Embedding nonrelativistic physics inside a gravitational wave

Gravitational waves with parallel rays are known to have remarkable properties: Their orbit space of null rays possesses the structure of a non-relativistic spacetime of codimension-one. Their geodesics are in one-to-one correspondence with dynamical trajectories of a non-relativistic system. Similarly, the null dimensional reduction of Klein-Gordon's equation on this class of gravitational waves leads to a Schroedinger equation on curved space. These properties are generalized to the class of gravitational waves with a null Killing vector field, of which we propose a new geometric definition, as conformally equivalent to the previous class and such that the Killing vector field is preserved. This definition is instrumental for performing this generalization, as well as various applications. In particular, results on geodesic completeness are extended in a similar way. Moreover, the classification of the subclass with constant scalar invariants is investigated.Comment: 56 pages, 9 figures, v3:Minor correction

Finite NN corrections to Vlasov dynamics and the range of pair interactions

We explore the conditions on a pair interaction for the validity of the Vlasov equation to describe the dynamics of an interacting $N$ particle system in the large $N$ limit. Using a coarse-graining in phase space of the exact Klimontovich equation for the $N$ particle system, we evaluate, neglecting correlations of density fluctuations, the scalings with $N$ of the terms describing the corrections to the Vlasov equation for the coarse-grained one particle phase space density. Considering a generic interaction with radial pair force $F(r)$, with $F(r) \sim 1/r^\gamma$ at large scales, and regulated to a bounded behaviour below a "softening" scale $\varepsilon$, we find that there is an essential qualitative difference between the cases $\gamma < d$ and $\gamma > d$, i.e., depending on the integrability at large distances of the pair force. In the former case the corrections to the Vlasov dynamics for a given coarse-grained scale are essentially insensitive to the softening parameter $\varepsilon$, while for $\gamma > d$ the amplitude of these terms is directly regulated by $\varepsilon$, and thus by the small scale properties of the interaction. This corresponds to a simple physical criterion for a basic distinction between long-range ($\gamma \leq d$) and short range ($\gamma > d$) interactions, different to the canonical one ($\gamma \leq d +1$ or $\gamma > d +1$ ) based on thermodynamic analysis. This alternative classification, based on purely dynamical considerations, is relevant notably to understanding the conditions for the existence of so-called quasi-stationary states in long-range interacting systems.Comment: 12 pages, 2 figures, minor corrections and changes, published versio

Attractor non-equilibrium stationary states in perturbed long-range interacting systems

Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSS we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique non-equilibrium stationary state, completely different to its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g. spatial density or velocity distribution) of the system itself.Comment: 16 pages, 12 figure

Time course of evoked-potential changes in different forms of anomia in aphasia

No abstract available

What Allotment and Subcontracting in Procurement Bidding

Allotment and subcontracting are the two alternative mechanisms enabling the participation of SMEs in procurement. We compare these two alternatives in the context of a procurement contract awarded by a first-price sealed-bid auction. When the winning large firm is constrained with respect to the degree of subcontracting, we show that only a reduction of the chosen SME's profit can reduce the expected cost of the contract. However, when the large firm is allowed to choose the subcontracting level, subcontracting can be a Pareto dominating mechanism, i.e. simultaneously increasing both firms' profits and reducing the expected total cost of the contract.allotment; subcontracting; procurement; bidding