Adrian B. Burd

Inflationary models with exponential potentials

Abstract In this paper we consider cosmological models containing a self-interacting scalar field possessing a potential of the form V ( φ ) = Λ exp(− λφ ). We investigate the inflationary nature of the model in an ( N + 1)-dimensional Friedman space-time as well as in some (3 + 1)-dimensional anisotropic cosmological models. We determine the conditions under which power-law inflation occurs by a detailed stability analysis which determines all possible asymptotic behaviour. We also present some new exact solutions which exhibit the transition to power-law inflation. We determine the range of evolutionary behaviours in each case for all λ ⩾ 0 and find the range of λ values for which power-law inflation occurs. We also discuss how potentials of the exponential type may arise in realistic models of the early universe.

Prediction of the Export and Fate of Global Ocean Net Primary Production: The EXPORTS Science Plan

Ocean ecosystems play a critical role in the Earth’s carbon cycle and the quantification of their impacts for both present conditions and for predictions into the future remains one of the greatest challenges in oceanography. The goal of the EXport Processes in the Ocean from Remote Sensing (EXPORTS) Science Plan is to develop a predictive understanding of the export and fate of global ocean net primary production (NPP) and its implications for present and future climates. The achievement of this goal requires a quantification of the mechanisms that control the export of carbon from the euphotic zone as well as its fate in the underlying “twilight zone” where some fraction of exported carbon will be sequestered in the ocean’s interior on time scales of months to millennia. Here we present a measurement / synthesis / modeling framework aimed at quantifying the fates of upper ocean NPP and its impacts on the global carbon cycle based upon the EXPORTS Science Plan. The proposed approach will diagnose relationships among the ecological, biogeochemical and physical oceanographic processes that control carbon cycling across a range of ecosystem and carbon cycling states leading to advances in satellite diagnostic and numerical prognostic models. To collect these data, a combination of ship and robotic field sampling, satellite remote sensing and numerical modeling is proposed which enables the sampling of the many pathways of NPP export and fates. This coordinated, process-oriented approach has the potential to foster new insights on ocean carbon cycling that maximizes its societal relevance through the achievement of research goals of many international research agencies and will be a key step towards our understanding of the Earth as an integrated system.

A model for the distribution of particle flux in the mid-water column controlled by subsurface biotic interactions

The sub-euphotic zone water column is important in controlling the downward transport of material falling from the surface waters. Descriptions of the carbon flux as a function of depth have focused on empirical relationships that neglect biological processes that might control them. We develop here a series of simple models of the region that describe changes in flux in terms of the population dynamics of a particle feeder and its predator. One model predicts that the flux and predator concentration at steady state decrease exponentially with depth while the concentration of the particle feeders is constant; a second predicts that flux, particle feeder, and predator concentrations are proportional and decrease at rates that are approximately inversely proportional to depth. Away from steady state, variations in particle flux leaving the surface can induce oscillations in the near-surface animal populations but not the deeper populations. As a result of the animal oscillations associated with the surface flux variations, there can be large swings in the deep vertical particle flux that are not synchronized to the surface variations for one model formulation; a second formulation predicts that fluctuations in surface flux are damped out near the bottom. The differences in predictions for the various models make it possible to verify the utility of one or the other formulation.

A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, λ, and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating λ is invalid in the case of a cosmological model.

Predicting particle coagulation and sedimentation rates for a pulsed input

Particles provide an important transport mechanism for distributing chemically and biologically reactive elements in the ocean. To aid in predicting the fate of colloidal particles, we update an existing model, developed by Farley and Morel [1986] for predicting particle sedimentation rates in the presence of aggregation. We add some effects of the fractal structure of the particles as well as the hydrodynamic interactions between particles. Changes due to the hydrodynamics have a lesser effect than the fractal dimension. Simulated sedimentation rates can vary by as much as 6 orders of magnitude as the fractal dimension is varied between D=3 and D=2. Following Farley and Morel we develop simple expressions for the sedimentation rate. We make use of special initial conditions and particle input rates as well as a value of 1 for the particle stickiness. Introducing the particle fractal dimension revealed limitations with this class of models, restricting the range of D which we could successfully use.

Stress Response Model for the Tropical Seagrass Thalassia testudinum: The Interactions of Light, Temperature, Sedimentation, and Geochemistry

