A measurement of the equation of state of carbon envelopes of white dwarfs.

White dwarfs represent the final state of evolution for most stars1-3. Certain classes of white dwarfs pulsate4,5, leading to observable brightness variations, and analysis of these variations with theoretical stellar models probes their internal structure. Modelling of these pulsating stars provides stringent tests of white dwarf models and a detailed picture of the outcome of the late stages of stellar evolution6. However, the high-energy-density states that exist in white dwarfs are extremely difficult to reach and to measure in the laboratory, so theoretical predictions are largely untested at these conditions. Here we report measurements of the relationship between pressure and density along the principal shock Hugoniot (equations describing the state of the sample material before and after the passage of the shock derived from conservation laws) of hydrocarbon to within five per cent. The observed maximum compressibility is consistent with theoretical models that include detailed electronic structure. This is relevant for the equation of state of matter at pressures ranging from 100 million to 450 million atmospheres, where the understanding of white dwarf physics is sensitive to the equation of state and where models differ considerably. The measurements test these equation-of-state relations that are used in the modelling of white dwarfs and inertial confinement fusion experiments7,8, and we predict an increase in compressibility due to ionization of the inner-core orbitals of carbon. We also find that a detailed treatment of the electronic structure and the electron degeneracy pressure is required to capture the measured shape of the pressure-density evolution for hydrocarbon before peak compression. Our results illuminate the equation of state of the white dwarf envelope (the region surrounding the stellar core that contains partially ionized and partially degenerate non-ideal plasmas), which is a weak link in the constitutive physics informing the structure and evolution of white dwarf stars9.

Statistics of extremes in oil spill risk analysis.

The Deepwater Horizon oil spill (DWH) in 2010 in the Gulf of Mexico is the largest accidental marine oil spill in the history of the petroleum industry. After DWH, key questions were asked: What is the likelihood that a similar catastrophic oil spill (with a volume over 1 million barrels) will happen again? Is DWH an extreme event or will it happen frequently in the future? The extreme value theory (EVT) has been widely used in studying rare events, including damage from hurricanes, stock market crashes, insurance claims, flooding, and earthquakes. In this paper, the EVT is applied to analyze oil spills in the U.S. outer continental shelf (OCS). Incorporating the 49 years (1964-2012) of OCS oil spill data, the EVT is capable of describing the oil spills reasonably well. The return period of a catastrophic oil spill in OCS areas is estimated to be 165 years, with a 95% confidence interval between 41 years and more than 500 years. Sensitivity tests indicate that the EVT results are relatively stable. The results of this study are very useful for oil spill risk assessment, contingency planning, and environmental impact statements on oil exploration, development, and production.

Black-body radiation shifts and theoretical contributions to atomic clock research.

A review of theoretical calculations of black-body radiation (BBR) shifts in various systems of interest to atomic clock research is presented. Calculations for monovalent systems, such as Ca(+), Sr(+), and Rb are carried out using a relativistic all-order single-double method, where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. A recently developed method for accurate calculations of BBR shifts in divalent atoms such as Sr is discussed. This approach combines the relativistic allorder method and the configuration interaction method. The evaluation of uncertainties in theoretical values of BBR shifts is discussed in detail.

Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range.

We present the calculated prediction and the experimental confirmation that doubly ionized Ag and Sn plasmas can have an index of refraction greater than one for soft x-ray wavelengths. Interferometry experiments conducted using a capillary discharge soft x-ray laser operating at a wavelength of confirm that in few times ionized laser-created plasmas of these elements the anomalous dispersion from bound electrons can dominate the free electron contribution, making the index of refraction greater than one. The results confirm that bound electrons can strongly influence the index of refraction of numerous plasmas over a broad range of soft x-ray wavelengths confirming recent observations. The understanding of index of refraction at short wavelengths will become even more essential during the next decade as x-ray free electron lasers will become available to probe a wider variety of plasmas at higher densities and shorter wavelengths.

Plasma interferometry and how the bound-electron contribution can bend fringes in unexpected ways.

Utilizing a new average atom code, we calculate the index of refraction in C, Al, Ti, and Pd plasmas and show many conditions over which the bound-electron contribution dominates the free electrons as we explore photon energies from the optical to 100 eV (12 nm) soft x rays. For decades measurement of the electron density in plasmas by interferometers has relied on the approximation that the index of refraction in a plasma is due solely to the free electrons and therefore is less than 1. Recent measurements of Al plasmas using x-ray laser interferometers observed fringes bending in the opposite direction than expected due to the bound-electron contribution causing the index of refraction to be larger than 1. During the next decade x-ray free-electron lasers and other sources will be available to probe a wider variety of plasmas at higher densities and shorter wavelengths, so understanding the index of refraction in plasmas is essential.