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

Comment on ``New ansatz for metric operator calculation in pseudo-Hermitian field theory''

In a recent Brief Report by Shalaby a new first-order perturbative calculation of the metric operator for an $i\phi^3$ scalar field theory is given. It is claimed that the result is an improvement on a previous calculation by Bender, Brody and Jones because it is local. Unfortunately Shalaby's calculation is not valid because of sign errors.Comment: 2 pages, no figures. This comment replaces the previous comment on the Brief Report by Shalaby. In the previous comment we pointed out that Shalaby's calculation failed in all but 2 space-time dimensions. We have subsequently found additional errors which mean that the calculation is not valid even in that cas

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

A Superbubble Feedback Model for Galaxy Simulations

We present a new stellar feedback model that reproduces superbubbles. Superbubbles from clustered young stars evolve quite differently to individual supernovae and are substantially more efficient at generating gas motions. The essential new components of the model are thermal conduction, sub-grid evaporation and a sub-grid multi-phase treatment for cases where the simulation mass resolution is insufficient to model the early stages of the superbubble. The multi-phase stage is short compared to superbubble lifetimes. Thermal conduction physically regulates the hot gas mass without requiring a free parameter. Accurately following the hot component naturally avoids overcooling. Prior approaches tend to heat too much mass, leaving the hot ISM below $10^6$ K and susceptible to rapid cooling unless ad-hoc fixes were used. The hot phase also allows feedback energy to correctly accumulate from multiple, clustered sources, including stellar winds and supernovae. We employ high-resolution simulations of a single star cluster to show the model is insensitive to numerical resolution, unresolved ISM structure and suppression of conduction by magnetic fields. We also simulate a Milky Way analog and a dwarf galaxy. Both galaxies show regulated star formation and produce strong outflows.Comment: 13 pages, 13 figures; replaced with version accepted to MNRA

Early assessment of vestibular function after unilateral cochlear implant surgery

Introduction : Cochlear implantation (CI) has been reported to negatively effect on the vestibular function. The study of the vestibular function has variably been conducted by different types of diagnostic tools. The combined use of modern, rapidly performable diagnostic tools could reveal useful for standardizing the evaluation protocol. Methods: In a group of 28 subjects undergoing CI, the video Head Impulse Test (vHIT), the cervical Vestibular Evoked Myogenic Potentials (cVEMPS) and the short-form of Dizziness Handicap Inventory (DHI) questionnaire were investigated pre-operatively and post-operatively (implant on and off) in both the implanted and the contralateral, non-implanted ear. All surgeries were performed with a round window approach (RWA), except for three otosclerosis cases were the extended RWA (eRWA) was used. Results: The vHIT of the lateral semicircular canal showed a pre-operative vestibular involvement in nearly 50% of the cases, whilst the three canals were contemporarily affected in only 14% of them. In all the hypo-functional subjects, cVEMPs were absent. A low VOR gain in all the investigated SSCC was found in 4 subjects (14%). In those subjects, (21.7%) in whom cVEMPs were pre-operatively present and normal in the operated side, absence of response was post-operatives recorded. Discussion/Conclusion: The vestibular protocol applied for the study showed to be appropriate for distinguishing between the CI operated and the non-operated ear. In this regard, cVEMPs showed to be more sensitive than vHIT for revealing a vestibular sufferance after CI, although without statistical significance. Finally, the use of the RWA surgery was apparently not avoiding signs of vestibular impairment to occur

Note on graviton MHV amplitudes

Two new formulas which express n-graviton MHV tree amplitudes in terms of sums of squares of n-gluon amplitudes are discussed. The first formula is derived from recursion relations. The second formula, simpler because it involves fewer permutations, is obtained from the variant of the Berends, Giele, Kuijf formula given in Arxiv:0707.1035.Comment: 10 page