General solution of an exact correlation function factorization in conformal field theory

We discuss a correlation function factorization, which relates a three-point function to the square root of three two-point functions. This factorization is known to hold for certain scaling operators at the two-dimensional percolation point and in a few other cases. The correlation functions are evaluated in the upper half-plane (or any conformally equivalent region) with operators at two arbitrary points on the real axis, and a third arbitrary point on either the real axis or in the interior. This type of result is of interest because it is both exact and universal, relates higher-order correlation functions to lower-order ones, and has a simple interpretation in terms of cluster or loop probabilities in several statistical models. This motivated us to use the techniques of conformal field theory to determine the general conditions for its validity. Here, we discover a correlation function which factorizes in this way for any central charge c, generalizing previous results. In particular, the factorization holds for either FK (Fortuin-Kasteleyn) or spin clusters in the Q-state Potts models; it also applies to either the dense or dilute phases of the O(n) loop models. Further, only one other non-trivial set of highest-weight operators (in an irreducible Verma module) factorizes in this way. In this case the operators have negative dimension (for c < 1) and do not seem to have a physical realization.Comment: 7 pages, 1 figure, v2 minor revision

Research Factsheet: Woodfuel experiment - North Thurlbar, Newton Rigg

An experiment has been set up to assess the economic viability and environmental impacts of woodfuel harvesting in North Thurlbar, a small wood land on the University of Cumbria Newton Rigg campus estate. This factsheet describes the aim of the study and the experiment design

Color and texture associations in voice-induced synesthesia

Voice-induced synesthesia, a form of synesthesia in which synesthetic perceptions are induced by the sounds of people's voices, appears to be relatively rare and has not been systematically studied. In this study we investigated the synesthetic color and visual texture perceptions experienced in response to different types of “voice quality” (e.g., nasal, whisper, falsetto). Experiences of three different groups—self-reported voice synesthetes, phoneticians, and controls—were compared using both qualitative and quantitative analysis in a study conducted online. Whilst, in the qualitative analysis, synesthetes used more color and texture terms to describe voices than either phoneticians or controls, only weak differences, and many similarities, between groups were found in the quantitative analysis. Notable consistent results between groups were the matching of higher speech fundamental frequencies with lighter and redder colors, the matching of “whispery” voices with smoke-like textures, and the matching of “harsh” and “creaky” voices with textures resembling dry cracked soil. These data are discussed in the light of current thinking about definitions and categorizations of synesthesia, especially in cases where individuals apparently have a range of different synesthetic inducers

Preliminary Test of Prescribed Burning for Control of Maple Leaf Cutter (Lepidoptera: Incurvariidae)

Leaf litter burning in the spring resulted in 87.5% mortality of maple leaf cutter pupae, Paraclemensia acerifoliella (Fitch). No apparent damage was observed on sugar maple or beech trees within the burn area

Determination of thermodynamic properties of AeroZINE-50, phase 1

Literature survey of, and test procedure for determination of thermodynamic properties of AeroZINE-5

Twist operator correlation functions in O(n) loop models

Using conformal field theoretic methods we calculate correlation functions of geometric observables in the loop representation of the O(n) model at the critical point. We focus on correlation functions containing twist operators, combining these with anchored loops, boundaries with SLE processes and with double SLE processes. We focus further upon n=0, representing self-avoiding loops, which corresponds to a logarithmic conformal field theory (LCFT) with c=0. In this limit the twist operator plays the role of a zero weight indicator operator, which we verify by comparison with known examples. Using the additional conditions imposed by the twist operator null-states, we derive a new explicit result for the probabilities that an SLE_{8/3} wind in various ways about two points in the upper half plane, e.g. that the SLE passes to the left of both points. The collection of c=0 logarithmic CFT operators that we use deriving the winding probabilities is novel, highlighting a potential incompatibility caused by the presence of two distinct logarithmic partners to the stress tensor within the theory. We provide evidence that both partners do appear in the theory, one in the bulk and one on the boundary and that the incompatibility is resolved by restrictive bulk-boundary fusion rules.Comment: 18 pages, 8 figure

Factorization of correlations in two-dimensional percolation on the plane and torus

Recently, Delfino and Viti have examined the factorization of the three-point density correlation function P_3 at the percolation point in terms of the two-point density correlation functions P_2. According to conformal invariance, this factorization is exact on the infinite plane, such that the ratio R(z_1, z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2, z_3)]^{1/2} is not only universal but also a constant, independent of the z_i, and in fact an operator product expansion (OPE) coefficient. Delfino and Viti analytically calculate its value (1.022013...) for percolation, in agreement with the numerical value 1.022 found previously in a study of R on the conformally equivalent cylinder. In this paper we confirm the factorization on the plane numerically using periodic lattices (tori) of very large size, which locally approximate a plane. We also investigate the general behavior of R on the torus, and find a minimum value of R approx. 1.0132 when the three points are maximally separated. In addition, we present a simplified expression for R on the plane as a function of the SLE parameter kappa.Comment: Small corrections (final version). In press, J. Phys.

Biology, Injury, and Control of the European Needle-bending Midge (Diptera: Cecidomyiidae) on Scotch Pine in Michigan

Contarinia baeri is univoltine in Michigan. Adults emerge in spring, and females deposit eggs in small clusters in the sheaths of new-growth pine needles. Larvae hatch shortly thereafter and there are three larval instars. Larval feeding causes the needles to at first droop, discolor, and eventually drop, reducing the quality of Christmas trees and occasionally killing shoots. Larvae overwinter on the ground in cocoons, and pupate in spring. Adults were suppressed (\u3e 75% control) with formulations of Pydrin® (fenvalerate) and Tempo® (cyfluthrin) applied within a week after adult emergence