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, $\Box$, 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 $\Box - {{1/2}}R$ where $R$ 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 $\Box$. 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 $\Box - \frac{1}{2}R$, where $R$ 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