Rob Sturman
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Loss of Exponential Mixing in a Non-Monotonic Toral Map Open
We consider a Lebesgue measure preserving map of the 2-torus, given by the composition of orthogonal tent shaped shears. We establish strong mixing properties with respect to the invariant measure and polynomial decay of correlations for H…
Rigorous bounds on Lyapunov exponents of linked twist maps Open
Rigorous, elementary upper and lower bounds upon the Lyapunov exponents of a parametrised family of linked twist maps are given, and obtained explicitly for a specific range of parameter values. The method used to obtain the bounds utilise…
Stability of heteroclinic cycles in ring graphs Open
Networks of interacting nodes connected by edges arise in almost every branch of scientific inquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical syste…
Stability of heteroclinic cycles in rings of coupled oscillators Open
Networks of interacting nodes connected by edges arise in almost every branch of scientific enquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical syste…
Developing computational mathematics provision in undergraduate mathematics degrees Open
Over the last ten years we have comprehensively embedded computational mathematics, and in doing so programming, into the undergraduate mathematics degree programmes at the University of Leeds. This case study discusses some of the practic…
Lyapunov Exponents for the Random Product of Two Shears Open
We give lower and upper bounds on both the Lyapunov exponent and generalised Lyapunov exponents for the random product of positive and negative shear matrices. These types of random products arise in applications such as fluid stirring dev…
View article: Frontiers of chaotic advection
Frontiers of chaotic advection Open
We review the present position of and survey future perspectives in the physics of chaotic advection; the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of appl…
A Graph-Theoretic Approach to Efficient Voice-Leading Open
We study the Neo-Riemannian principle of parsimonious voice-leading using tools and techniques from classical graph theory and the modern field of complex networks. We quantify the relative importance of particular chords within this frame…