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Stochastic patterns of tissue inclusions

Biological tissue growth involves the secretion of new tissue (extracellular matrix, collagen fibers) by cells. This secretion incorporates scattered inclusions such as proteins and minerals into the new tissue. During bone tissue growth, some of the tissue-secreting cells themselves become incorporated into the new tissue. The distribution of these tissue-embedded cells is believed to influence subsequent tissue growth processes.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Size patterns in Turing patterns: how to grow body segments

Certain repeating elements of the body, such as teeth, fingers, limbs and vertebrae, follow the rule that the size of the middle element of a group of three is the average size of the three elements. This simple rule constrains how the relative sizes of segments develop in the embryo and evolve over long periods of time. The precise mechanisms that determine the number and size of repeating structures, such as fingers and teeth, remain largely unknown.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Stochastic patterns of inclusions during tissue growth

Biological tissue growth involves the secretion of new tissue (extracellular matrix, collagen fibers) by cells. This secretion incorporates scattered inclusions such as proteins and minerals into the new tissue. During bone tissue growth, some of the tissue-secreting cells themselves become incorporated into the new tissue. The distribution of these embedded cells is believed to influence subsequent tissue growth processes.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Pattern formation and nonlinear dynamics

Pattern formation is a field of research within the nonlinear sciences where the traditional disciplines of mathematics, physics, chemistry and biology merge, interact and exchange ideas.There are opportunities to conduct research into various aspects of the pattern formation processes from a mathematical perspective. These include the study (existence, stability and interaction) of localised structures such as travelling waves, pulses, stripes and spots in low-dimensional paradigm models, and the effect of small defects or heterogeneities on the pattern formation process. …

Study level
Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

The dynamics of planar localised structures

While patterns observed in the natural sciences are in general (at least) two-dimensional, our mathematical understanding of the interaction of two-dimensional, or planar, localised structures is still in its infancy. In this project, we aim to further this understanding and examine the interaction of fundamental two-dimensional, or planar, patterns such as spots and stripes in reaction-diffusion equations, by developing and extending state-of-the-art mathematical techniques. These fundamental planar structures form the backbone of more complex patterns and are, for example, observed …

Study level
PhD
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

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