Learn More
In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can be generated through lateral inhibition--a type of cell-cell interaction whereby a cell that adopts a particular fate inhibits its immediate neighbors from doing(More)
1. Lecture Notes aim to report new developments in all areas of mathematics and their applications-quickly, informally and at a high level. Mathematical texts analysing new developments in modelling and numerical simulation are welcome. Manuscripts should be reasonably self-contained and rounded off. Thus they may, and often will, present not only results(More)
We present a diffusion-competition model to describe the interaction between the externally introduced grey squirrel and the indigenous red squirrel in Britain. We estimate the model parameters from field data. Solution of the model predicts waves of grey squirrel invasion with speed of invasion typical of that observed in the field. Numerical solution of(More)
Tumor spheroids grown in vitro have been widely used as models of in vivo tumor growth because they display many of the characteristics of in vivo growth, including the effects of nutrient limitations and perhaps the effect of stress on growth. In either case there are numerous biochemical and biophysical processes involved whose interactions can only be(More)
Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow. This is an important factor on which both nutrient and metabolite supply depend. In this paper we aim to address this shortcoming by developing a mathematical model which shows how blood flow and red blood cell heterogeneity influence the growth of(More)
The healing of adult mammalian skin wounds involves a complex sequence of spatially and temporally coordinated processes. Wound contraction, by reducing the size of the injury, is an intrinsic component of full-thickness excisional dermal wound healing. The underlying biomechanics of wound contraction, however, are not fully understood, and little is known(More)
Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending(More)
In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are mini-organs that undergo cyclic regeneration throughout adult life, and are an important model for organ regeneration. Hair stem cells located in the follicle bulge are regulated by the surrounding microenvironment, or niche.(More)
We investigate the sequence of patterns generated by a reaction-diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction-diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence(More)
Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during embryogenesis and also one of the major unresolved events in developmental biology. In this article, we develop a mathematical formulation of a(More)