Comparative Monte Carlo Efficiency by Monte Carlo Analysis

We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfuction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing the $\lambda_2$ of various Markov chain transition matrices. We first computed ${\lambda_2}$ for several one and two dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as a function of temperature and applied magnetic field. Next, we computed $\lambda_2$ for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size $\Delta$. Based on the $\lambda_2$ criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule-of-thumb of adjusting $\Delta$ so the Metropolis acceptance rate is around 50% range is often sub-optimal. In general, as a function of temperature or $\Delta$, $\lambda_2$ for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model.Comment: 23 pages, 8 figure

P and T Violation From Certain Dimension Eight Weinberg Operators

Dimension eight operators of the Weinberg type have been shown to give important contributions to CP violating phenomena, such as the electric dipole moment of the neutron. In this note we show how operators related to these (and expected to occur on equal footing) can give rise to time-reversal violating phenomena such as atomic electric dipole moments. We also estimate the induced parity violating phenomena such as small ``wrong'' parity admixtures in atomic states and find that they are negligible. Uses harvmac.tex and epsf.tex; one figure submitted as a uuencoded, compressed EPS file.Comment: 6 pages, EFI-92-5

Scenario and modelling uncertainty in global mean temperature change derived from emission-driven global climate models

We compare future changes in global mean temperature in response to different future scenarios which, for the first time, arise from emission-driven rather than concentration-driven perturbed parameter ensemble of a global climate model (GCM). These new GCM simulations sample uncertainties in atmospheric feedbacks, land carbon cycle, ocean physics and aerosol sulphur cycle processes. We find broader ranges of projected temperature responses arising when considering emission rather than concentration-driven simulations (with 10–90th percentile ranges of 1.7 K for the aggressive mitigation scenario, up to 3.9 K for the high-end, business as usual scenario). A small minority of simulations resulting from combinations of strong atmospheric feedbacks and carbon cycle responses show temperature increases in excess of 9 K (RCP8.5) and even under aggressive mitigation (RCP2.6) temperatures in excess of 4 K. While the simulations point to much larger temperature ranges for emission-driven experiments, they do not change existing expectations (based on previous concentration-driven experiments) on the timescales over which different sources of uncertainty are important. The new simulations sample a range of future atmospheric concentrations for each emission scenario. Both in the case of SRES A1B and the Representative Concentration Pathways (RCPs), the concentration scenarios used to drive GCM ensembles, lies towards the lower end of our simulated distribution. This design decision (a legacy of previous assessments) is likely to lead concentration-driven experiments to under-sample strong feedback responses in future projections. Our ensemble of emission-driven simulations span the global temperature response of the CMIP5 emission-driven simulations, except at the low end. Combinations of low climate sensitivity and low carbon cycle feedbacks lead to a number of CMIP5 responses to lie below our ensemble range. The ensemble simulates a number of high-end responses which lie above the CMIP5 carbon cycle range. These high-end simulations can be linked to sampling a number of stronger carbon cycle feedbacks and to sampling climate sensitivities above 4.5 K. This latter aspect highlights the priority in identifying real-world climate-sensitivity constraints which, if achieved, would lead to reductions on the upper bound of projected global mean temperature change. The ensembles of simulations presented here provides a framework to explore relationships between present-day observables and future changes, while the large spread of future-projected changes highlights the ongoing need for such work

The Cause and Consequence of Ontogenetic Changes in Social Aggregation in New Zealand Spiny Lobsters

