arXiv subjects

A. Jamie Wood

Publications and source records attributed to A. Jamie Wood.

4 recordsLinked to original sources

arXiv2023

Robustness of steady state and stochastic cyclicity in generalized coalescence-fragmentation models

Processes of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may result in a steady state or in stable deterministic or stochastic cycles. Motivated by applications in insurgency warfare we investigate coalescence-fragmentation systems. We begin with a simple model of size-biased coalescence accompanied by shattering into monomers. Depending on the parameters this model has an approximately power-law-distributed steady state or stochastic cycles of alternating gelation and shattering. We conduct stochastic simulations of this model and its generalizations to include different kernel types, accretion and erosion, and various distributions of non-shattering fragmentation. Our central aim is to explore the robustness of the steady state and gel-shatter cycles to these variations. We show that an approximate power-law steady state persists with the addition of accretion and erosion, and with partial rather than total shattering. However, broader distributions of fragment sizes typically vitiate both the power law steady state and gel-shatter cyclicity. This work clarifies features shown in coalescence/fragmentation model simulations and elucidates the relationship between the microscopic dynamics and observed phenomena in this widely applicable interdisciplinary model type.

cond-mat.other↗

arXiv2021

Stochastic gel-shatter cycles in coalescence-fragmentation models

We describe a new phenomenon in models of coalescence and fragmentation, that of gel-shatter cycles. These are dynamical, unforced, stochastic cycles in which slow, approximately deterministic coalescence up to and beyond gelation is followed by abrupt random shattering. We describe their appearance in simulations of stochastic models with multiplicative kernels for coalescence and spontaneous fragmentation into monomers (`shattering'). The regime in which such cycles occur is characterized by a cyclicity order parameter, and we provide a simple scaling argument which describes both this regime and those which border it.

math.DS↗

arXiv2019

Changepoint analysis of historical battle deaths

It has been claimed and disputed that World War II has been followed by a `long peace', an unprecedented decline of war. We conduct a full changepoint analysis of well-documented, publicly-available battle deaths datasets, using new techniques that enable the robust detection of changes in the statistical properties of such heavy-tailed data. We first test and calibrate these techniques. We then demonstrate the existence of changes, independent of data presentation, at around 1910 and 1950 CE, bracketing the World Wars, and around the 1830s and 1994 CE. Our analysis provides a methodology for future investigations and an empirical basis for political and historical discussions.

stat.AP↗

arXiv2015

Host control and nutrient trading in a photosynthetic symbiosis

Photosymbiosis is one of the most important evolutionary trajectories, resulting in the chloroplast and the subsequent development of all complex photosynthetic organisms. The ciliate Paramecium bursaria and the alga Chlorella have a well established and well studied light dependent endosymbiotic relationship. Despite its prominence there remain many unanswered questions regarding the exact mechanisms of the photosymbiosis. Of particular interest is how a host maintains and manages its symbiont load in response to the allocation of nutrients between itself and its symbionts. Here we construct a detailed mathematical model, parameterised from the literature, that explicitly incorporates nutrient trading within a deterministic model of both partners. The model demonstrates how the symbiotic relationship can manifest as parasitism of the host by the symbionts, mutualism, wherein both partners benefit, or exploitation of the symbionts by the hosts. We show that the precise nature of the photosymbiosis is determined by both environmental conditions (how much light is available for photosynthesis) and the level of control a host has over its symbiont load. Our model provides a framework within which it is possible to pose detailed questions regarding the evolutionary behaviour of this important example of an established light dependent endosymbiosis; we focus on one question in particular, namely the evolution of host control, and show using an adaptive dynamics approach that a moderate level of host control may evolve provided the associated costs are not prohibitive.

q-bio.PE↗