Melting of Branched RNA Molecules

Stability of the branching structure of an RNA molecule is an important condition for its function. In this letter we show that the melting thermodynamics of RNA molecules is very sensitive to their branching geometry for the case of a molecule whose groundstate has the branching geometry of a Cayley Tree and whose pairing interactions are described by the Go model. Whereas RNA molecules with a linear geometry melt via a conventional continuous phase transition with classical exponents, molecules with a Cayley Tree geometry are found to have a free energy that seems smooth, at least within our precision. Yet, we show analytically that this free energy in fact has a mathematical singularity at the stability limit of the ordered structure. The correlation length appears to diverge on the high-temperature side of this singularity.Comment: 4 pages, 3 figure

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

Analytical description of finite size effects for RNA secondary structures

The ensemble of RNA secondary structures of uniform sequences is studied analytically. We calculate the partition function for very long sequences and discuss how the cross-over length, beyond which asymptotic scaling laws apply, depends on thermodynamic parameters. For realistic choices of parameters this length can be much longer than natural RNA molecules. This has to be taken into account when applying asymptotic theory to interpret experiments or numerical results.Comment: 10 pages, 13 figures, published in Phys. Rev.

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

Quantification of the differences between quenched and annealed averaging for RNA secondary structures

The analytical study of disordered system is usually difficult due to the necessity to perform a quenched average over the disorder. Thus, one may resort to the easier annealed ensemble as an approximation to the quenched system. In the study of RNA secondary structures, we explicitly quantify the deviation of this approximation from the quenched ensemble by looking at the correlations between neighboring bases. This quantified deviation then allows us to propose a constrained annealed ensemble which predicts physical quantities much closer to the results of the quenched ensemble without becoming technically intractable.Comment: 9 pages, 14 figures, submitted to Phys. Rev.

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

Superconducting ``metals'' and ``insulators''

We propose a characterization of zero temperature phases in disordered superconductors on the basis of the nature of quasiparticle transport. In three dimensional systems, there are two distinct phases in close analogy to the distinction between normal metals and insulators: the superconducting "metal" with delocalized quasiparticle excitations and the superconducting "insulator" with localized quasiparticles. We describe experimental realizations of either phase, and study their general properties theoretically. We suggest experiments where it should be possible to tune from one superconducting phase to the other, thereby probing a novel "metal-insulator" transition inside a superconductor. We point out various implications of our results for the phase transitions where the superconductor is destroyed at zero temperature to form either a normal metal or a normal insulator.Comment: 18 page