability of the ground state.Comment: 7 figures; uses revtex

Localization-delocalization transition of disordered d-wave superconductors in class CI

A lattice model for disordered d-wave superconductors in class CI is reconsidered. Near the band-center, the lattice model can be described by Dirac fermions with several species, each of which yields WZW term for an effective action of the Goldstone mode. The WZW terms cancel out each other because of the four-fold symmetry of the model, which suggests that the quasiparticle states are localized. If the lattice model has, however, symmetry breaking terms which generate mass for any species of the Dirac fermions, remaining WZW term which avoids the cancellation can derive the system to a delocalized strong-coupling fixed point.Comment: 4 pages, revte

Quantum and classical localisation, the spin quantum Hall effect and generalisations

We consider network models for localisation problems belonging to symmetry class C. This symmetry class arises in a description of the dynamics of quasiparticles for disordered spin-singlet superconductors which have a Bogoliubov - de Gennes Hamiltonian that is invariant under spin rotations but not under time-reversal. Our models include but also generalise the one studied previously in the context of the spin quantum Hall effect. For these systems we express the disorder-averaged conductance and density of states in terms of sums over certain classical random walks, which are self-avoiding and have attractive interactions. A transition between localised and extended phases of the quantum system maps in this way to a similar transition for the classical walks. In the case of the spin quantum Hall effect, the classical walks are the hulls of percolation clusters, and our approach provides an alternative derivation of a mapping first established by Gruzberg, Read and Ludwig, Phys. Rev. Lett. 82, 4254 (1999).Comment: 11 pages, 5 figure

Leaf litter breakdown along an elevational gradient in Australian alpine streams

The breakdown of allochthonous organic matter, is a central step in nutrient cycling in stream ecosystems. There is concern that increased temperatures from climate change will alter the breakdown rate of organic matter, with important consequences for the ecosystem functioning of alpine streams. This study investigated the rate of leaf litter breakdown and how temperature and other factors such as microbial and invertebrate activities influenced this over elevational and temporal gradients. Dried leaves of Snow Gum (Eucalyptus pauciflora) and cotton strips were deployed in coarse (6 mm), and fine (50 mu m) mesh size bags along an 820 m elevation gradient. Loss of mass in leaf litter and cotton tensile strength per day (k per day), fungal biomass measured as ergosterol concentration, invertebrate colonization of leaf litter, and benthic organic matter (mass and composition) were determined. Both microbial and macroinvertebrate activities were equally important in leaf litter breakdown with the abundance of shredder invertebrate taxa. The overall leaf litter breakdown rate and loss of tensile strength in cotton strips (both k per day) were greater during warmer deployment periods and at lower elevations, with significant positive relationships between mean water temperature and leaf breakdown and loss of tensile strength rate, but no differences between sites, after accounting for the effects of temperature. Despite considerably lower amounts of benthic organic matter in streams above the tree line relative to those below, shredders were present in coarse mesh bags at all sites. Ergosterol concentration was greater on leaves in coarse mesh bags than in fine mesh bags, implying differences in the microbial communities. The importance of water temperatures on the rate of leaf litter breakdown suggests the potential effects of climate change-induced temperature increases on ecological processes in such streams

Quasiparticle localization in superconductors with spin-orbit scattering

We develop a theory of quasiparticle localization in superconductors in situations without spin rotation invariance. We discuss the existence, and properties of superconducting phases with localized/delocalized quasiparticle excitations in such systems in various dimensionalities. Implications for a variety of experimental systems, and to the properties of random Ising models in two dimensions, are briefly discussed.Comment: 10 page