Incubation of penguin eggs

The preservation of rare and endangered species of birds requires finding efficient, and above all successful, methods of breeding them in captivity. One strategy adopted is to remove eggs from the mother, making her lay more eggs, and then incubating the removed eggs artificially. Artificial incubation machines must attempt to replicate the conditions of natural incubation as closely as possible. Aside from careful control of temperature and humidity within the artificial incubator, an important factor to reproduce is that eggs must be turned about their long axis from time to time. Hatching will not occur in an egg that is not subjected to some form of occasional rotation. The reason why eggs are turned and the way in which they should be turned are still not well understood. The Study Group attempted to gain some insight into why eggs have to be turned from a fluid dynamic perspective. A simple egg-turning model for an egg at the first stages of incubation was constructed, based on lubrication theory

Insights into the dynamics of ligand-induced dimerisation via mathematical modelling and analysis

The vascular endothelial growth factor (VEGF) receptor (VEGFR) system plays a role in cancer and many other diseases. It is widely accepted that VEGFR receptors dimerise in response to VEGF binding. However, analysis of these mechanisms and their implications for drug development still requires further exploration. In this paper, we present a mathematical model representing the binding of VEGF to VEGFR and the subsequent ligand-induced dimerisation. A key factor in this work is the qualitative and quantitative effect of binding cooperativity, which describes the effect that the binding of a ligand to a receptor has on the binding of that ligand to a second receptor, and the dimerisation of these receptors. We analyse the ordinary differential equation system at equilibrium, giving analytical solutions for the total amount of ligand bound. For time-course dynamics, we use numerical methods to explore possible behaviours under various parameter regimes, while perturbation analysis is used to understand the intricacies of these behaviours. Our simulation results show an excellent fit to experimental data, towards validating the model

Modelling honey bee colonies in winter using a Keller-Segel model with a sign-changing chemotactic coefficient

Thermoregulation in honey bee colonies during winter is thought to be self-organised. We added mortality of individual honey bees to an existing model of thermoregulation to account for elevated losses of bees that are reported worldwide. The aim of analysis is to obtain a better fundamental understanding of the consequences of individual mortality during winter. This model resembles the well-known Keller-Segel model. In contrast to the often studied Keller-Segel models, our model includes a chemotactic coefficient of which the sign can change as honey bees have a preferred temperature: when the local temperature is too low, they move towards higher temperatures, whereas the opposite is true for too high temperatures. Our study shows that we can distinguish two states of the colony: one in which the colony size is above a certain critical number of bees in which the bees can keep the core temperature of the colony above the threshold temperature, and one in which the core temperature drops below the critical threshold and the mortality of the bees increases dramatically, leading to a sudden death of the colony. This model behaviour may explain the globally observed honey bee colony losses during winter.Comment: 20 pages, 12 figure

Classical structural identifiability methodology applied to low-dimensional dynamic systems in receptor theory

Mathematical modelling has become a key tool in pharmacological analysis, towards understanding dynamics of cell signalling and quantifying ligand-receptor interactions. Ordinary differential equation (ODE) models in receptor theory may be used to parameterise such interactions using timecourse data, but attention needs to be paid to the theoretical identifiability of the parameters of interest. Identifiability analysis is an often overlooked step in many bio-modelling works. In this paper we introduce structural identifiability analysis (SIA) to the field of receptor theory by applying three classical SIA methods (transfer function, Taylor Series and similarity transformation) to ligand-receptor binding models of biological importance (single ligand and Motulsky-Mahan competition binding at monomers, and a recently presented model of a single ligand binding at receptor dimers). New results are obtained which indicate the identifiable parameters for a single timecourse for Motulsky-Mahan binding and dimerised receptor binding. Importantly, we further consider combinations of experiments which may be performed to overcome issues of non-identifiability, to ensure the practical applicability of the work. The three SIA methods are demonstrated through a tutorial-style approach, using detailed calculations, which show the methods to be tractable for the low-dimensional ODE models

Near critical, self-similar, blow-up solutions of the generalised Korteweg–de Vries equation:Asymptotics and computations