Our modeling objective was to better define the relationship between subtropical seagrass and potential water column and sediment stressors (light, organic and particle sedimentation, sediment nutrients, and the porewater sulfide system). The model was developed and optimized for sediments inThalassia testudinum seagrass beds of Lower Laguna Madre, Texas, U.S., and is composed of a plant submodel and a sediment diagenetic submodel. Simulations were developed for a natural stressor (harmful algal bloom,Aureoumbra lagunensis) and an anthropogenic, stressor (dredging event). The observed harmful algal bloom (HAB) was of limited duration and the simulations of that bloom showed no effect of the algal bloom on biomass trends but did suggest that sediment sulfides could inhibit growth if the bloom duration and intensity were greater. To examine this hypothesis we ran a simulation using data collected during a sustained 4-yr bloom in Upper Laguna Madre. Simulations suggested that light attenuation by the HAB could cause a small reduction inT. testudinum biomass, while input of organic matter from the bloom could promote development of a sediment geochemical environment toxic toT. testudinum leading to a major reduction in biomass. A 3-wk dredging event resulted in sedimentation of a layer of rich organic material and reduction of canopy light for a period of months. The simulations suggested that the seagrass could have recovered from the effects of temporary light reduction but residual effects of high sulfides in the sediments would make the region inhospitable for seagrasses for up to 2.5 yr. These modeling exercises illustrate that both natural and anthropogenic stressors can result in seagrass losses by radically altering the sedimentary geochemical environment.

Viscous fluid cosmology

In this paper we shall examine the effects of both bulk and shear viscosities upon a variety of cosmological models. We assume that the viscous terms can be modelled by dimensionless equations of state, and this allows us to write the Einstein equations as a system of autonomous differential equations. After briefly discussing the Friedmann--Robertson--Walker and Bianchi I models, we discuss in some detail the Bianchi V and Kantowski--Sachs models. In all cases we find the critical points of the flow and elucidate their nature, making use of the energy conditions. Because of our choice of dimensionless variables, (almost) all critial points represent self-similar solutions to the field equations. We also study the case of a Bianchi V perfect fluid model with a non-linear equation of state. We find that the models are structurally stable under the addition of shear viscosity, whereas they are structurally unstable under the introduction of bulk viscosity. Almost all of the Bianchi V models examined have initial singularities where the matter is dynamically unimportant; the Kantowski--Sachs models have final singularities where the matter is dynamically important.

Terrestrial and marine perspectives on modeling organic matter degradation pathways

Organic matter (OM) plays a major role in both terrestrial and oceanic biogeochemical cycles. The amount of carbon stored in these systems is far greater than that of carbon dioxide (CO2 ) in the atmosphere, and annual fluxes of CO2 from these pools to the atmosphere exceed those from fossil fuel combustion. Understanding the processes that determine the fate of detrital material is important for predicting the effects that climate change will have on feedbacks to the global carbon cycle. However, Earth System Models (ESMs) typically utilize very simple formulations of processes affecting the mineralization and storage of detrital OM. Recent changes in our view of the nature of this material and the factors controlling its transformation have yet to find their way into models. In this review, we highlight the current understanding of the role and cycling of detrital OM in terrestrial and marine systems and examine how this pool of material is represented in ESMs. We include a discussion of the different mineralization pathways available as organic matter moves from soils, through inland waters to coastal systems and ultimately into open ocean environments. We argue that there is strong commonality between aspects of OM transformation in both terrestrial and marine systems and that our respective scientific communities would benefit from closer collaboration.

Linking light attenuation and suspended sediment loading to benthic productivity within an Arctic kelp‐bed community1

Annual growth and productivity of kelp in the Stefansson Sound Boulder Patch, located along the Arctic coast of Alaska, is regulated almost entirely by PAR received during the summer open‐water period. Increased water turbidity during summer, often in response to storm activity, has been linked to low levels of ambient PAR and measurable decreases in kelp elongation. However, the relationship between PAR and water transparency has not been quantified, which compromises efforts to assess the effects of changing climate and weather conditions on kelp production. During the 2001–2002 summer periods, the inherent optical properties (IOPs) of Stefansson Sound waters were measured in conjunction with total suspended sediments (TSS) concentrations, which differed significantly between the 2 years, for input into a radiative transfer equation (RTE). In both years, the highest TSS levels (24.2 and 18.5 mg · L−1 in 2001 and 2002, respectively) occurred in nearshore areas and were coincident with increased beam attenuations (13.8 and 8.3 m−1). Lower TSS concentrations and attenuations were measured offshore. Data input to the RTE provided a TSS‐concentration‐specific attenuation coefficient that was used in a productivity model to estimate annual kelp productivities throughout the Boulder Patch based on modeled irradiance and averaged site‐specific TSS concentrations. Production estimates varied across the Boulder Patch but were lower in 2001 (0.12–0.34 g C · g dwt−1 · year−1, where dwt stands for dry weight) compared to 2002 (0.24–0.80 g C · g dwt−1 · year−1). Production in both years was greater in offshore locations with lower TSS loads. Results suggest that PAR availability during the summer is heavily influenced by TSS concentrations, and that changes in storm intensity and frequency, associated with current warming trends, may have significant effects on the primary production of these unique benthic algal communities.

Chaos, entropy and cosmology

Customarily the dynamical behaviour of the Bianchi IX model is studied either directly, i.e. numerically, or indirectly by approximating it to a map which is conducive to analytical treatment. These studies have given rise to results that appear somewhat incongruent. The authors clarify the relationship between these two treatments by firstly clearing the status of chaos in each setting and secondly by studying the possibility of the increase in entropy in each case.