11,380 research outputs found
The Scalar Curvature of a Causal Set
A one parameter family of retarded linear operators on scalar fields on
causal sets is introduced. When the causal set is well-approximated by 4
dimensional Minkowski spacetime, the operators are Lorentz invariant but
nonlocal, are parametrised by the scale of the nonlocality and approximate the
continuum scalar D'Alembertian, , when acting on fields that vary slowly
on the nonlocality scale. The same operators can be applied to scalar fields on
causal sets which are well-approximated by curved spacetimes in which case they
approximate where is the Ricci scalar curvature. This can
used to define an approximately local action functional for causal sets.Comment: Typo in definition of equation (3) and definition of n(x,y)
corrected. Note: published version still contains typ
The continuum limit of a 4-dimensional causal set scalar d'Alembertian
The continuum limit of a 4-dimensional, discrete d'Alembertian operator for
scalar fields on causal sets is studied. The continuum limit of the mean of
this operator in the Poisson point process in 4-dimensional Minkowski spacetime
is shown to be the usual continuum scalar d'Alembertian . It is shown
that the mean is close to the limit when there exists a frame in which the
scalar field is slowly varying on a scale set by the density of the Poisson
process. The continuum limit of the mean of the causal set d'Alembertian in
4-dimensional curved spacetime is shown to equal , where
is the Ricci scalar, under certain conditions on the spacetime and the
scalar field.Comment: 31 pages, 2 figures. Slightly revised version, accepted for
publication in Classical and Quantum Gravit
Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back
We use numerical integrations to study the asymptotical behaviour of a
homogeneous but anisotropic Bianchi type IX model in General Relativity with a
massive scalar field. As it is well known, for a Brans-Dicke theory, the
asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke
coupling constant with respect to the value -3/2. In this paper we examine if
such a condition still exists with a massive scalar field. We also show that,
contrary to what occurs for a massless scalar field, the singularity
oscillatory approach may exist in presence of a massive scalar field having a
positive energy density.Comment: 31 pages, 7 figures (low resolution
Human Communication Systems Evolve by Cultural Selection
Human communication systems, such as language, evolve culturally; their
components undergo reproduction and variation. However, a role for selection in
cultural evolutionary dynamics is less clear. Often neutral evolution (also
known as 'drift') models, are used to explain the evolution of human
communication systems, and cultural evolution more generally. Under this
account, cultural change is unbiased: for instance, vocabulary, baby names and
pottery designs have been found to spread through random copying.
While drift is the null hypothesis for models of cultural evolution it does
not always adequately explain empirical results. Alternative models include
cultural selection, which assumes variant adoption is biased. Theoretical
models of human communication argue that during conversation interlocutors are
biased to adopt the same labels and other aspects of linguistic representation
(including prosody and syntax). This basic alignment mechanism has been
extended by computer simulation to account for the emergence of linguistic
conventions. When agents are biased to match the linguistic behavior of their
interlocutor, a single variant can propagate across an entire population of
interacting computer agents. This behavior-matching account operates at the
level of the individual. We call it the Conformity-biased model. Under a
different selection account, called content-biased selection, functional
selection or replicator selection, variant adoption depends upon the intrinsic
value of the particular variant (e.g., ease of learning or use). This second
alternative account operates at the level of the cultural variant. Following
Boyd and Richerson we call it the Content-biased model. The present paper tests
the drift model and the two biased selection models' ability to explain the
spread of communicative signal variants in an experimental micro-society
On Pair Creation of Extremal Black Holes and Kaluza-Klein Monopoles
Classical solutions describing charged dilaton black holes accelerating in a
background magnetic field have recently been found. They include the Ernst
metric of the Einstein-Maxwell theory as a special case. We study the extremal
limit of these solutions in detail, both at the classical and quantum levels.
It is shown that near the event horizon, the extremal solutions reduce
precisely to the static extremal black hole solutions. For a particular value
of the dilaton coupling, these extremal black holes are five dimensional
Kaluza-Klein monopoles. The euclidean sections of these solutions can be
interpreted as instantons describing the pair creation of extremal black
holes/Kaluza-Klein monopoles in a magnetic field. The action of these
instantons is calculated and found to agree with the Schwinger result in the
weak field limit. For the euclidean Ernst solution, the action for the extremal
solution differs from that of the previously discussed wormhole instanton by
the Bekenstein-Hawking entropy. However, in many cases quantum corrections
become large in the vicinity of the black hole, and the precise description of
the creation process is unknown.Comment: 45 pages, 5 figures, EFI-93-74, UCSBTH-93-38. (Omitted
acknowledgements added, typos fixed
An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime
A simple approximation formula is derived here for the dependence of the
period of a simple pendulum on amplitude that only requires a pocket calculator
and furnishes an error of less than 0.25% with respect to the exact period. It
is shown that this formula describes the increase of the pendulum period with
amplitude better than other simple formulas found in literature. A good
agreement with experimental data for a low air-resistance pendulum is also
verified and it suggests, together with the current availability/precision of
timers and detectors, that the proposed formula is useful for extending the
pendulum experiment beyond the usual small-angle oscillations.Comment: 15 pages and 4 figures. to appear in American Journal of Physic
Effect of spin orbit scattering on the magnetic and superconducting properties of nearly ferromagnetic metals: application to granular Pt
We calculate the effect of scattering on the static, exchange enhanced, spin
susceptibility and show that in particular spin orbit scattering leads to a
reduction of the giant moments and spin glass freezing temperature due to
dilute magnetic impurities. The harmful spin fluctuation contribution to the
intra-grain pairing interaction is strongly reduced opening the way for BCS
superconductivity. We are thus able to explain the superconducting and magnetic
properties recently observed in granular Pt as due to scattering effects in
single small grains.Comment: 9 pages 3 figures, accepted for publication in Phys. Rev. Letter
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