3,070 research outputs found
Stochastic Ergodicity Breaking: a Random Walk Approach
The continuous time random walk (CTRW) model exhibits a non-ergodic phase
when the average waiting time diverges. Using an analytical approach for the
non-biased and the uniformly biased CTRWs, and numerical simulations for the
CTRW in a potential field, we obtain the non-ergodic properties of the random
walk which show strong deviations from Boltzmann--Gibbs theory. We derive the
distribution function of occupation times in a bounded region of space which,
in the ergodic phase recovers the Boltzmann--Gibbs theory, while in the
non-ergodic phase yields a generalized non-ergodic statistical law.Comment: 5 pages, 3 figure
Why does gravitational radiation produce vorticity?
We calculate the vorticity of world--lines of observers at rest in a
Bondi--Sachs frame, produced by gravitational radiation, in a general Sachs
metric. We claim that such an effect is related to the super--Poynting vector,
in a similar way as the existence of the electromagnetic Poynting vector is
related to the vorticity in stationary electrovacum spacetimes.Comment: 9 pages; to appear in Classical and Quantum Gravit
On the structure of the new electromagnetic conservation laws
New electromagnetic conservation laws have recently been proposed: in the
absence of electromagnetic currents, the trace of the Chevreton superenergy
tensor, is divergence-free in four-dimensional (a) Einstein spacetimes
for test fields, (b) Einstein-Maxwell spacetimes. Subsequently it has been
pointed out, in analogy with flat spaces, that for Einstein spacetimes the
trace of the Chevreton superenergy tensor can be rearranged in the
form of a generalised wave operator acting on the energy momentum
tensor of the test fields, i.e., . In this
letter we show, for Einstein-Maxwell spacetimes in the full non-linear theory,
that, although, the trace of the Chevreton superenergy tensor can
again be rearranged in the form of a generalised wave operator
acting on the electromagnetic energy momentum tensor, in this case the result
is also crucially dependent on Einstein's equations; hence we argue that the
divergence-free property of the tensor has
significant independent content beyond that of the divergence-free property of
Magnetic hyperthermia in single-domain monodisperse FeCo nanoparticles: Evidences for Stoner-Wohlfarth behaviour and large losses
We report on hyperthermia measurements on a colloidal solution of 15 nm
monodisperse FeCo nanoparticles (NPs). Losses as a function of the magnetic
field display a sharp increase followed by a plateau, which is what is expected
for losses of ferromagnetic single-domain NPs. The frequency dependence of the
coercive field is deduced from hyperthermia measurement and is in quantitative
agreement with a simple model of non-interacting NPs. The measured losses (1.5
mJ/g) compare to the highest of the literature, though the saturation
magnetization of the NPs is well below the bulk one.Comment: 14 pages, 3 figure
A local potential for the Weyl tensor in all dimensions
In all dimensions and arbitrary signature, we demonstrate the existence of a
new local potential -- a double (2,3)-form -- for the Weyl curvature tensor,
and more generally for all tensors with the symmetry properties of the Weyl
curvature tensor. The classical four-dimensional Lanczos potential for a Weyl
tensor -- a double (2,1)-form -- is proven to be a particular case of the new
potential: its double dual.Comment: 7 pages; Late
Reference frames and rigid motions in relativity: Applications
The concept of rigid reference frame and of constricted spatial metric, given
in the previous work [\emph{Class. Quantum Grav.} {\bf 21}, 3067,(2004)] are
here applied to some specific space-times: In particular, the rigid rotating
disc with constant angular velocity in Minkowski space-time is analyzed, a new
approach to the Ehrenfest paradox is given as well as a new explanation of the
Sagnac effect. Finally the anisotropy of the speed of light and its measurable
consequences in a reference frame co-moving with the Earth are discussed.Comment: 13 pages, 1 figur
Consequences of a Killing symmetry in spacetime's local structure
In this paper we discuss the consequences of a Killing symmetry on the local
geometrical structure of four-dimensional spacetimes. We have adopted the point
of view introduced in recent works where the exterior derivative of the Killing
plays a fundamental role. Then, we study some issues related with this approach
and clarify why in many circumstances its use has advantages with respect to
other approaches. We also extend the formalism developed in the case of vacuum
spacetimes to the general case of an arbitrary energy-momentum content.
