Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling

We propose a way of including the next-to-leading (NLO) order spin-spin coupling into an effective-one-body (EOB) Hamiltonian. This work extends [S. Balmelli and P. Jetzer, Phys. Rev. D 87, 124036 (2013)], which is restricted to the case of equatorial orbits and aligned spins, to general orbits with arbitrary spin orientations. This is done applying appropriate canonical phase-space transformations to the NLO spin-spin Hamiltonian in Arnowitt-Deser-Misner (ADM) coordinates, and systematically adding "effectiv" quantities at NLO to all spin-squared terms appearing in the EOB Hamiltonian. As required by consistency, the introduced quantities reduce to zero in the test- mass limit. We expose the result both in a general gauge and in a gauge-fixed form. The last is chosen such as to minimize the number of new coefficients that have to be inserted into the effective spin squared. As a result, the 25 parameters that describe the ADM NLO spin-spin dynamics get condensed into only 12 EOB terms.Comment: 12 pages, 1 figure. Submitted to Phys. Rev.

Quasiuniversal properties of neutron star mergers

Binary neutron star mergers are studied using nonlinear 3+1 numerical relativity simulations and the analytical effective-one-body (EOB) model. The EOB model predicts quasiuniversal relations between the mass-rescaled gravitational wave frequency and the binding energy at the moment of merger, and certain dimensionless binary tidal coupling constants depending on the stars Love numbers, compactnesses and the binary mass ratio. These relations are quasiuniversal in the sense that, for a given value of the tidal coupling constant, they depend significantly neither on the equation of state nor on the mass ratio, though they do depend on stars spins. The spin dependence is approximately linear for small spins aligned with the orbital angular momentum. The quasiuniversality is a property of the conservative dynamics; nontrivial relations emerge as the binary interaction becomes tidally dominated. This analytical prediction is qualitatively consistent with new, multi-orbit numerical relativity results for the relevant case of equal-mass irrotational binaries. Universal relations are thus expected to characterize neutron star mergers dynamics. In the context of gravitational wave astronomy, these universal relations may be used to constrain the neutron star equation of state using waveforms that model the merger accurately

Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling for two nonprecessing black holes with aligned spins

The canonical Arnowitt-Deser-Misner (ADM) Hamiltonian with next-to-leading order spin-spin coupling [J. Steinhoff, S. Hergt, and G. Schäfer, Phys. Rev. D 77, 081501 (2008); 78, 101503 (2008)] is converted into the effective-one-body (EOB) formalism of [T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 78, 024009 (2008)] for the special case of spinning black hole binaries whose spins are aligned with the angular momentum. In particular, we propose to include the new terms by adding a dynamical term of next-to-leading order to the Kerr parameter squared entering the effective metric. The modified EOB Hamiltonian consistently reduces to the Kerr Hamiltonian as the mass ratio tends to zero; moreover, it predicts the existence of an innermost stable circular orbit. We also derive, for the general case of arbitrarily oriented spins but in the vanishing mass-ratio limit, a coordinate transformation that maps the next-to-leading order spin-spin contribution of the ADM Hamiltonian to the EOB Hamiltonian

Coordination of plug-in electric vehicle charging in a stochastic framework ::a decentralized tax/incentive-based mechanism to reach global optimality

We address the problem of charging plug-in electric vehicles (PEVs) in a decentralized way and under stochastic dynamics affecting the real-time electricity tariff. The model is formulated as a Nash equilibrium seeking problem, where players wish to minimize the costs for charging their own PEVs. For finite PEVs populations, the Nash equilibrium does not correspond to the social optimum, i.e., to a control strategy minimizing the total electricity costs at the aggregate level. We accordingly introduce some taxes/incentives on the price of electricity for charging PEVs and show that it is possible to tune them so that (a) the social optimum is reached as a Nash equilibrium, (b) in correspondence with this equilibrium, players do not pay any net total tax, nor receive any net total incentive

Decentralized computation of charging controls for plug-in electric vehicles in the S-adapted information structure

We study the problem of charging an arbitrary number of plug-in electric vehicles (PEV) under a real-time electricity tariff that depends on the instantaneous grid load, with the addition of a stochastic process that affects the non-PEV demand. Each PEV is subjected to individual and coupling constraints. Formally, we are facing a Generalized Nash Equilibrium (GNE) seeking problem for stochastic aggregative games. The stochastic dynamics is modelized as an event tree and included according to the S-adapted information structure, which is suitable to describe stochastic processes that are independent of the players’ control. The equilibrium is calculated by employing a decentralized scheme. We observe that the valley-filling behavior, which has been observed in previous studies concerning the PEV problem, can be significantly altered by the stochastic dynamics

Estimating the market share for new products with a split questionnaire survey

When designing a new product, conjoint analysis is a powerful tool to estimate the perceived value of the prospects. However, it has a drawback: when the product has too many attributes and levels, it may be difficult to administrate the survey to respondents because they will be overwhelmed by the too numerous questions. In this paper, we propose an alternative approach that permits us to bypass this problem. Contrary to conjoint analysis, which estimates respondents’ utility functions, our approach directly estimates market shares. This enables us to split the questionnaire among respondents and, therefore, to reduce the burden on each respondent as much as desired. However, this new method has two weaknesses that conjoint analysis does not have: first, inferences on a single respondent cannot be made; second, the competition’s product profiles have to be known before administrating the survey. Therefore, our method has to be used when traditional methods are less easily implementable, i.e., when the number of attributes and levels is large. View Full-Tex