Visualising and quantifying the variability of hydrological state in intermittent rivers

The hydrology of intermittent rivers has been characterised using either flow regimes, with limited spatial resolution, or network contraction, with limited temporal resolution. Exploration of the dynamic behaviour of these rivers, on which highly diverse biological communities depend, requires longitudinal, year-round observations with a more detailed classification of hydrological state than can be provided by gauging stations or wet/dry mapping alone. Observations of dry, ponded, moderate flow and high flow hydrological states spanning 20 years with approximately monthly frequency along ten chalk rivers in the south-east of England were visualised. There was slower transitioning between hydrological states and less spatial fragmentation on rivers with groundwater-dominated regimes than on those more influenced by superficial deposits. Seasonal patterns in both the composition and configuration of states were demonstrated using adapted landscape metrics. Responses to hydrological extremes and anthropogenic influences included drying downstream of the source and an artificially near-perennial reach. A framework is proposed for the categorisation of metrics of hydrological state and demonstrates that the classification and dimensional limitations of traditional approaches cannot fully characterise the hydrological behaviour of intermittent rivers. Such characterisation is an important step towards the tailored assessments required for effective management of these dynamic systems

Onset of inflation in inhomogeneous cosmology

We study how the initial inhomogeneities of the universe affect the onset of inflation in the closed universe. We consider the model of a chaotic inflation which is driven by a massive scalar field. In order to construct an inhomogeneous universe model, we use the long wavelength approximation ( the gradient expansion method ). We show the condition of the inhomogeneities for the universe to enter the inflationary phase.Comment: 22 pages including 12 eps figures, RevTe

Long wavelength iteration of Einstein's equations near a spacetime singularity

We clarify the links between a recently developped long wavelength iteration scheme of Einstein's equations, the Belinski Khalatnikov Lifchitz (BKL) general solution near a singularity and the antinewtonian scheme of Tomita's. We determine the regimes when the long wavelength or antinewtonian scheme is directly applicable and show how it can otherwise be implemented to yield the BKL oscillatory approach to a spacetime singularity. When directly applicable we obtain the generic solution of the scheme at first iteration (third order in the gradients) for matter a perfect fluid. Specializing to spherical symmetry for simplicity and to clarify gauge issues, we then show how the metric behaves near a singularity when gradient effects are taken into account.Comment: 35 pages, revtex, no figure

Solving the Hamilton-Jacobi Equation for General Relativity

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparameterizations of the spatial coordinates (``gauge-invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the 3-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients, we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the 3-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.Comment: 13 pages, RevTeX, DAMTP-R93/2

Dilogarithm Identities in Conformal Field Theory and Group Homology

Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the computation of central charges in conformal field theory. We show that the Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be interpreted as a lift of a generator of the third integral homology of a finite cyclic subgroup sitting inside the projective special linear group of all $2 \times 2$ real matrices viewed as a {\it discrete} group. This connection allows us to clarify a few of the assertions and conjectures stated in the work of Nahm-Recknagel-Terhoven concerning the role of algebraic $K$-theory and Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related to hyperbolic 3-manifolds as suggested but is more appropriately related to the group manifold of the universal covering group of the projective special linear group of all $2 \times 2$ real matrices viewed as a topological group. This also resolves the weaker version of the conjecture as formulated by Kirillov. We end with the summary of a number of open conjectures on the mathematical side.Comment: 20 pages, 2 figures not include

Confinement Effects in Antiferromagnets

Phase equilibrium in confined Ising antiferromagnets was studied as a function of the coupling (v) and a magnetic field (h) at the surfaces, in the presence of an external field H. The ground state properties were calculated exactly for symmetric boundary conditions and nearest-neighbor interactions, and a full zero-temperature phase diagram in the plane v-h was obtained for films with symmetry-preserving surface orientations. The ground-state analysis was extended to the H-T plane using a cluster-variation free energy. The study of the finite-T properties (as a function of v and h) reveals the close interdependence between the surface and finite-size effects and, together with the ground-state phase diagram, provides an integral picture of the confinement in anisotropic antiferromagnets with surfaces that preserve the symmetry of the order parameter.Comment: 10 pages, 8 figures, Accepted in Phys. Rev.

Developing a predictive modelling capacity for a climate change-vulnerable blanket bog habitat: Assessing 1961-1990 baseline relationships

Aim: Understanding the spatial distribution of high priority habitats and developing predictive models using climate and environmental variables to replicate these distributions are desirable conservation goals. The aim of this study was to model and elucidate the contributions of climate and topography to the distribution of a priority blanket bog habitat in Ireland, and to examine how this might inform the development of a climate change predictive capacity for peat-lands in Ireland. Methods: Ten climatic and two topographic variables were recorded for grid cells with a spatial resolution of 1010 km, covering 87% of the mainland land surface of Ireland. Presence-absence data were matched to these variables and generalised linear models (GLMs) fitted to identify the main climatic and terrain predictor variables for occurrence of the habitat. Candidate predictor variables were screened for collinearity, and the accuracy of the final fitted GLM was evaluated using fourfold cross-validation based on the area under the curve (AUC) derived from a receiver operating characteristic (ROC) plot. The GLM predicted habitat occurrence probability maps were mapped against the actual distributions using GIS techniques. Results: Despite the apparent parsimony of the initial GLM using only climatic variables, further testing indicated collinearity among temperature and precipitation variables for example. Subsequent elimination of the collinear variables and inclusion of elevation data produced an excellent performance based on the AUC scores of the final GLM. Mean annual temperature and total mean annual precipitation in combination with elevation range were the most powerful explanatory variable group among those explored for the presence of blanket bog habitat. Main conclusions: The results confirm that this habitat distribution in general can be modelled well using the non-collinear climatic and terrain variables tested at the grid resolution used. Mapping the GLM-predicted distribution to the observed distribution produced useful results in replicating the projected occurrence of the habitat distribution over an extensive area. The methods developed will usefully inform future climate change predictive modelling for Irelan

Holography, diffeomorphisms, and scaling violations in the CMB

We analyze diffeomorphism invariance in inflationary spacetimes regulated by a boundary at late time. We present the action for quadratic fluctuations in the presence of a boundary, and verify that it is gauge invariant precisely when the correct local counterterms are included. The scaling behavior of bulk correlation functions at the boundary is determined by Callan-Symanzik equations which predict scaling violations in agreement with the standard inflationary predictions for spectral indices of the CMB.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49149/2/jhep072004062.pd