On the Critical Temperature of Non-Periodic Ising Models on Hexagonal Lattices

The critical temperature of layered Ising models on triangular and honeycomb lattices are calculated in simple, explicit form for arbitrary distribution of the couplings.Comment: to appear in Z. Phys. B., 8 pages plain TEX, 1 figure available upon reques

Universal Critical Behavior of Aperiodic Ferromagnetic Models

We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of $q$-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange interactions according to some two-letter substitutional sequences, and irrelevant geometric fluctuations, the exact recursion relations in parameter space display a non-trivial diagonal fixed point that governs the universal critical behavior. For relevant fluctuations, this fixed point becomes fully unstable, and we show the apperance of a two-cycle which is associated with a novel critical behavior. We use scaling arguments to calculate the critical exponent $\alpha$ of the specific heat, which turns out to be different from the value for the uniform case. We check the scaling predictions by a direct numerical analysis of the singularity of the thermodynamic free-energy. The agreement between scaling and direct calculations is excellent for stronger singularities (large values of $q$). The critical exponents do not depend on the strengths of the exchange interactions.Comment: 4 pages, 1 figure (included), RevTeX, submitted to Phys. Rev. E as a Rapid Communicatio

Identifying and prioritising services in European terrestrial and freshwater ecosystems

Ecosystems are multifunctional and provide humanity with a broad array of vital services. Effective management of services requires an improved evidence base, identifying the role of ecosystems in delivering multiple services, which can assist policy-makers in maintaining them. Here, information from the literature and scientific experts was used to systematically document the importance of services and identify trends in their use and status over time for the main terrestrial and freshwater ecosystems in Europe. The results from this review show that intensively managed ecosystems contribute mostly to vital provisioning services (e.g. agro-ecosystems provide food via crops and livestock, and forests provide wood), while semi-natural ecosystems (e.g. grasslands and mountains) are key contributors of genetic resources and cultural services (e.g. aesthetic values and sense of place). The most recent European trends in human use of services show increases in demand for crops from agro-ecosystems, timber from forests, water flow regulation from rivers, wetlands and mountains, and recreation and ecotourism in most ecosystems, but decreases in livestock production, freshwater capture fisheries, wild foods and virtually all services associated with ecosystems which have considerably decreased in area (e.g. semi-natural grasslands). The condition of the majority of services show either a degraded or mixed status across Europe with the exception of recent enhancements in timber production in forests and mountains, freshwater provision, water/erosion/natural hazard regulation and recreation/ecotourism in mountains, and climate regulation in forests. Key gaps in knowledge were evident for certain services across all ecosystems, including the provision of biochemicals and natural medicines, genetic resources and the regulating services of seed dispersal, pest/disease regulation and invasion resistance

Demonstration and comparison of tuned and detuned signal recycling in a large-scale gravitational wave detector

The British/German gravitational wave detector GEO 600 located near Hannover in Germany is the first large-scale gravitational-wave detector using the advanced technique of signal recycling. Currently the instrument operates in detuned signal recycling mode. Several problems arise due to the fact that the signal recycling cavity changes amplitude and phase of all light fields (carrier and sidebands) present at the dark-port. In addition, in the case of detuned signal recycling this leads to unbalanced sideband fields at the detector output. The large amplitude modulation caused by this asymmetry does not carry any gravitational wave information, but might be the cause of saturation and nonlinearities on the main photodiode. We developed and demonstrated a new control method to realize tuned signal recycling operation in a large-scale gravitational wave detector. A detailed comparison of tuned and detuned signal recycling operation is given. The response function of the system (optical gain) was measured and compared, as was the size of amplitude modulation on the main photodiode. Some important noise couplings were measured and partly found to be strongly reduced in the case of tuned signal recycling operation

Feedforward correction of mirror misalignment fluctuations for the GEO 600 gravitational wave detector

The core instrument of the GEO 600 gravitational wave detector is a Michelson interferometer with folded arms. The five main optics that form this interferometer are suspended in vacuum by triple pendulums with quasi-monolithic lower stages of fused silica. After installation of these pendulums in early 2003, a larger than expected coupling of longitudinal ground motion to tilt misalignment of the suspended optics was observed. Because of this, the uncontrolled misalignment of the optics during average conditions was several µrad Hz−1/2 in the frequency band around the pendulum resonance frequencies (0.5–4 Hz). In addition, it was found that longitudinal control signals applied to the intermediate pendulum stages also resulted in excessive mirror tilt. The resulting misalignment exceeded the level tolerable for stable operation of GEO 600. In order to reduce the level of mirror tilt, a bipartite feedforward system was implemented. One part feeds signals derived from seismic measurements to piezo-electric crystals in the stacks supporting the suspensions, reducing the longitudinal motion of the uppermost suspension points. The other applies tilt correction signals, derived from longitudinal control signals, to the intermediate level of the suspensions. The seismic feedforward correction reduces the root-mean-squared tilt misalignment of each main optic between 0.1 and 5 Hz by about 10 dB, typically. The intermediate-mass feedforward correction reduces the differential tilt misalignment of the Michelson interferometer by about 10 dB between 0.1 and 0.8 Hz, typically

Results from the first burst hardware injections performed on GEO 600

GEO 600 is a 600 m arm-length, laser interferometric gravitational wave detector, located about 25 km from Hannover, Germany. Starting in November 2003, GEO 600 took part in a coincident data taking period with other detectors around the world. During this time, GEO 600 acquired three weeks of 'science quality' data. These data are currently being processed to search for gravitational wave signatures. One such search is that for burst gravitational waves. To investigate the performance of any burst-search codes used to analyse the data, burst-like signals were injected into the detector after the data taking run; this was done by differentially driving the end mirrors of the interferometer. In this paper, we report on how the first burst hardware injections were performed on GEO 600, the type of signals injected and the analysis of the data from the period of injections. Results from the analysis are also presented and discussed

Damping and tuning of the fibre violin modes in monolithic silica suspensions

High Q mirror suspensions are a key element of the advanced interferometric gravitational-wave detectors. In December 2002 the last of the final interferometer optics of GEO 600 were monolithically suspended, using fused silica fibres. The violin modes of the suspension fibres can have Q greater than 10(8) and can therefore interfere with the interferometer length control servo. Hence, the violin modes need to be damped, without degrading the pendulum Q itself. Furthermore, the frequency spread of the fibres used has to be small to allow for high Q notch filtering in the length control servo. ne requirements for the violin modes of the two GEO 600 inboard suspensions are Q lt 3 x 10(6) for the fundamental and Q lt 2 x 10(6) for the first harmonic mode, respectively. The frequency spread should not exceed 10% within one mode. To accomplish that, two sections of the fibres were coated with amorphous Teflon. By applying the coating, the Q of the relevant modes can be degraded to the desired values and furthermore, the frequencies of these modes can be tuned almost independently with a good accuracy over a wide range. After welding the fibres in the monolithic suspension, a corrective coating was applied to some fibres, to compensate for the frequency spread due to the tension spread of the four fibres within a suspension. We present the method and the results achieved

A photon pressure calibrator for the GEO 600 gravitational wave detector

Interferometer mirror displacement induced by radiation pressure is used to demonstrate an alternative calibration method for the GEO 600 detector. The photon calibrator utilizes an amplitude modulated laser diode with up to 1.4 W output power at a wavelength of 1035 nm. The achieved accuracy of the strain amplitude calibration is dominated by the laser power calibration error, which is in the range of ±4% for the measurements presented in this Letter