In this article we give a detailed asymptotic analysis of the near critical self-similar blowup solutions to the Generalised Korteweg–de Vries equation (GKdV). We compare this analysis to some careful numerical calculations. It has been known that for a nonlinearity that has a power larger than the critical value p=5, solitary waves of the GKdV can become unstable and become infinite in finite time, in other words they blow up. Numerical simulations presented in Klein and Peter (2015) indicate that if p>5 the solitary waves travel to the right with an increasing speed, and simultaneously, form a similarity structure as they approach the blow-up time. This structure breaks down at p=5. Based on these observations, we rescale the GKdV equation to give an equation that will be analysed by using asymptotic methods as p→5+. By doing this we resolve the complete structure of these self-similar blow-up solutions and study the singular nature of the solutions in the critical limit. In both the numerics and the asymptotics, we find that the solution has sech-like behaviour near the peak. Moreover, it becomes asymmetric with slow algebraic decay to the left of the peak and much more rapid algebraic decay to the right. The asymptotic expressions agree to high accuracy with the numerical results, performed by adaptive high-order solvers based on collocation or finite difference methods

Roses are unselfish: a greenhouse growth model to predict harvest rates.

We consider the question of how rose production in a greenhouse can be optimised. Based on realistic assumptions, a rose growth model is derived that can be used to predict the rose harvest. The model is made up of two constituent parts: (i) a local model that calculates the photosynthetic rate per area of leaf and (ii) a global model of the greenhouse that transforms the photosynthesis of the leaves into an increase in mass of the rose crop. The growth rate of the rose stems depends not only on the time-dependent ambient conditions within the greenhouse, which include temperature, relative humidity, CO$_2$ concentration and light intensity, but also on the location and age distribution of the leaves and the form of the underlying rose bush supporting the crop

Phase-separation physics underlies new theory for the resilience of patchy ecosystems

Spatial self-organization of ecosystems into large-scale (from micron to meters) patterns is an important phenomenon in ecology, enabling organisms to cope with harsh environmental conditions and buffering ecosystem degradation. Scale-dependent feedbacks provide the predominant conceptual framework for self-organized spatial patterns, explaining regular patterns observed in, e.g., arid ecosystems or mussel beds. Here, we highlight an alternative mechanism for self-organized patterns, based on the aggregation of a biotic or abiotic species, such as herbivores, sediment, or nutrients. Using a generalized mathematical model, we demonstrate that ecosystems with aggregation-driven patterns have fundamentally different dynamics and resilience properties than ecosystems with patterns that formed through scale-dependent feedbacks. Building on the physics theory for phase-separation dynamics, we show that patchy ecosystems with aggregation patterns are more vulnerable than systems with patterns formed through scale-dependent feedbacks, especially at small spatial scales. This is because local disturbances can trigger large-scale redistribution of resources, amplifying local degradation. Finally, we show that insights from physics, by providing mechanistic understanding of the initiation of aggregation patterns and their tendency to coarsen, provide a new indicator framework to signal proximity to ecological tipping points and subsequent ecosystem degradation for this class of patchy ecosystems

Mathematical modelling of the Germasogeia aquifer

Two challenges related to improving the management of the Germasogeia aquifer were presented to the Study Group by the Cyprus Water Development Department (WDD), the public organisation responsible for managing the wa- ter resources in Cyprus. The rst challenge was how to optimally recharge the aquifer in order to compensate for the extraction of drinking and irrigation water whilst preventing sea water intrusion. In order to address this challenge we developed model for the water in the aquifer. Note that by exploiting the long, thin nature of the aquifer we only develop two-dimensional models in this work. We rst develop a simple model based on Darcy ows for porous media which gives the water table height for given dam seepage rate, recharge and extraction rates; we neglect seawater intrusion. We then use the steady version of this model to develop an optimized recharge strategy with which we can identify minimal recharge required for a desired extracted water volume such that the minimum prescribed water table is respected. We explore 4 di erent scenarios and we nd that in certain cases there can be a considerable reduction in the amount of recharged water compared to the current empirical strategy the Water Development Department is employing, where water is recharged and extracted in equal proportions. To incorporate the e ects of seawater intrusion, which can be very damaging to the water quality, we next develop transient two- dimensional models of saturated-unsaturated groundwater ow and solve them numerically using the open source software SUTRASuite and the commercial package ANSYS FLUENT; the position of the water table and the seawater- freshwater interface are determined for various extraction/recharge strategies. Data from the WDD are used in some of the simulations. The second important challenge we were asked to look at was to predict the transport of pollutants in the aquifer in the case of an accidental leakage. An advection-difusion equation for the contaminant concentration is introduced and simulations are under- taken using the commercial package COMSOL. The concentration pro les of the contaminant are studied and we nd that the e ect of contamination varies depending on where the contamination site is; the closer the contamination site is to the dam, the larger the extent of contamination will be