Meander, Folding and Arch Statistics

The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a direct recursive relation for building (semi) meanders (ii) the equivalence with a random matrix model (iii) the exact solution of simpler related problems, such as arch configurations or irreducible meanders.Comment: 82 pages, uuencoded, uses harvmac (l mode) and epsf, 26+7 figures include

Topology in SU(2) Yang-Mills theory

New results on the topology of the SU(2) Yang-Mills theory are presented. At zero temperature we obtain the value of the topological susceptibility by using the recently introduced smeared operators as well as a properly renormalized geometric definition. Both determinations are in agreement. At non-zero temperature we study the behaviour of the topological susceptibility across the confinement transition pointing out some qualitative differences with respect to the analogous result for the SU(3) gauge theory.Comment: 3 pages, 4 figures, contribution to Lattice-97. Latex file including espcrc2.st

Instantons and Fixed Point Actions in SU(2) Gauge Theory

We describe the properties of instantons in lattice gauge theory when the action is a fixed point action of some renormalization group transformation. We present a theoretically consistent method for measuring topological charge using an inverse renormalization group transformation. We show that, using a fixed point action, the action of smooth configurations with non-zero topological charge is greater than or equal to its continuum value $8\pi^2/g^2$.Comment: uufiles plain latex mss, epsf figures appended as .eps file

Increasing dominance of large lianas in Amazonian forests

Ecological orthodoxy suggests that old-growth forests should be close to dynamic equilibrium, but this view has been challenged by recent findings that neotropical forests are accumulating carbon and biomass, possibly in response to the increasing atmospheric concentrations of carbon dioxide. However, it is unclear whether the recent increase in tree biomass has been accompanied by a shift in community composition. Such changes could reduce or enhance the carbon storage potential of old-growth forests in the long term. Here we show that non-fragmented Amazon forests are experiencing a concerted increase in the density, basal area and mean size of woody climbing plants (lianas). Over the last two decades of the twentieth century the dominance of large lianas relative to trees has increased by 1.7–4.6% a year. Lianas enhance tree mortality and suppress tree growth, so their rapid increase implies that the tropical terrestrial carbon sink may shut down sooner than current models suggest. Predictions of future tropical carbon fluxes will need to account for the changing composition and dynamics of supposedly undisturbed forests

Meanders and the Temperley-Lieb algebra

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight $q$ per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function of $q$, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.Comment: 85p, uuencoded, uses harvmac (l mode) and epsf, 88 figure

An optically actuated surface scanning probe

We demonstrate the use of an extended, optically trapped probe that is capable of imaging surface topography with nanometre precision, whilst applying ultra-low, femto-Newton sized forces. This degree of precision and sensitivity is acquired through three distinct strategies. First, the probe itself is shaped in such a way as to soften the trap along the sensing axis and stiffen it in transverse directions. Next, these characteristics are enhanced by selectively position clamping independent motions of the probe. Finally, force clamping is used to refine the surface contact response. Detailed analyses are presented for each of these mechanisms. To test our sensor, we scan it laterally over a calibration sample consisting of a series of graduated steps, and demonstrate a height resolution of ∼ 11 nm. Using equipartition theory, we estimate that an average force of only ∼ 140 fN is exerted on the sample during the scan, making this technique ideal for the investigation of delicate biological samples

Quantum Fluctuations versus Topology - a Study in U(1)_2 Lattice Gauge Theory

Using the geometric definition of the topological charge we decompose the path integral of 2-dimensional U(1) lattice gauge theory into topological sectors. In a Monte Carlo simulation we compute the average value of the action as well as the distribution of its values for each sector separately. These numbers are compared with analytic lower bounds of the action which are relevant for classical configurations carrying topological charge. We find that quantum fluctuations entirely dominate the path integral. Our results for the probability distribution of the Monte Carlo generated configurations among the topological sectors can be understood by a semi-phenomenological argument.Comment: 11 pages, 3 figure

Very High Resolution Solar X-ray Imaging Using Diffractive Optics

This paper describes the development of X-ray diffractive optics for imaging solar flares with better than 0.1 arcsec angular resolution. X-ray images with this resolution of the \geq10 MK plasma in solar active regions and solar flares would allow the cross-sectional area of magnetic loops to be resolved and the coronal flare energy release region itself to be probed. The objective of this work is to obtain X-ray images in the iron-line complex at 6.7 keV observed during solar flares with an angular resolution as fine as 0.1 arcsec - over an order of magnitude finer than is now possible. This line emission is from highly ionized iron atoms, primarily Fe xxv, in the hottest flare plasma at temperatures in excess of \approx10 MK. It provides information on the flare morphology, the iron abundance, and the distribution of the hot plasma. Studying how this plasma is heated to such high temperatures in such short times during solar flares is of critical importance in understanding these powerful transient events, one of the major objectives of solar physics. We describe the design, fabrication, and testing of phase zone plate X-ray lenses with focal lengths of \approx100 m at these energies that would be capable of achieving these objectives. We show how such lenses could be included on a two-spacecraft formation-flying mission with the lenses on the spacecraft closest to the Sun and an X-ray imaging array on the second spacecraft in the focal plane \approx100 m away. High resolution X-ray images could be obtained when the two spacecraft are aligned with the region of interest on the Sun. Requirements and constraints for the control of the two spacecraft are discussed together with the overall feasibility of such a formation-flying mission

Increasing biomass in Amazonian forest plots

A previous study by Phillips et al. of changes in the biomass of permanent sample plots in Amazonian forests was used to infer the presence of a regional carbon sink. However, these results generated a vigorous debate about sampling and methodological issues. Therefore we present a new analysis of biomass change in old-growth Amazonian forest plots using updated inventory data. We find that across 59 sites, the above-ground dry biomass in trees that are more than 10 cm in diameter (AGB) has increased since plot establishment by 1.22 ± 0.43 Mg per hectare per year (ha-1 yr-1), where 1 ha = 104 m2), or 0.98 ± 0.38 Mg ha-1 yr-1 if individual plot values are weighted by the number of hectare years of monitoring. This significant increase is neither confounded by spatial or temporal variation in wood specific gravity, nor dependent on the allometric equation used to estimate AGB. The conclusion is also robust to uncertainty about diameter measurements for problematic trees: for 34 plots in western Amazon forests a significant increase in AGB is found even with a conservative assumption of zero growth for all trees where diameter measurements were made using optical methods and/or growth rates needed to be estimated following fieldwork. Overall, our results suggest a slightly greater rate of net stand-level change than was reported by Phillips et al. Considering the spatial and temporal scale of sampling and associated studies showing increases in forest growth and stem turnover, the results presented here suggest that the total biomass of these plots has on average increased and that there has been a regional-scale carbon sink in old-growth Amazonian forests during the previous two decades