Intermittency and non-Gaussian fluctuations of the global energy transfer in fully developed turbulence

We address the experimentally observed non-Gaussian fluctuations for the energy injected into a closed turbulent flow at fixed Reynolds number. We propose that the power fluctuations mirror the internal kinetic energy fluctuations. Using a stochastic cascade model, we construct the excess kinetic energy as the sum over the energy transfers at different levels of the cascade. We find an asymmetric distribution that strongly resembles the experimental data. The asymmetry is an explicit consequence of intermittency and the global measure is dominated by small scale events correlated over the entire system. Our calculation is consistent with the statistical analogy recently made between a confined turbulent flow and a critical system of finite size.Comment: To appear in Physical Review Letter

An electric-field representation of the harmonic XY model

The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.Comment: 13 pages, 10 figure

Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.Comment: 11 pages, 6 figure

Phase order in superfluid helium films

Classic experimental data on helium films are transformed to estimate a finite-size phase order parameter that measures the thermal degradation of the condensate fraction in the two-dimensional superfluid. The order parameter is found to evolve thermally with the exponent $\beta = 3 \pi^2/128$, a characteristic, in analogous magnetic systems, of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Universal scaling near the BKT fixed point generates a collapse of experimental data on helium and ferromagnetic films, and implies new experiments and theoretical protocols to explore the phase order. These results give a striking example of experimental finite-size scaling in a critical system that is broadly relevant to two-dimensional Bose fluids.Comment: 6 pages, 2 figure

Quantum order by disorder and accidental soft mode Er2Ti2O7

Motivated by recent neutron scattering experiments, we derive and study an effective "pseudo-dipolar" spin-1/2 model for the XY pyrochlore antiferromagnet Er2Ti2O7. While a bond-dependent in-plane exchange anisotropy removes any continuous symmetry, it does lead to a one-parameter `accidental' classical degeneracy. This degeneracy is lifted by quantum fluctuations in favor of the non-coplanar spin structure observed experimentally -- a rare experimental instance of quantum order by disorder. A non-Goldstone low-energy mode is present in the excitation spectrum in accordance with inelastic neutron scattering data. Our theory also resolves the puzzle of the experimentally observed continuous ordering transition, absent from previous models.Comment: 5 pages, 4 figures, final versio

Synthesis and thermal analytical screening of metal complexes as potential novel fire retardants in polyamide 6.6

The development of new flame retardants is of ever increasing importance because of ecotoxicity concerns over existing systems and related regulatory pressures. From a range of low-toxicity, water-insoluble reagents, a total of 151 metal complexes were assessed for their potential to impart flame retardant behaviour in polymer matrices. These were successfully synthesised on a small scale and possible interactions were explored with a model engineering polymer, namely polyamide 6.6 (PA66). Powder mixtures of each complex with PA66 in a 1:3 mass ratio were analysed under air using TGA/DTA. Based on the stability of each at the typical processing temperature of 290 °C and its char forming potential (the final residue requirement at 580 °C being > 25%), selected mixtures were then analysed further using a differential mass loss technique. Metal complex/PA66 mixtures in which the differential residual mass above 470 °C was >10% with respect to the theoretical value were considered to have a positive char forming interaction. Only eight of the metal complexes passed this last criterion including aluminium, tin (II) and zinc tungstates, three tin (II) phosphorus oxyanion complexes, iron (II) aluminate and iron (III) hypophosphite. These selected compounds were synthesised on a larger scale (c.a. 100 g), characterised and compounded into PA66 at 5 wt% for flammability assessment using LOI, UL94 and cone calorimetry. Of these, only aluminium tungstate and iron (II) aluminate showed some degree of FR behaviour with LOI values ≥ 23.0 vol% compared with PA66 (LOI = 22.9 vol%) and the former almost achieved a UL94 V-2 rating. However, while up to 32% reductions in total heat releases and up to 49% reduction in PHRR in cone calorimetric tests were observed for the metal complex/PA66 composites generally, those for Al2(WO4)3 were 6 and 29% respectively and for Fe(AlO2)2 were 18 and 45% respectively

Neutron scattering from fragmented frustrated magnets

The fragmentation description is used to analyse calculated neutron scattering intensities from kagom\'e ice and spin ice systems. The longitudinal, transverse and harmonic fragments produce independent contributions to the neutron scattering intensity. This framework is used to analyse the ordering due to quantum fluctuations in the topologically constrained phase of kagom\'e ice and the monopole crystal phase of spin ice. Here, quantum fluctuations are restricted to the transverse fragment and they drive the system into a double-$q$ structure in which longitudinal and transverse fragments have a different ordering wave vector. The intensity reduction of the Bragg peaks for the transverse fragments, compared with known classical limits can be used as a diagnostic tool for quantum fluctuations. Published quantum Monte Carlo data for spin ice in a $[111]$ field are consistent with the proposed protocol.Comment: 13 pages, 8 figure

Reply to Comment on " Universal Fluctuations in Correlated Systems"

Reply to the comment, cond-mat/0209398 by by N.W. Watkins, S.C. Chapman, and G. RowlandsComment: To appear In Physical Review Letter

Exploiting changes in the tumour microenvironment with sequential cytokine and matrix metalloprotease inhibitor treatment in a murine breast cancer model

The study of treatment-induced changes in the tumour microenvironment might lead to effective combinations of biological therapy. IL-12 induced tumour regression and cure of an experimental murine breast cancer, HTH-K, but only after long-term treatment that was associated with chronic toxicity. During IL-12 therapy, tumour levels of the matrix metalloprotease MMP-9 declined and its inhibitor TIMP-1 was strongly induced. We therefore administered alternate cycles of IL-12 and the MMP inhibitor Batimastat (BB94) to mice. Therapeutic efficacy was increased compared with short-term IL-12 therapy but without the chronic toxicity associated with long-term IL-12 treatment. Image analysis of treated tumours revealed that BB94 prevented regeneration of tumour and stromal compartments that normally occurred after short-term IL-12 therapy. © 2000 Cancer Research Campaign http://www.bjcancer.co