Kohn-Sham calculations combined with an average pair-density functional theory

A recently developed formalism in which Kohn-Sham calculations are combined with an ``average pair density functional theory'' is reviewed, and some new properties of the effective electron-electron interaction entering in this formalism are derived. A preliminary construction of a fully self-consitent scheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th International Workshop on Condensed Matter Theories

The interaction-strength interpolation method for main-group chemistry: benchmarking, limitations, and perspectives

We have tested the original interaction-strength-interpolation (ISI) exchange-correlation functional for main group chemistry. The ISI functional is based on an interpolation between the weak and strong coupling limits and includes exact-exchange as well as the G\"orling-Levy second-order energy. We have analyzed in detail the basis-set dependence of the ISI functional, its dependence on the ground-state orbitals, and the influence of the size-consistency problem. We show and explain some of the expected limitations of the ISI functional (i.e. for atomization energies), but also unexpected results, such as the good performance for the interaction energy of dispersion-bonded complexes when the ISI correlation is used as a correction to Hartree-Fock.Comment: 20 pages, 20 figure

Strictly correlated uniform electron droplets

We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching the tighter forms of the Lieb-Oxford bound recently proposed by Rasanen et al. [Phys. Rev. Lett. 102, 206406 (2009)]. The bound is satisfied in three-, two-, and one-dimensional droplets, and in the latter case it is reached exactly - regardless of the type of interaction considered. Our results provide useful reference data for delocalized strongly correlated systems, and they can be used in the development and testing of exchange-correlation density functionals in the framework of density-functional theory

System-adapted correlation energy density functionals from effective pair interactions

We present and discuss some ideas concerning an ``average-pair-density functional theory'', in which the ground-state energy of a many-electron system is rewritten as a functional of the spherically and system-averaged pair density. These ideas are further clarified with simple physical examples. We then show that the proposed formalism can be combined with density functional theory to build system-adapted correlation energy functionals. A simple approximation for the unknown effective electron-electron interaction that enters in this combined approach is described, and results for the He series and for the uniform electron gas are briefly reviewed.Comment: to appear in Phil. Mag. as part of Conference proceedings for the "Electron Correlations and Materials Properties", Kos Greece, July 5-9, 200

Experimental investigation of the mooring system of a wave energy converter in operating and extreme wave conditions

A proper design of the mooring systems for Wave Energy Converters (WECs) requires an accurate investigation of both operating and extreme wave conditions. A careful analysis of these systems is required to design a mooring configuration that ensures station keeping, reliability, maintainability, and low costs, without affecting the WEC dynamics. In this context, an experimental campaign on a 1:20 scaled prototype of the ISWEC (Inertial Sea Wave Energy Converter), focusing on the influence of the mooring layout on loads in extreme wave conditions, is presented and discussed. Two mooring configurations composed of multiple slack catenaries with sub-surface buoys, with or without clump-weights, have been designed and investigated experimentally. Tests in regular, irregular, and extreme waves for a moored model of the ISWEC device have been performed at the University of Naples Federico II. The aim is to identify a mooring solution that could guarantee both correct operation of the device and load carrying in extreme sea conditions. Pitch motion and loads in the rotational joint have been considered as indicators of the device hydrodynamic behavior and mooring configuration impact on the WEC

Incumbents, opposition and international lenders: governing Portugal in times of crisis

The Portuguese case provides a unique opportunity to study the opposition's behaviour in a variety of political conditions. It offers an insight into the impact of the financial crisis on the opposition's behaviour in both majority and minority political settings. It allows the comparison of the opposition's relationship with a minority government, during which non-collaboration could have dramatic consequences, and also with a majority government, when such a choice does not have major political or policy implications. Moreover, it enables us to study the effect of an additional veto player (the so-called troika composed of the European Commission, the European Central Bank and the International Monetary Fund), which not only constrains both majority and opposition parties, but also gives political entrepreneurs a unique opportunity to push ahead with liberal measures \u2013 in this case, clearly in disagreement with the moderate and radical left programmes. Relying on quantitative data on the legislative behaviour of the parliamentary party groups in the period 1995\u20132012, and on qualitative process-tracking of the opposition's positions on key economic issues \u2013 such as the decision to vote against Prime Minister S\uf3crates' last austerity package after a series of approvals \u2013 this article aims to determine whether, and if yes how, the financial crisis has affected the behaviour of the Portuguese opposition parties in parliament, by examining and comparing their behaviour in hard and in normal times

Regularity of higher codimension area minimizing integral currents

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L. Ambrosio Ed., Edizioni SNS (CRM Series

Restoring size consistency of approximate functionals constructed from the adiabatic connection

Approximate exchange-correlation functionals built by modeling in a non-linear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameters-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than the second-order perturbation theory.Comment: 6 pages, 3 figure

SBV regularity for Hamilton-Jacobi equations in Rn\mathbb R^n

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$\partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.Comment: 15 page