[show abstract][hide abstract] ABSTRACT: Numerical techniques for moving meshes are many and varied. In this paper we present a novel application of a moving grid finite element method applied to biological problems related to pattern formation where the mesh movement is prescribed through a specific definition to mimic the growth that is observed in nature. Through the use of a moving grid finite element technique, we pres- ent numerical computational results illustrating how period doubling behaviour occurs as the domain doubles in size.
Journal of Scientific Computing 01/2005; 24:247-262. · 1.71 Impact Factor
[show abstract][hide abstract] ABSTRACT: this paper we present a novel application of a moving grid nite element method applied to biological problems related to pattern formation where the mesh movement is prescribed through a speci c de nition to mimic the growth that is observed in nature. Through the use of a moving grid nite element technique, we present numerical computational results illustrating how period doubling actually occurs as the domain doubles in size
[show abstract][hide abstract] ABSTRACT: Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who have tried to understand the underlying genetic, chemical and physical processes that lead to patterning. In this paper, we present a brief review of this field by first considering the generation of the localised, eyespot, patterns and then the formation of more globally controlled patterns. We present some new results applied to pattern formation on the wing of the mimetic butterfly Papilio dardanus.
[show abstract][hide abstract] ABSTRACT: Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we present a novel application of the moving grid finite element method to compute solutions of reaction–diffusion systems in two-dimensional continuously deforming Euclidean domains. A numerical software package has been developed as a result of this research that is capable of solving generalised Turing models for morphogenesis.
[show abstract][hide abstract] ABSTRACT: this paper we present a novel application of the moving grid nite element method to compute solutions of reactiondi usion systems in two-dimensional continuously deforming Euclidean domains
[show abstract][hide abstract] ABSTRACT: We investigate pigmentation patterns in the buttery wing of Papilio dardanus by numerical simulations of a reaction-diusion model on a geometrically accurate wing domain. Our results suggest that the wing coloration is due to a simple underlying stripe-like pattern of some pigment-inducing morphogen. In this paper, we present some of our numerical results and discuss the validity of our model by comparing our results with pictures of male and female wing patterns of the buttery.
[show abstract][hide abstract] ABSTRACT: In this paper, we employ the novel application of a reaction-diffusion model on a growing domain to examine growth patterns of the ligaments of arcoid bivalves (marine molluscs) using realistic growth functions. Solving the equations via a novel use of the finite element method on a moving mesh, we show how a reaction-diffusion model can mimic a number of different ligament growth patterns with modest changes in the parameters. Our results imply the existence of a common mode of ligament pattern formation throughout the Arcoida. Consequently, arcoids that share a particular pattern cannot be assumed, on this basis alone, to share an immediate common ancestry. Strikingly different patterns within the set can easily be generated by the same developmental program. We further show how the model can be used to make quantitatively testable predictions with biological implications.
Bulletin of Mathematical Biology 06/2002; 64(3):501-30. · 2.02 Impact Factor
[show abstract][hide abstract] ABSTRACT: Previously, we have proposed a mathematical model based on a modified Turing mechanism to account for pigmentation patterning in the butterfly wing of Papilio dardanus, well-known for the spectacular phenotypic polymorphism in the female of the species (Sekimura, et al., Proc. Roy. Soc. Lond. B 267, 851-859 (2000)). In the present paper, we use our model to predict the outcome of a number of dierent types of cutting experiments and compare our results with those of a model based on dierent hypotheses.
[show abstract][hide abstract] ABSTRACT: Domain growth can play an important role in pattern formation duringearly embryonic development. By considering the Turing reaction-diusion modelfor pattern formation, we show how growth can inuence patterning. We considerhow growth aects mode selection and robustness of patterns. Specically, we investigateligament patterns in arcoid bivalves.