Ontogenetic changes in the behavior, spatial distribution, or habitat use of a species are presumably adaptations to ecological forces that differ in their effect on various life stages. The New Zealand rock lobster Jasus edwardsii is one of several species of spiny lobster that exhibits dramatic ontogenetic shifts in sociality and spatial distribution, and we tested whether such changes are adaptive. We first surveyed several natural populations of J. edwardsii to document size-specific differences in aggregation. To determine if chemical cues discharged by conspecifics promote aggregation of certain ontogenetic stages, we tested the responsiveness of lobsters of 3 ontogenetic stages (early benthic juvenile, juvenile, and subadult) to the chemical cues produced by conspecifics of different sizes. Finally, we tethered lobsters of different ontogenetic stages alone and in groups to test the effect of lobster size and aggregation on mortality. Our results offer compelling evidence that pre-reproductive J. edwardsii undergo an ontogenetic change in sociality that alters their spatial distribution and survival. Our field surveys show that J. edwardsii are solitary as early benthic juveniles and become social and aggregate as they grow larger. We then demonstrate, using laboratory experiments, that there is a size-specific increase in the response of pre-reproductive J. edwardsii to the chemical cues of larger conspecifics which facilitates these ontogenetic changes in aggregation. Finally, our tethering results confirm that this change in social condition is selectively advantageous: aggregation does not increase the survival of small lobsters, but larger lobsters survive better in groups. Thus, in this study we demonstrate the linkage between ontogenetic changes in the spatial distribution of a species, the behavioral process that creates the pattern, and the selective advantage conferred by these developmental changes

Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric

A new definition of quasi--local angular momentum of non--axisymmetric marginally outer trapped surfaces is proposed. It is based on conformal decomposition of the two--dimensional metric and the action of the group of conformal symmetries. The definition is completely general and agrees with the standard one in axi--symmetric surfaces.Comment: Final version to appear in Classical and Quantum Gravity. One reference adde

The impact of structural error on parameter constraint in a climate model

Uncertainty in the simulation of the carbon cycle contributes significantly to uncertainty in the projections of future climate change. We use observations of forest fraction to constrain carbon cycle and land surface input parameters of the global climate model FAMOUS, in the presence of an uncertain structural error. Using an ensemble of climate model runs to build a computationally cheap statistical proxy (emulator) of the climate model, we use history matching to rule out input parameter settings where the corresponding climate model output is judged sufficiently different from observations, even allowing for uncertainty. Regions of parameter space where FAMOUS best simulates the Amazon forest fraction are incompatible with the regions where FAMOUS best simulates other forests, indicating a structural error in the model. We use the emulator to simulate the forest fraction at the best set of parameters implied by matching the model to the Amazon, Central African, South East Asian, and North American forests in turn. We can find parameters that lead to a realistic forest fraction in the Amazon, but that using the Amazon alone to tune the simulator would result in a significant overestimate of forest fraction in the other forests. Conversely, using the other forests to tune the simulator leads to a larger underestimate of the Amazon forest fraction. We use sensitivity analysis to find the parameters which have the most impact on simulator output and perform a history-matching exercise using credible estimates for simulator discrepancy and observational uncertainty terms. We are unable to constrain the parameters individually, but we rule out just under half of joint parameter space as being incompatible with forest observations. We discuss the possible sources of the discrepancy in the simulated Amazon, including missing processes in the land surface component and a bias in the climatology of the Amazon.This work was supported by the Joint UK BEIS/Defra Met Office Hadley Centre Climate Programme (GA01101). Doug McNeall was supported on secondment to Exeter University by the Met Office Academic Partnership (MOAP) for part of the work. Jonny Williams was supported by funding from Statoil ASA, Norwa

A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter

We consider stationary, axially and equatorially symmetric systems consisting of a central rotating and charged degenerate black hole and surrounding matter. We show that $a^2+Q^2=M^2$ always holds provided that a continuous sequence of spacetimes can be identified, leading from the Kerr-Newman solution in electrovacuum to the solution in question. The quantity $a=J/M$ is the black hole's intrinsic angular momentum per unit mass, $Q$ its electric charge and $M$ the well known black hole mass parameter introduced by Christodoulou and Ruffini.Comment: 19 pages, 2 figures, replaced with published versio

Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries

A general recipe to define, via Noether theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge-Teitelboim-like approach applied to the variation of Noether conserved quantities. The Hamiltonian for General Relativity in presence of non-orthogonal boundaries is analysed and the energy is defined as the on-shell value of the Hamiltonian. The role played by boundary conditions in the formalism is outlined and the quasilocal internal energy is defined by imposing metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with Brown-York original formulation of the first principle of black hole thermodynamics is finally established.Comment: 29 pages with 1 figur