J. Brindley

Ocean plankton populations as excitable media

Plankton populations undergo dramatic surges. Rapid increases and decreases by a factor of 10 or more are observed, often separated by relatively stable interludes. We propose a description of plankton communities as excitable systems. In particular, we present a model for the evolution of phytoplankton and zooplankton populations which resembles models for the behaviour of excitable media. The parameter dependency of the various “excitable” phenomena, trigger mechanism, threshold, and slow recovery, is clear, and permits ready investigation of the influence of properties of the physical environment, including variations in nutrient fluxes, temperature or pollution levels.

Oscillatory behaviour in a three-component plankton population model

We examine the qualitative behaviour of an NPZ (nutrient-phyto- plankton-zooplankton) model for parameter ranges consistent with values used in the literature. The wide range of values partly reflects variations of conditions in different environtments for the plankton, but in many cases is a measure of the difficulties in making observations and consequent uncertainties. We pay particular attention to the bifurcational behaviour of the system, and to the regions of parameter space for which oscillatory behaviour is possible; such oscillatory behaviour has recently been found in both observational data and in more complex ecosystem models. In some regions of parameter space, we also find that multiple attractors occur. Finally, we examine in more detail the behaviour for a range of values of nutrient input.

Mechanism reduction for the oscillatory oxidation of hydrogen; Sensitivity and quasi-steady-state analyses

In this paper, a strategy for reducing complex chemical reaction mechanisms is developed and illustrated with reference to the oscillatory H[sub 2] + O[sub 2] system in a CSTR in the region of the second explosion limit. The approach involves the identification of redundant species via rate sensitivity analysis and of redundant reactions by the principal component analysis of the rate sensitivity matrix. Temperature sensitivity analysis is also employed and the application of the quasi-steady-state approximation is discussed briefly and used n the final stages of the reduction. The above procedures are shown to assist the understanding of the underlying mechanisms of the reaction for the chosen conditions and the competition between branching steps during oscillatory ignitions is discussed. The reduced mechanism is compared with models discussed elsewhere.

Equilibria, stability and excitability in a general class of plankton population models

In a recent paper we proposed a simple ODE model for the behaviour of populations of phytoplankton and zooplankton which had a mathematical structure analogous to models of excitable media. That model comprised a two-component system, in which limiting effects on the phytoplankton growth rate such as nutrient shortage and self-shading were represented parametrically. Here, we demonstrate the relationship of such a two-component system to a general class of three-component models in which nutrient is more realistically regarded as a third evolving variable, and self-shading is included as a growth rate modulation. We derive conditions for the existence and stability of equilibrium states which are generally valid for this class, and interprete the behaviour of particular models, proposed elsewhere, within this picture.

Feedback processes in cellulose thermal decomposition. Implications for fire-retarding strategies and treatments.

A simple dynamical system that models the competitive thermokinetics and chemistry of cellulose decomposition is examined, with reference to evidence from experimental studies indicating that char formation is a low activation energy exothermal process and volatilization is a high activation energy endothermal process. The thermohydrolysis chemistry at the core of the primary competition is described. Essentially, the competition is between two nucleophiles, a molecule of water and an −OH group on C6 of an end glucosyl cation, to form either a reducing chain fragment with the propensity to undergo the bond-forming reactions that ultimately form char, or a levoglucosan end-fragment that depolymerizes to volatile products. The results of this analysis suggest that promotion of char formation under thermal stress can actually increase the production of flammable volatiles. Thus, we would like to convey an important safety message in this paper: in some situations where heat and mass transfer is restricted in cellulosic materials, such as furnishings, insulation, and stockpiles, the use of char-promoting treatments for fire retardation may have the effect of increasing the risk of flaming combustion.

Antiphase synchronization of chaos by noncontinuous coupling: two impacting oscillators

Abstract We show that two identical chaotic oscillators can evolve in antiphase synchronization regime when noncontinuous coupling between them is introduced. As an example, we consider dynamics of two mechanical oscillators coupled by impacts.

