Existence and Stability of a Model for Three-Dimensional Toroidal Plasma Equilibria. There is great physical interest in modelling strongly non-axisymmetric toroidal plasmas, but fundamental existence problems have made rigorous numerical analysis so far impossible. We seek to overcome this by investigating a class of idealized, but physically motivated, magnetohydrodynamic equilibria with stepped pressure profiles for which existence in the neighbourhood of axisymmetry has been proven. We will ....Existence and Stability of a Model for Three-Dimensional Toroidal Plasma Equilibria. There is great physical interest in modelling strongly non-axisymmetric toroidal plasmas, but fundamental existence problems have made rigorous numerical analysis so far impossible. We seek to overcome this by investigating a class of idealized, but physically motivated, magnetohydrodynamic equilibria with stepped pressure profiles for which existence in the neighbourhood of axisymmetry has been proven. We will (i) develop numerical techniques to extend these piece-wise Beltrami states far away from axisymmetry (ii) develop practical tests to determine when existence breaks down (iii) analyze the frequency spectrum of small oscillations about such equilibria (iv) extend the model to two-fluid MHD.Read moreRead less
Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few ....Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few years ago. The outcome will be a
combination of theoretical results and practical achievements,
whose usefulness will be demonstrated with some serious
applications in physics and mathematics.
Read moreRead less
Structure enumeration, applications and analysis. Structure enumeration and analysis is at the heart of finite mathematics and its many fields of application in diverse scientific disciplines. Australia has a substantial status in this field both in mathematics and physics. This project will enhance that status and develop greater ties with the centres of structure research in other parts of the world.