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Modelling and simulation of industrial processes and products

Industrial processes and products can be described as 'multi-problems' in that they are often multi-scale, multi-phase and multi-component in nature. The analysis of such problems sits in the exciting nexus of applied mathematics, physical science and engineering science.

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

The mathematics of robustness in molecular communication networks

Robustness, and the ability to function and thrive amid changing and unfavourable environments, is a fundamental requirement for living systems. In the past, it has been a mystery how large and complex biological networks can exhibit robust performance since complexity is generally associated with fragility.Exciting recent research here at QUT has suggested a resolution to this paradox through the discovery that robust adaptive signalling networks must be constructed from a small number of well-defined universal modules ("motifs"). The existence of …

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

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

Collisions with evolving surfaces

The density of impacts of particles colliding with an evolving surface is of particular interest for several industrial and biological applications. These include etching and deposition processes [1], the incorporation of molecules in a tissue during its growth, budding cell membranes, and biological tissue growth [2]. Impacts on an evolving surface are generated unevenly depending on the relative velocity between the particles and the surface. The distribution of impacts further evolves in a curvature-dependent manner due to the local distortions …

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

Creation of fibre meshworks at moving interfaces

Extracellular matrix (ECM) secreted by cells is composed of a meshwork of fibres infiltrated with proteins and/or minerals. This fibre meshwork often matures after its creation by rearranging its structure, e.g. according to local mechanical clues, or by the infiltration of new molecules [1]. In this project, the fibre meshwork will be represented by a continuous tensorial field [2].ReferencesBidan C et al. Gradual conversion of cellular stress patterns into pre-stressed matrix architecture during in vitro tissue growth, J R Soc …

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

Mathematical modelling of heat conduction in skin

Scald burns from exposure to hot liquids are the most common cause of thermal injury in children. To assist in the development of burn prevention strategies, a theoretical understanding of how heat is conducted through skin is essential. One way to achieve this is to apply a mathematical model to interpret experimental data. Such models are commonly based on the Pennes bioheat equation, a partial differential equation that describes the temperature in the skin as a function of spatial depth …

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

Investigation of roughness and wettability model of nanostructured surfaces for biomedical devices

All nanostructured surfaces have unique surface roughness which mathematically describes by the surface architecture or the geometry. Moreover, the nanostructured surfaces may have variable water contact angle values due to the combination of surface roughness and surface composition. The correlation of surface roughness and wettability of nanostructured surfaces to the antibacterial activity becomes significant in designing a numerical model for biomedical devices.

Study level
Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Chemistry, Physics and Mechanical Engineering

Computational models of interacting proteins inside a cell

Inside each living cell are vast networks of interacting proteins. These protein networks allow the cell to monitor and interpret its environment, and turn this information into a set of instructions that tell the cell what to do – when to divide, when to move/migrate, when to make new proteins, when to switch to an alternative energy source, etc.Although the human genome has now been sequenced, giving us the full set of instructions (genes) contained within the DNA molecule, we …

Study level
Honours
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

Complex networks as computational devices

Inside each living cell is a tiny universe unto itself: vast interconnected communication networks of signaling molecules (mostly proteins, including enzymes, scaffolds and small molecules ('second messengers'), that dynamically assemble and disassemble in order to interpret stimuli and signals generated both outside and within the cell.We are now beginning to decipher the extraordinary mathematical properties of cellular signalling networks. The remarkable characteristics of these complex networks enable them to represent a kind of 'brain for the cell - allowing the …

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

The reduction of multi-scale porous electrode models using approximation methods

Two-phase porous electrodes are at the heart of many modern day energy storage technologies such as batteries and solar cells. To effectively simulate the operation of these structures a multi-scale mathematical modelling approach is required. This approach results in a system of stiff, coupled, nonlinear partial differential equations that require numerical solution.

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

Optimising bone shape with memory networks

Bone is a dynamic tissue that optimises its shape to the mechanical loads that it carries. Bone mass is accrued where loads are high, and reduced where loads are low. This adaptation of bone tissue to mechanical loads is well-known and observed in many instances. However, what serves as a reference mechanical state in this shape optimisation remains largely unknown.

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

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