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We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of Einstein’s field equations with a perfect fluid matter source as an autonomous system of evolution equations and… (More)

- Laura K. Turnbull, John Wainwright, Richard E. Brazier, Roland N. Bol
- Ecosystems
- 2010

In this study, we investigate changes in ecosystem structure that occur over a gradient of land-degradation in the southwestern USA, where shrubs are encroaching into native grassland. We evaluate a conceptual model which posits that the development of biotic and abiotic structural connectivity is due to ecogeomorphic feedbacks. Three hypotheses are… (More)

- John Wainwright, Anthony J. Parsons, Athol D. Abrahams

Rainfall-simulation experiments have been carried out on a series of plots ranging in size from 1 m to c 500 m in order to observe process and ̄ux-rate changes resulting from the replacement of the dominant vegetation type from grassland to shrubland in the American South-west. Results have demonstrated variations in in®ltration rates, ̄ow hydraulics,… (More)

We study the late time evolution of a class of exact anisotropic cosmological solutions of Einstein’s equations, namely spatially homogeneous cosmologies of Bianchi type VII0 with a perfect fluid source. We show that, in contrast to models of Bianchi type VIIh which are asymptotically self-similar at late times, Bianchi VII0 models undergo a complicated… (More)

- James D. A. Millington, Raul Romero-Calcerrada, John Wainwright, George L. W. Perry
- J. Artificial Societies and Social Simulation
- 2008

Humans have a long history of activity in Mediterranean Basin landscapes. Spatial heterogeneity in these landscapes hinders our understanding about the impacts of changes in human activity on ecological processes, such as wildfire. The use of spatially-explicit models that simulate processes at fine scales should aid the investigation of spatial patterns at… (More)

In this paper we give, for the first time, a complete description of the dynamics of tilted spatially homogeneous cosmologies of Bianchi type II. The source is assumed to be a perfect fluid with equation of state p = (γ − 1)μ, where γ is a constant. We show that unless the perfect fluid is stiff, the tilt destabilizes the Kasner solutions, leading to a… (More)

In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution equations of the Einstein field equations as a system of autonomous partial differential equations in first-order symmetric… (More)

In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological constant near the de Sitter equilibrium state at late times, and near the flat FL equilibrium state at early times. Our results show that there exists an open… (More)

- Woei Chet Lim, Claes Ugglaand, John Wainwright
- 2006

We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and singularities that break asymptotic silence. The emphasis in this paper is… (More)

In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI−1/9. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies,… (More)