Marginal instability in Taylor–Couette flows at a very high Taylor number

We report on a set of turbulent flow experiments of the Taylor type in which the fluid is contained between a rotating inner circular cylinder and a fixed concentric outer cylinder, focusing our attention on very large Taylor number values, i.e. \[ 10^3 \leqslant T/T_c \leqslant 10^5, \] where T c is the critical value of the Taylor number T for onset of Taylor vortices. At such large values of T , the turbulent vortex flow structure is similar to the one observed when T – T c is small and this structure is apparently insensitive to further increases in T . These flows are characterized by two widely separated length scales: the scale of the gap width which characterizes the Taylor vortex flow and a much smaller scale which is made visible by streaks in the form of a ‘herring-bone’-like pattern visible at the walls. These are conjectured to be Gortler vortices which arise as a result of centrifugal instability in the wall boundary layers. Ideas of marginal instability by which we postulate that both the Taylor and Gortler vortex structures are marginally unstable on their own scale seem to provide good quantitative agreement between predicted and observed Gortler vortex spacings.

The relationship between plankton blooms, the hatching of fish larvae, and recruitment

Models of fish recruitment must include a realistic description of the underlying prey population dynamics. In the example presented here a model for the growth of haddock larvae (Melanogrammus aeglefinus) and recruitment to the population of juvenile fish is coupled to an excitable medium representation of the planktonic ecosystem. The results elucidate and quantify non-trivial interactions between the larval and planktonic populations. Fish spawning can act to influence the date of onset of the spring phytoplankton bloom, and to increase bloom duration. Simulations show the effects of different reproductive strategies in a stochastic and evolving environment.

Linear stability analysis of laminar premixed spray flames

We present an analysis of instability to transverse perturbations of laminar premixed plane spray flames. To this end, a thermal‐diffusional model of a flame front propagating through an overall fuel‐rich or fuel‐lean droplet‐vapour‐air mixture is presented. The fuel droplets are permitted to vaporize at a finite rate so that their interaction with, and possible traversal of, the flame front is accounted for. After establishing steady‐state solutions by means of high activation energy asymptotics, a detailed linear stability analysis is carried out in order to determine neutral stability boundaries. For the fuel‐rich case, it is demonstrated that under certain circumstances a spray flame may be cellular even though its equivalent non‐spray flame is completely stable. In addition, even when the non‐spray flame is itself cellular, the equivalent spray flame will have a finer cellular structure. To our knowledge, these results are the first theoretical qualitative verification of sparse but compelling experimental evidence from the literature. The main effect of the spray on the stability of these flames is due to heat loss from the absorption of heat by the droplets for vaporization. The influence of the initial liquid fuel loading, the latent heat of vaporization and the vaporization coefficient on the critical wavenumber associated with cellularity provides strong evidence of the major role of the heat‐loss mechanism in these sprayrelated phenomena. For fuel‐lean spray flames, it is found that the heat‐loss mechanism manifests itself prominently via the pulsating stability boundary which penetrates into the region of realistic Lewis numbers, thus verifying recent experimental observations of pulsating cellular spray flames. Finally, the cellularity of the spray flames, with their attendant increase in flame front area, suggests a plausible rationale for those circumstances in which burning velocity enhancement, induced by the use of a spray of droplets, was observed experimentally.

Patchiness in plankton populations

We consider and contrast two mechanisms for the production of spatial pattern in an excitable medium model for plankton populations. The first is Turing or diffusion-driven instability. We find that, since in a turbulent environment the effective diffusivities of phytoplankton and zooplankton are similar, this mechanism is unlikely to produce observable spatial pattern in the ocean. The second mechanism is spatially varying forcing of the system. In order to display the sensitivity to small spatial variation in forcing, we consider the dynamics of an ordinary differential equation system with spatial perturbations to parameters and initial conditions. In the absence of diffusion the excitable nature of the system means that small perturbations can produce very sharp spatial structures, when diffusion is introduced, we find that this patchiness can persist on realistic scales.