Hydrogen, helium and lithium plasmas at high pressures

The equations of state (EoS) and other thermodynamic properties of plasmas of the light elements H, He, and Li, are calculated using inverted fugacity expansions. Fugacity expansions are known as an alternative to density expansions but show often an inferior convergence. If, however, the inversion can be solved, the fugacity representations may be very efficient. In particular, the contributions of deeply bound states are included in the fugacity expansion in a very effective way. The mathematical problems on nonlinearity connected with the inversion of fugacities to densities are reduced to solvable algebraic problems. The inversion of fugacities to densities is solved separately for two density regions: (i) In the low density, non-degenerate region we consider ring contributions describing screening effects and ladder contributions describing bound state formation. (ii) In the high density, degenerate region the electrons are described by the Fermi–Dirac distribution. Hartree–Fock contributions and Pauli blocking have to be taken into account. The ions are considered as classical, strongly correlated subsystem eventually forming a Wigner lattice. We solve the inversion problem for each of the regions. Near the crossing point, the separate solutions are connected to each other, either by smooth concatenation at the crossing point or by Padé approximations.

Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

Virial Approximation for Load and Loss in High-Speed Journal Bearings Using Pressurized Gases

We consider steady, laminar, compressible lubrication flows in a high-speed two-dimensional journal bearing governed by the appropriate Reynolds equation. The thermodynamic states correspond to pressurized gases and are in the single-phase regime. Simple explicit formulas for the load capacity, power loss, and attitude angle are derived by applying the virial (or small density) expansions of pressure and shear viscosity to results developed in previous studies. The present virial approximation was compared to the exact numerical solutions to the Reynolds equation. It was shown that the results based on our virial expansions are quite accurate at thermodynamic states corresponding to dense and supercritical gases. The first virial correction is seen to significantly improve predictions based on the ideal gas theory.

Addressing the determinants of built-up expansion and densification processes at the regional scale

An in-depth understanding of the main factors behind built-up development is a key prerequisite for designing policies dedicated to a more efficient land use. Infill development policies are essential to curb sprawl and allow a progressive recycling of low-density areas inherited from the past. This paper examines the controlling factors of built-up expansion and densification processes in Wallonia (Belgium). Unlike the usual urban/built-up expansion studies, our approach considers various levels of built-up densities to distinguish between different types of developments, ranging from low-density extensions (or sprawl) to high-density infill development. Belgian cadastral data for 1990, 2000 and 2010 were used to generate four classes of built-up areas, namely, non-, low-, medium- and high-density areas. A number of socioeconomic, geographic and political factors related to built-up development were operationalised following the literature. We then used a multinomial logistic regression model to analyse the effects of these factors on the transitions between different densities in the two decades between 1990 and 2010. The findings indicate that all the controlling factors show distinctive variations based on density. More specifically, the centrality of zoning policies in explaining expansion processes is highlighted. This is especially the case for high-density expansions. In contrast, physical and neighbourhood factors play a larger role in infill development, especially for dense infill development.