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

Refeeding Hypophosphatemia in Adolescents With Anorexia Nervosa: A Systematic Review

The rate of adolescents presenting with anorexia nervosa (AN) is increasing. Medically unstable adolescents are admitted to the hospital for nutrition restoration. A lack of global consensus on appropriate refeeding practices of malnourished patients has resulted in inconsistent refeeding practices. Refeeding hypophosphatemia (RH) is the most common complication associated with refeeding the malnourished patient. This review sought to identify the range of refeeding rates adopted globally and the implication that total energy intake and malnutrition may have on RH while refeeding adolescents with anorexia nervosa. Studies were identified by a systematic electronic search of medical databases from 1980 to September 2012. Seventeen publications were identified, including 6 chart reviews, 1 observational study, and 10 case reports, with a total of 1039 subjects. The average refeeding energy intake was 1186 kcal/d, ranging from 125–1900 kcal/d, with a mean percentage median body mass index (% mBMI) of 78%. The average incidence rate of RH was 14%. A significant correlation between malnutrition (% mBMI) and post-refeeding phosphate was identified (R 2 = 0.6, P = .01). This review highlights the disparity in refeeding rates adopted internationally in treating malnourished adolescents with anorexia nervosa. Based on this review, the severity of malnutrition seems to be a marker for the development of RH more so than total energy intake

A Review of the Erosion of Thermal Barrier Coatings.

The application of thermal barrier coatings (TBCs) to components with internal cooling in the hot gas stream of gas turbine engines has facilitated a steep increase in the turbine entry temperature and the associated increase in performance and efficiency of gas turbine engines. However, TBCs are susceptible to various life limiting issues associated with their operating environment including erosion, corrosion, oxidation, sintering and foreign object damage (FOD). This is a review paper that examines various degradation and erosion mechanisms of TBCs, especially those produced by electron beam physical vapour deposition (EB-PVD). The results from a number of laboratory tests under various impact conditions are discussed before the different erosion and FOD mechanisms are reviewed. The transitions between the various erosion mechanisms are discussed in terms of the D/d ratio (contact area diameter/column diameter), a relatively new concept that relates the impact size to the erosion mechanism. The effects of ageing, dopant additions and calciumâ  magnesiumâ  aluminaâ  silicates on the life of TBCs are examined. It is shown that while ageing increases the erosion rate of EB-PVD TBCs, ageing of plasma sprayed TBCs in fact lowers the erosion rate. Finally modelling of EB-PVD TBCs is briefly intr

Erosion, corrosion and erosion-corrosion of EB PVD thermal barrier coatings

Electron beam (EB) physical vapour deposited (PVD) thermal barrier coatings (TBCs) have been used in gas turbine engines for a number of years. The primary mode of failure is attributed to oxidation of the bond coat and growth of the thermally grown oxide (TGO), the alumina scale that forms on the bond coat and to which the ceramic top coat adheres. Once the TGO reaches a critical thickness, the TBC tends to spall and expose the underlying substrate to the hot gases. Erosion is commonly accepted as a secondary failure mechanism, which thins the TBC thus reducing its insulation capability and increasing the TGO growth rate. In severe conditions, erosion can completely remove the TBC over time, again resulting in the exposure of the substrate, typically Ni-based superalloys. Since engine efficiency is related to turbine entry temperature (TET), there is a constant driving force to increase this temperature. With this drive for higher TETs comes corrosion problems for the yttria stabilised zirconia (YSZ) ceramic topcoat. YSZ is susceptible to attack from molten calciumâ  magnesiumâ  aluminaâ  silicates (CMAS) which degrades the YSZ both chemically and micro-structurally. CMAS has a melting point of around 1240 à °C and since it is common in atmospheric dust it is easily deposited onto gas turbine blades. If the CMAS then melts and penetrates into the ceramic, the life of the TBC can be significantly reduced. This paper discusses the various failure mechanisms associated with the erosion, corrosion and erosionâ  corrosion of EB PVD TBCs. The concept of a dimensionless ratio D/d, where D is the contact footprint diameter and d is the column diameter, as a means of determining the erosion mechanism is introduced and discussed for E

Nano and Micro indentation studies of bulk zirconia and EB PVD TBCs

In order to model the erosion of a material it is necessary to know the material properties of both the impacting particles as well as the target. In the case of electron beam (EB) physical vapour deposited(PVD) thermal barrier coatings (TBCs) the properties of the columns as opposed to the coating as a whole are important. This is due to the fact that discrete erosion events are on a similar scale as the size of the individual columns. Thus nano* and micro* indentation were used to determine the hardness and the Young"s modulus of the columns. However, care had to be taken to ensure that it was the hardness of the columns that was being measured and not the coating as a whole. This paper discusses the differences in the results obtained when using the two different tests and relates them to the interactions between the indent and the columns of the EB PVD TBC microstructure. It was found that individual columns had a hardness of 14 GPa measured using nano indentation, while the hardness of the coating, using micro indentation decreased from 13 to 2.4 GPa as the indentation load increased from 0.1 to 3N. This decrease in hardness was attributed to the interaction between the indenter and a number of adjacent columns and the ability of the columns to move laterally under indentation

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

Erosion of gadolinia doped EB-PVD TBCs

Gadolinia additions have been shown to significantly reduce the thermal conductivity of EB-PVD TBCs. The aim of this paper is to further the understanding on the effects of dopants on the erosion resistance of EB-PVD TBCs by studying the effects of 2 mol% Gd2O3 additions on the room and high temperature erosion resistance of as received and aged EB-PVD TBCs. Previously it has been reported that gadolinia additions increased the erosion rate of EB- PVD TBCs, this is indeed the case for room temperature erosion, however under high temperature (825 à °C) erosion conditions this is not the case and the doped TBCs have a slightly lower erosion rate than the standard YSZ EB-PVD TBCs. This has been attributed to a change in the erosion mechanisms that operate at the different temperatures. This change in mechanism was not expected under the impact conditions used and has been attributed to a change in the column diameter, and how this influences the dynamics of particle impactio

The Civil Law of Quebec: Some Disjointed Notes for a Lecture

Quebec private law, though not the public law, can be regarded as a reasonably characteristic example of that system of law known as the Civil Law, one of the world\u27s great legal systems; and you live in the province of Prince Edward Island and I of Nova Scotia, where another of the world\u27s great systems flourishes, the Common Law - you will notice that I say another , not the other . It is right and proper that we should attempt to familiarize ourselves with at least one other system of law besides our own, not necessarily with the detailed rules, which may or may not differ from ours, but with the approach of that other system to human problems, its method. For there is no better avenue to improved knowledge of other peoples than through their law, and no one can deny that a better understanding of French Canada in other parts of our country is badly needed