Pattern formation in developing organisms can be regulated at a variety of levels, from gene sequence to anatomy. At this level of complexity, mechanistic models of development become essential for integrating data, guiding future experiments, and predicting the effects of genetic and physical perturbations. However, the formulation and analysis of quantitative models of development are limited...

We derive models for chemosensitive movement based on Cattaneo’s law of heat propagation with finite speed. We apply the model to pattern formation as observed in experiments with Dictyostelium discoideum, with Salmonella typhimurium and with Escherichia coli. For Salmonella typhimurium we make predictions on pattern formation which can be tested in experiments. We discuss the relations of the ...

This paper is devoted to the overview of recent results concerning nonlocal systems of conservation laws. First, we present a predator – prey model and, second, a model for the laser cutting of metals. In both cases, these equations lead to interesting pattern formation.

We studied the effect of nearest pattern interaction on a global pattern formation in a two-dimensional space, where patterns are to grow initially from a noise in the presence of a periodic supply of energy. Although our approach is general, we found that this study is relevant in particular to the pattern formation on a periodically vibrated granular layer, as it gives a unified perspective o...

Watson and Lovelock’s daisyworld model [1] was devised to demonstrate how the biota of a world could stabilise it, driving it to a temperature regime that favoured survival of the biota. The subsequent studies have focused on the behaviour of daisyworld in various fields. This study looks at the emergent patterns that arise in 2D daisyworlds at different parameter settings, demonstrating that a...

Based on a recently proposed non-equilibrium mechanism for spatial pattern formation [13] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problem of domain formation and proportion regulation in the presence of noise and cell ...

In this article, we discuss the relationships between thermodynamic quantities and the spatial pattern in a reaction-diffusion model based on the reversible Gray-Scott model. This model is introduced for calculation of the entropy production in a reaction-diffusion system. First, we show the relationship between entropy production and pattern formation, and suggest that the entropy production c...

We examine sequential spatial pattern formation in a tissue interaction model for skin organ morphogenesis. Pattern formation occurs as a front sweeps across the domain leaving in its wake a steady state spatial pattern. Extensive numerical simulations show that these fronts travel with constant wave speed. By considering the envelope of the solution profile we present a novel method of calcula...

Difference patterns are vital for the successful function of tracking radar employing monopulse techniques to estimate target direction. Traditional monopulse antenna pattern synthesis methods require the use of two independent distributions, e.g., Taylor and Bayliss distributions, for formation of sum and difference patterns for one antenna. Hence, these approaches require a feed network of co...