The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

Choice of calibration equations of the TSM method

For the reciprocal-test fixtures, there are six independent S-parameters to. be determined, and the thru-short-match (TSM) calibration can provide eight calibration equations. In this paper, the relation of calibration equations is investigated. It has been shown that the four equations obtained from the measurement with a transmission standard can be used simultaneously in the calibration. Experimental results show that the different choice of equations will lead to quite different solution, and the calibration accuracy can be improved by taking advantages of the established relation among the calibration equations and properly choosing calibration equations.

Available potential energy density for a multicomponent Boussinesq fluid with arbitrary nonlinear equation of state

In this paper, the concept of available potential energy (APE) density is extended to a multicomponent Boussinesq fluid with a nonlinear equation of state. As shown by previous studies, the APE density is naturally interpreted as the work against buoyancy forces that a parcel needs to perform to move from a notional reference position at which its buoyancy vanishes to its actual position; because buoyancy can be defined relative to an arbitrary reference state, so can APE density. The concept of APE density is therefore best viewed as defining a class of locally defined energy quantities, each tied to a different reference state, rather than as a single energy variable. An important result, for which a new proof is given, is that the volume integrated APE density always exceeds Lorenz’s globally defined APE, except when the reference state coincides with Lorenz’s adiabatically re-arranged reference state of minimum potential energy. A parcel reference position is systematically defined as a level of neutral buoyancy (LNB): depending on the nature of the fluid and on how the reference state is defined, a parcel may have one, none, or multiple LNB within the fluid. Multiple LNB are only possible for a multicomponent fluid whose density depends on pressure. When no LNB exists within the fluid, a parcel reference position is assigned at the minimum or maximum geopotential height. The class of APE densities thus defined admits local and global balance equations, which all exhibit a conversion with kinetic energy, a production term by boundary buoyancy fluxes, and a dissipation term by internal diffusive effects. Different reference states alter the partition between APE production and dissipation, but neither affect the net conversion between kinetic energy and APE, nor the difference between APE production and dissipation. We argue that the possibility of constructing APE-like budgets based on reference states other than Lorenz’s reference state is more important than has been previously assumed, and we illustrate the feasibility of doing so in the context of an idealised and realistic oceanic example, using as reference states one with constant density and another one defined as the horizontal mean density field; in the latter case, the resulting APE density is found to be a reasonable approximation of the APE density constructed from Lorenz’s reference state, while being computationally cheaper.

Transport properties and equation of state of quark-nuclear matter

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two-State Thermodynamics of Supercooled Water

Water has been called the “most studied and least understood” of all liquids, and upon supercooling its behavior becomes even more anomalous. One particularly fruitful hypothesis posits a liquid-liquid critical point terminating a line of liquid-liquid phase transitions that lies just beyond the reach of experiment. Underlying this hypothesis is the conjecture that there is a competition between two distinct hydrogen-bonding structures of liquid water, one associated with high density and entropy and the other with low density and entropy. The competition between these structures is hypothesized to lead at very low temperatures to a phase transition between a phase rich in the high-density structure and one rich in the low-density structure. Equations of state based on this conjecture have given an excellent account of the thermodynamic properties of supercooled water. In this thesis, I extend that line of research. I treat supercooled aqueous solutions and anomalous behavior of the thermal conductivity of supercooled water. I also address supercooled water at negative pressures, leading to a framework for a coherent understanding of the thermodynamics of water at low temperatures. I supplement analysis of experimental results with data from the TIP4P/2005 model of water, and include an extensive analysis of the thermodynamics of this model.

Fear, trust and Aborigines : The historical experience of state institutions and current encounters in the health system

Troubled dynamics between residents of an Aboriginal town in Queensland and the local health system were established during colonisation and consolidated during those periods of Australian history where the policies of 'protection' (segregation), integration and then assimilation held sway. The status of Aboriginal health is, in part, related to interactions between the residents' current and historical experiences of the health and criminal justice systems as together these agencies used medical and moral policing to legitimate dispossession, marginalisation, institutionalisation and control of the residents. The punitive regulations and ethnocentric strategies used by these institutions are within the living memory of many of the residents or in the published accounts of preceding generations. This paper explores current residents' memories and experiences.