Finally, we illustrate our framework with the case of spacetimes with a
gravitating electromagnetic field.Comment: 20 pages, LaTeX2e, IOP style. Revised version accepted for
publication in Classical and Quantum Gravit
Cosmology in the Solar System: Pioneer effect is not cosmological
Does the Solar System and, more generally, a gravitationally bound system
follow the cosmic expansion law ? Is there a cosmological influence on the
dynamics or optics in such systems ? The general relativity theory provides an
unique and unambiguous answer, as a solution of Einstein equations with a local
source in addition to the cosmic fluid, and obeying the correct (cosmological)
limiting conditions. This solution has no analytic expression. A Taylor
development of its metric allows a complete treatment of dynamics and optics in
gravitationally bound systems, up to the size of galaxy clusters, taking into
account both local and cosmological effects. In the solar System, this provides
an estimation of the (non zero) cosmological influence on the Pioneer probe: it
fails to account for the " Pioneer effect " by about 10 orders of magnitude. We
criticize contradictory claims on this topic
Spacetime dynamics of spinning particles - exact electromagnetic analogies
We compare the rigorous equations describing the motion of spinning test
particles in gravitational and electromagnetic fields, and show that if the
Mathisson-Pirani spin condition holds then exact gravito-electromagnetic
analogies emerge. These analogies provide a familiar formalism to treat
gravitational problems, as well as a means for comparing the two interactions.
Fundamental differences are manifest in the symmetries and time projections of
the electromagnetic and gravitational tidal tensors. The physical consequences
of the symmetries of the tidal tensors are explored comparing the following
analogous setups: magnetic dipoles in the field of non-spinning/spinning
charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter
spacetimes. The implications of the time projections of the tidal tensors are
illustrated by the work done on the particle in various frames; in particular,
a reciprocity is found to exist: in a frame comoving with the particle, the
electromagnetic (but not the gravitational) field does work on it, causing a
variation of its proper mass; conversely, for "static observers," a stationary
gravitomagnetic (but not a magnetic) field does work on the particle, and the
associated potential energy is seen to embody the Hawking-Wald spin-spin
interaction energy. The issue of hidden momentum, and its counterintuitive
dynamical implications, is also analyzed. Finally, a number of issues regarding
the electromagnetic interaction and the physical meaning of Dixon's equations
are clarified.Comment: 32+11 pages, 5 figures. Edited and further improved version, with new
Section C.2 unveiling analogies for arbitrary spin conditions, and new Sec.
3.2.3 in the Supplement making connection to the post-Newtonian
approximation; former Sec. III.B.4 and Appendix C moved to the (reshuffled)
Supplement; references updated. The Supplement is provided in ancillary file.
Matches the final published versio
Dynamical laws of superenergy in General Relativity
The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an
attempt to generalize to gravitation the energy-momentum tensor of
electromagnetism. This generalization was successful from the mathematical
point of view because these tensors share mathematical properties which are
remarkably similar to those of the energy-momentum tensor of electromagnetism.
However, the physical role of these tensors in General Relativity has remained
obscure and no interpretation has achieved wide acceptance. In principle, they
cannot represent {\em energy} and the term {\em superenergy} has been coined
for the hypothetical physical magnitude lying behind them. In this work we try
to shed light on the true physical meaning of {\em superenergy} by following
the same procedure which enables us to give an interpretation of the
electromagnetic energy. This procedure consists in performing an orthogonal
splitting of the Bel and Bel-Robinson tensors and analysing the different parts
resulting from the splitting. In the electromagnetic case such splitting gives
rise to the electromagnetic {\em energy density}, the Poynting vector and the
electromagnetic stress tensor, each of them having a precise physical
interpretation which is deduced from the {\em dynamical laws} of
electromagnetism (Poynting theorem). The full orthogonal splitting of the Bel
and Bel-Robinson tensors is more complex but, as expected, similarities with
electromagnetism are present. Also the covariant divergence of the Bel tensor
is analogous to the covariant divergence of the electromagnetic energy-momentum
tensor and the orthogonal splitting of the former is found. The ensuing {\em
equations} are to the superenergy what the Poynting theorem is to
electromagnetism. See paper for full abstract.Comment: 27 pages, no figures. Typos corrected, section 9 suppressed and more
acknowledgments added. To appear in Classical and Quantum Gravit
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