arXiv subjects

Peter R. Law

Publications and source records attributed to Peter R. Law.

4 recordsLinked to original sources

arXiv2012

Real AlphaBeta-Geometries

By a real alphabeta-geometry we mean a four-dimensional manifold M equipped with a neutral metric h such that (M,h) admits both an integrable distribution of alpha-planes and an integrable distribution of beta-planes. We obtain a local characterization of the metric when at least one of the distributions is parallel (i.e., is a Walker geometry) and the three-dimensional distribution spanned by the alpha- and beta-distributions is integrable. The case when both distributions are parallel, which has been called two-sided Walker geometry, is obtained as a special case. We also consider real αβ-geometries for which the corresponding spinors are both multiple Weyl principal spinors.

math.DG↗

arXiv2011

Algebraically Special, Real Alpha Geometries

We exploit the spinor description of four-dimensional Walker geometry, and conformal rescalings of such, to describe the local geometry of four-dimensional neutral geometries with algebraically degenerate self-dual Weyl curvature and an integrable distribution of alpha-planes (algebraically special real alpha-geometry). In particular, we determine the behaviour of (four-dimensional neutral) Walker geometry under conformal rescalings and provide a derivation of the hyperheavenly equation from conformal rescaling formulae.

math.DG↗

arXiv2009

Spin coefficients for four-dimensional neutral metrics, and null geometry

Notation for spin coefficients for metrics of neutral signature in four dimensions is introduced. The utility and interpretation of spin coefficients is explored through themes in null geometry familiar from (complex) general relativity. Four-dimensional Walker geometry is exploited to provide examples and the generalization of the real neutral version of Plebañski's (1975) second heavenly equation to certain Walker geometries given in Law and Matsushita [16] is extended further.

math.DG↗

arXiv2007

Modelling Sex Ratio and Numbers for Translocation in Meta-Population Management

The management of endangered species as metapopulations is becoming increasingly common. Diverse aspects of metapopulation dynamics and management have received attention in recent years. In particular, translocation of individuals between subpopulations of a metapopulation is practiced, or envisaged, for a variety of reasons and requires careful consideration. Linklater (2003) proposed that the number of individuals of each sex translocated into a target population for the purposes of maintaining genetic diversity could be chosen on the basis of parental investment theory. In this paper, following basic ideas in the parental investment literature, I propose a simple model to capture Linklater's proposal and provide a thorough mathematical analysis of the model. Granted the necessary species-specific biological information which would determine the model parameters in any instance of application, the analysis indicates that a practical algorithm can be constructed to generate the model's predictions for the optimal translocation.

q-bio.PE↗