Spontaneous magnetisation in the plane

The Arak process is a solvable stochastic process which generates coloured patterns in the plane. Patterns are made up of a variable number of random non-intersecting polygons. We show that the distribution of Arak process states is the Gibbs distribution of its states in thermodynamic equilibrium in the grand canonical ensemble. The sequence of Gibbs distributions form a new model parameterised by temperature. We prove that there is a phase transition in this model, for some non-zero temperature. We illustrate this conclusion with simulation results. We measure the critical exponents of this off-lattice model and find they are consistent with those of the Ising model in two dimensions.Comment: 23 pages numbered -1,0...21, 8 figure

Effect of microstructure and temperature on the erosion rates and mechanisms of modified EB PVD TBCs

Thermal barrier coatings (TBCs) have now been used in gas turbine engines for a number of decades and are now considered to be an accepted technology. As there is a constant drive to increase the turbine entry temperature, in order to increase engine efficiency, the coatings operate in increasingly hostile environments. Thus there is a constant drive to both increase the temperature capabilities of TBCs while at the same time reducing their thermal conductivities. The thermal conductivity of standard 7 wt% yttria stabilized zirconia (7YSZ) electron beam (EB) physical vapour deposited (PVD) TBCs can be reduced in two ways: the first by modification of the microstructure of the TBC and the second by addition of ternary oxides. By modifying the microstructure of the TBC such that there are more fine pores, more photon scattering centres are introduced into the coatings, which reduce the heat transfer by radiation. While ternary oxides will introduce lattice defects into the coating, which increases the phonon scattering, thus reducing the thermal conductivity via lattice vibrations. Unfortunately, both of these methods can have a negative effect on the erosion resistance of EB PVD TBCs. This paper compares the relative erosion rates of ten different EB PVD TBCs tested at 90à ° impact at room temperature and at high temperature and discusses the results in term of microstructural and temperature effects. It was found that by modifying the coating deposition, such that a low density coating with a highly â  featheredâ  microstructure formed, generally resulted in an increase in the erosion rate at room temperature. When there was a significant change between the room temperature and the high temperature erosion mechanism it was accompanied by a significant decrease in the erosion rate, while additions of dopents was found to significantly increase the erosion rate at room and high temperature. However, all the modified coatings still had a lower erosion rate than a plasma sprayed coatings. So, although, relative to a standard 7YSZ coating, the modified coatings have a lower erosion resistance, they still perform better than PS TBCs and their lower thermal conductivities could make them viable alternatives to 7YSZ for use in gas turbine en

Tidal influence on Rutford Ice Stream, West Antarctica: observations of surface flow and basal processes from closely-spaced GPS and passive seismic stations

High-resolution surface velocity measurements and passive seismic observations from Rutford Ice Stream, West Antarctica, 40 km upstream from the grounding line are presented. These measurements indicate a complex relationship between the ocean tides and currents, basal conditions and ice-stream flow. Both the mean basal seismicity and the velocity of the ice stream are modulated by the tides. Seismic activity increases twice during each semi-diurnal tidal cycle. The tidal analysis shows the largest velocity variation is at the fortnightly period, with smaller variations superimposed at diurnal and semi-diurnal frequencies. The general pattern of the observed velocity is two velocity peaks during each semi-diurnal tidal cycle, but sometimes three peaks are observed. This pattern of two or three peaks is more regular during spring tides, when the largest-amplitude velocity variations are observed, than during neap tides. This is the first time that velocity and level of seismicity are shown to correlate and respond to tidal forcing as far as 40 km upstream from the grounding line of a large ice stream

Andreev Probe of Persistent Current States in Superconducting Quantum Circuits

Using the extraordinary sensitivity of Andreev interferometers to the superconducting phase difference associated with currents, we measure the persistent current quantum states in superconducting loops interrupted by Josephson junctions. Straightforward electrical resistance measurements of the interferometers give continuous read-out of the states, allowing us to construct the energy spectrum of the quantum circuit. The probe is estimated to be more precise and faster than previous methods, and can measure the local phase difference in a wide range of superconducting circuits.Comment: Changes made in light of referees comments; to appear in PR

Dobrushin-Kotecky-Shlosman theorem for polygonal Markov fields in the plane

We consider the so-called length-interacting Arak-Surgailis polygonal Markov fields with V-shaped nodes - a continuum and isometry invariant process in the plane sharing a number of properties with the two-dimensional Ising model. For these polygonal fields we establish a low-temperature phase separation theorem in the spirit of the Dobrushin-Kotecky-Shlosman theory, with the corresponding Wulff shape deteremined to be a disk due to the rotation invariant nature of the considered model. As an important tool replacing the classical cluster expansion techniques and very well suited for our geometric setting we use a graphical construction built on contour birth and death process, following the ideas of Fernandez, Ferrari and Garcia.Comment: 59 pages, new version revised according to the referee's suggestions and now publishe

Physics of Eclipsing Binaries: Heartbeat Stars and Tidally Induced Pulsations

Heartbeat stars are a relatively new class of eccentric ellipsoidal variable first discovered by Kepler. An overview of the current field is given with details of some of the interesting objects identified in our current Kepler sample of 135 heartbeats stars. Three objects that have recently been or are undergoing detailed study are described along with suggestions for further avenues of research. We conclude by discussing why heartbeat stars are an interesting new tool to study tidally induced pulsations and orbital dynamics