MISSION

Making Mathematics meaningful through critical thinking and problem solving M3

VISION

Shaping the aspirations of our students by providing a supportive environment for learning mathematics.

Vision Statement

Shaping the aspirations of our students by providing a supportive environment for learning mathematics.

VALUES

1. Teamwork

(collaboration, fun, support one other, collegiality)

2. Commitment

(perseverance, conscientiousness and effort)

3. Integrity

(honesty, proud, ethics, best you can even when no one is watching, authentic, trust)

4. Passion

(showing/ passing on a love for knowledge; sharing; love what you do)

5. Discovery

(why, curiosity, critical thinking, cause/ effect)

RESEARCH

Dynamical Systems Research

The Dynamical Systems Research group conducts research in 4 key focus areas:

Relativistic Astrophysics,

Causal Thermodynamics and

Lie Symmetries, Differential Equations and Dissipative Collapse.

Large-scale Fluid Dynamics.

Transformational Educational Studies

The research group focuses on the important task of understanding education transformation in two ways: how education systems transform students, and how the transformation of the education systems themselves affect the educational experience, especially for at-risk students.

In a latest project at DUT, a paper reporting on first year civil engineering students working in groups, was published in Groupwork (a journal in the UK). This work is being extended to incorporate a larger sample of engineering students. One sub-group of our team is working on this problem. Another sub-group is researching the impact of E-learning in the teaching and learning of mathematics.

COLLABORATIONS

Relativistic Astrophysics

Einstein’s general theory of relativity is a metric theory of gravity in which the spacetime geometry is determined by the matter content. Einstein’s theory of gravity has been widely supported by experiments and observations. Our research in relativistic astrophysics focuses on: 1) dissipative collapse of radiating stars, 2) causal thermodynamics, 3) modelling relativistic compact objects and 4) the end states of continued gravitational collapse.

Causal Thermodynamics

The Eckart formulation of relativistic thermodynamics gives rise to superluminous propagation velocities for the dissipative signals. In addition, equilibrium states are unstable. Second order effects in the dissipative fluxes have to be included to generate a consistent theory of irreversible thermodynamics. We utilise the covariant relativistic Maxwell-Cattaneo heat transport equation to study heat flow in radiating collapsing fluids.

Lie Symmetries and Dissipative Collapse

A radiating star divides spacetime into two distinct regions – the interior of the star and the exterior of the star (atmosphere). The junction conditions required for the smooth matching of the interior spacetime to the exterior spacetime imply that the radial pressure at the boundary of the star is nonvanishing which ensures the continuity of the momentum flux across the boundary of the collapsing star. This boundary condition determines the temporal evolution of the gravitational potentials of the radiating model, and is an ordinary, nonlinear partial differential equation. We utilise Lie Symmetries to solve the boundary condition arising from the matching conditions.

Staff

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