8,199 research outputs found
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 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 particle system
in the large limit. Using a coarse-graining in phase space of the exact
Klimontovich equation for the particle system, we evaluate, neglecting
correlations of density fluctuations, the scalings with 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 , with at large scales, and regulated
to a bounded behaviour below a "softening" scale , we find that
there is an essential qualitative difference between the cases and
, 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 , while for the amplitude of these terms is
directly regulated by , and thus by the small scale properties of
the interaction. This corresponds to a simple physical criterion for a basic
distinction between long-range () and short range () interactions, different to the canonical one ( or ) 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
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