Topological optimisation of rod-stirring devices

There are many industrial situations where rods are used to stir a fluid, or where rods repeatedly stretch a material such as bread dough or taffy. The goal in these applications is to stretch either material lines (in a fluid) or the material itself (for dough or taffy) as rapidly as possible. The growth rate of material lines is conveniently given by the topological entropy of the rod motion. We discuss the problem of optimising such rod devices from a topological viewpoint. We express rod motions in terms of generators of the braid group, and assign a cost based on the minimum number of generators needed to write the braid. We show that for one cost function -- the topological entropy per generator -- the optimal growth rate is the logarithm of the golden ratio. For a more realistic cost function,involving the topological entropy per operation where rods are allowed to move together, the optimal growth rate is the logarithm of the silver ratio, $1+\sqrt{2}$. We show how to construct devices that realise this optimal growth, which we call silver mixers.Comment: 22 pages, 53 figures. PDFLaTeX with RevTex4 macros

Two-dimensional Stokes flow driven by elliptical paddles

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically

Topological Mixing with Ghost Rods

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call ghost rods, because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.Comment: 13 pages, 11 figures. RevTeX4 format. (Final version

Topological Entropy of Braids on the Torus

A fast method is presented for computing the topological entropy of braids on the torus. This work is motivated by the need to analyze large braids when studying two-dimensional flows via the braiding of a large number of particle trajectories. Our approach is a generalization of Moussafir's technique for braids on the sphere. Previous methods for computing topological entropies include the Bestvina--Handel train-track algorithm and matrix representations of the braid group. However, the Bestvina--Handel algorithm quickly becomes computationally intractable for large braid words, and matrix methods give only lower bounds, which are often poor for large braids. Our method is computationally fast and appears to give exponential convergence towards the exact entropy. As an illustration we apply our approach to the braiding of both periodic and aperiodic trajectories in the sine flow. The efficiency of the method allows us to explore how much extra information about flow entropy is encoded in the braid as the number of trajectories becomes large.Comment: 19 pages, 44 figures. SIAM journal styl

Media multitasking in adolescence

Media use has been on the rise in adolescents overall, and in particular, the amount of media multitasking—multiple media consumed simultaneously, such as having a text message conversation while watching TV—has been increasing. In adults, heavy media multitasking has been linked with poorer performance on a number of laboratory measures of cognition, but no relationship has yet been established between media-multitasking behavior and real-world outcomes. Examining individual differences across a group of adolescents, we found that more frequent media multitasking in daily life was associated with poorer performance on statewide standardized achievement tests of math and English in the classroom, poorer performance on behavioral measures of executive function (working memory capacity) in the laboratory, and traits of greater impulsivity and lesser growth mindset. Greater media multitasking had a relatively circumscribed set of associations, and was not related to behavioral measures of cognitive processing speed, implicit learning, or manual dexterity, or to traits of grit and conscientiousness. Thus, individual differences in adolescent media multitasking were related to specific differences in executive function and in performance on real-world academic achievement measures: More media multitasking was associated with poorer executive function ability, worse academic achievement, and a reduced growth mindset.Bill & Melinda Gates Foundatio

Topological Chaos in Spatially Periodic Mixers

Topologically chaotic fluid advection is examined in two-dimensional flows with either or both directions spatially periodic. Topological chaos is created by driving flow with moving stirrers whose trajectories are chosen to form various braids. For spatially periodic flows, in addition to the usual stirrer-exchange braiding motions, there are additional topologically-nontrivial motions corresponding to stirrers traversing the periodic directions. This leads to a study of the braid group on the cylinder and the torus. Methods for finding topological entropy lower bounds for such flows are examined. These bounds are then compared to numerical stirring simulations of Stokes flow to evaluate their sharpness. The sine flow is also examined from a topological perspective.Comment: 18 pages, 14 figures. RevTeX4 style with psfrag macros. Final versio

Ironless wheel motor for a direct drive vehicle application

An ironless motor for use as direct wheel drive is presented. The motor is intended for use in a lightweight (600kg), low drag, series hybrid commuter vehicle under development at The University of Queensland. The vehicle will utilise these ironless motors in each of its rear wheels, with each motor producing a peak torque output of 500Nm and a maximum rotational speed of 1500rpm. The axial flux motor consists of twin Ironless litz wire stators with a central magnetic ring and simplified Halbach magnet arrays on either side. A small amount of iron is used to support the outer Halbach arrays and to improve the peak magnetic flux density. Ducted air cooling is used to remove heat from the motor and will allow for a continuous torque rating of 250Nm. Ironless machines have previously been shown to be effective in high speed, high frequency applications (+1000Hz). They are generally regarded as non-optimal for low speed applications as iron cores allow for better magnet utilisation and do not significantly increase the weight of a machine. However, ironless machines can also be seen to be effective in applications where the average torque requirement is much lower than the peak torque requirement such as in some vehicle drive applications. The low spinning losses in ironless machines are shown to result in very high energy throughput efficiency in a wide range of vehicle driving cycles

The UltraCommuter : a viable and desirable solar-powered commuter vehicle

The University of Queensland UltraCommuter project is the demonstration of an ultra-light weight, low drag, energy efficient and low polluting, electric commuter vehicle equipped with a 2.5m2 on-board solar array. A key goal of the project is to make the vehicle predominantly self-sufficient from solar power for normal driving purposes , so that it does not require charging or refuelling from off-board sources. This paper examines the technical feasibility of the solar-powered commuter vehicle concept, as it applies the UltraCommuter project. A parametric description of a solar-powered commuter vehicle is presented. Real solar insolation data is then used to predict the solar driving range for the UltraCommuter and this is compared to typical urban usage patterns for commuter vehicles in Queensland. A comparative analysis of annual greenhouse gas emissions from the vehicle is also presented. The results show that the UltraCommuter’s on-board solar array can provide substantial supplementation of the energy required for normal driving, powering 90% of annual travel needs for an average QLD passenger vehicle. The vehicle also has excellent potential to reduce annual greenhouse gas emissions from the private transport sector, achieving a 98% reduction in CO2 emissions when compared to the average QLD passenger vehicle. Lastly, the vehicle battery pack provides for tolerance to consecutive days of poor weather without resorting to grid charging, giving uninterrupted functionality to the user. These results hold great promise for the technical feasibility of the solar-powered commuter vehicle concept

Energy constrained transport maximization across a fluid interface

With enhancing mixing in micro- or nanofluidic applications in mind, the problem of maximizing fluid transport across a fluid interface subject to an available energy budget is examined. The optimum cross-interface perturbing velocity is obtained explicitly in the time-periodic instance using an Euler-Lagrange constrained optimization approach. Numerical investigations which calculate transferred lobe areas and cross-interface flux are used to verify that the predicted strategy achieves optimum transport. Explicit active protocols for achieving this optimal transport are suggested.Sanjeeva Balasuriya, Matthew D. Fin