3D CFD simulations of a candidate R143a radial-inflow turbine for geothermal power applications

Optimisation of Organic Rankine Cycles (ORCs) for binary cycle applications could play a major role in determining the competitiveness of low to moderate renewable sources. An important aspect of the optimisation is to maximise the turbine output power for a given resource. This requires careful attention to the turbine design notably through numerical simulations. Challenges in the numerical modelling of radial-inflow turbines using high-density working fluids still need to be addressed in order to improve the turbine design and better optimise ORCs. This paper presents preliminary 3D numerical simulations of a radial-inflow turbine working with high-density fluids in realistic geothermal ORCs. Following extensive investigation of the operating conditions and thermodynamic cycle analysis, the refrigerant R143a is chosen as the high-density working fluid. The 1D design of the candidate radial-inflow turbine is presented in details. Furthermore, commercially-available software Ansys-CFX is used to perform the 3D CFD simulations for a number of operating conditions including off-design conditions. The real-gas properties are obtained using the Peng-Robinson equations of state. The preliminary design created using dedicated radial-inflow turbine software Concepts-Rital is discussed and the 3D CFD results are presented and compared against the meanline analysis.

Three-dimensional off-design numerical analysis of an organic Rankine cycle radial-inflow turbine

Optimisation of organic Rankine cycles(ORCs for binary cycle applications could play a major role in determining the competitiveness of low to moderate renewable sources. An important aspect of the optimisation is to maximise the turbine output power for a given resource. This requires careful attention to the turbine design notably through numerical simulations. Challenges in the numerical modelling of radial-inflow turbines using high-density working fluids still need to be addressed in order to improve the turbine design and better optimise ORCs. Thispaper presents preliminary 3D numerical simulations of a high-density radial-inflow ORC turbine in sensible geothermal conditions. Following extensive investigation of the operating conditions and thermodynamic cycle analysis, therefrigerant R143a is chosen as the high-density working fluid. The 1D design of the candidate radial-inflow turbine is presented in details. Furthermore, commercially-available software Ansys-CFX is used to perform preliminary steady-state 3D CFD simulations of the candidate R143a radial-inflow turbine for a number of operating conditions including off-design conditions. The real-gas properties are obtained using the Peng–Robinson equations of state.The thermodynamic ORC cycle is presented. The preliminary design created using dedicated radial-inflow turbine software Concepts-Rital is discussed and the 3D CFD results are presented and compared against the meanline analysis.

Reason of state and a new notion of fortune : Historicising the risk society

Since the 1980s the concept of risk has produced a large and diverse volume of sociological research. Ulrich Beck’s groundbreaking risk society thesis provides a particularly engaging contribution, since it seems that nearly every sociological account of risk engages with this work. For Beck, we are living in second modernity – a new epoch that breaks with pre-modernity and industrial society due to the centrality, incalculability and reflexivity of globalised risk. While Beck’s theory is compelling, a reading of other theorists such as Foucault (2007[1978]) and Hacking (1975,1990) suggests that a difficulty with Beck’s work is that in attempting to explain what is novel about risk in contemporary times, he too quickly passes over the complexities and ruptures of historical change that impact on the history and contingency of risk. This paper begins by presenting a brief analysis of the present state of risk by introducing Beck’s historical narrative of risk from pre-modernity to the risk society; it then outlines the challenges with the “risk as epoch” argument by considering a range of literature, which suggests risk has a more complex history than proposed by Beck; and finally it highlights the value in examining strategies of statecraft in early modern Europe, specifically Machiavelli’s The Prince (2008[1513]) and Giovanni Botero’s political treatise, Della Ragion di Stato (1956[1589]) – as a means of more thoroughly understanding how our current concept of risk emerges. In doing so, this paper seeks to open up new trajectories in the historicisation of risk for other interested scholars.

Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

Volumetric behavior of ethylene and ethylene-hydrogen mixtures

A Burnett apparatus deslgned and fabrlcated was used to collect volumetric data for ethylene and ethylene-hydrogen mixtures. Measurements were made In the temperature range 298.15-423.15 K at Intervals of 25 K and In the pressure range 0.3-7.0 MPa. Vlrlal coefflclents derlved from the compresslblllty data are tabulated. The data are fltted to different equations of state.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.