146 research outputs found
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 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 -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 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
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