Cosmological bounds on tachyonic neutrinos

Recent time-of-flight measurements on muon neutrinos in the OPERA neutrino oscillation experiment have found anomalously short times compared to the light travel-times, corresponding to a superluminal velocity, $v-1=2.37\pm0.32\times 10^{-5}$ in units where $c=1$. We show that cosmological bounds rule out an explanation involving a Lorentz invariant tachyonic neutrino. At the OPERA energy scale, nucleosynthesis constraints imply $v-1<0.86\times 10^{-12}$ and the Cosmic Microwave Background observations imply $v-1<7.1\times 10^{-23}$. The CMB limit on the velocity of a tachyon with an energy of 10 MeV is stronger than the SN1987A limit. Superluminal neutrinos that could be observed at particle accelerator energy scales would have to be associated with Lorentz symmetry violation.Comment: LaTeX, 4 page

A large-D Weyl invariant string model in anti-de sitter space

In this thesis we present a novel scheme for calculating the bosonic string partition function on certain curved backgrounds related to Anti-de Sitter [AdS] space. We take the concept of a large expansion from nonlinear sigma models in particle physics and apply it to the bosonic string theory sigma model, where the analogous large dimensionless parameter is the dimension of the target space, D. We then perform a perturbative expansion in negative powers of D, rather than in positive powers of α/ι(^2)(the conventional expansion parameter).As a specific example of a curved geometry of interest, we focus on an example of the metric proposed by Polyakov [1] to describe the dynamics of the Wilson loop of pure SU(N) Yang-Mills theory, namely AdS space. Using heat kernel methods, we find that within the large-D scheme one can obtain different conditions for Weyl invariance than those found in [2]. This is because our scheme is valid for backgrounds where a is no longer small. In particular, we find that it is possible to have a dilaton that depends on the holographic coordinate only, provided one allows mixing of the ghost and matter sectors of the worldsheet theory. This field preserves Poincare invariance in the gauge theory, unlike the conventional dilaton. We also compute a simple string amplitude by constructing certain vertex operators for a scalar field in AdS, and discuss the consequences for the string spectrum

Scale and abstraction : the sensitivity of fire regime simulation to nuisance parameters

Fire plays a key role in ecosystem dynamics and its impact on environmental, social and economic assets is increasingly a critical area of research. Fire regime simulation models are one of many approaches that provide insights into the relative importance of factors driving the dynamics of fire-vegetation systems. Fire propagates as a contagious process and simulation is an approach that captures this behaviour explicitly, integrating spatial and temporal data to produce auto-correlated patterns of fire regimes. However, when formulating these models, time and many aspects of space must be made discrete. These parameters are 'nuisance parameters': parameters necessary for the model formulation but not otherwise of interest. Fire growth simulations are therefore discrete approximations of continuous non-linear systems, and it might be expected that the values chosen for these nuisance parameters will be important. While it is well known that discrete geometries have consequences for the shape and area of simulated fires, no research has investigated the consequence this may have for estimates of the relative importance of the various drivers of fire regimes. I argue that nuisance parameters can be demonstrated to be unimportant for this class of model. I use the idea of 'importance' to underline the need for context with such an assertion. With sufficient replication, any parameter can be found statistically significant. A parameter is important, on the other hand, if different values produce qualitatively different outcomes. Models are commonly either re-parameterised to account for changes in resolution or scaling-up methods applied if such exist. I will further argue that such differences as there are in model outputs due to spatial resolution, cannot be accounted for by either re-parameterising or using a common approach that allows resolution to vary over the spatial extent. A set of experiments were devised using a published fire regime simulation model, modified, verified and validated, to isolate just those aspects of the model's sensitivity to resolution and discrete geometries that are unavoidable or intrinsic to these choices. This new model was used to test the above hypotheses, using peer-reviewed treatments that stand as yardsticks by which formal estimates of the importance of nuisance parameters can be made. As estimated by the model, neither spatio-temporal resolution nor any of the various choices available for discrete geometries, altered the model predictions. As expected, it is spatial resolution that has the greatest impact on running times for the model but this study finds that neither calibration, nor taking an approach that allows resolution to vary over the spatial extent, can account for differences in model outputs that arise from running simulations at coarser resolutions. All models are abstractions and a good model should ideally hold over levels of abstraction. This is rarely the case, but this study shows that results obtained through simulation in estimating the drivers of fire frequency in large landscapes, are robust with regard to these aspects of abstraction. This adds considerable confidence to a significant body of work that has used this approach over the last two decades