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

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

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

Online open neuroimaging mass meta-analysis

We describe a system for meta-analysis where a wiki stores numerical data in a simple format and a web service performs the numerical computation. We initially apply the system on multiple meta-analyses of structural neuroimaging data results. The described system allows for mass meta-analysis, e.g., meta-analysis across multiple brain regions and multiple mental disorders.Comment: 5 pages, 4 figures SePublica 2012, ESWC 2012 Workshop, 28 May 2012, Heraklion, Greec

The use of multilayer network analysis in animal behaviour

Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as \emph{multilayer network analysis}, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour as connected 'layers' of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population, and evolutionary levels of organisation. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.Comment: Thoroughly revised; title changed slightl

The Testbed for LISA Analysis Project

The Testbed for LISA Analysis (TLA) Project aims to facilitate the development, validation and comparison of different methods for LISA science data analysis, by the broad LISA Science Community, to meet the special challenges that LISA poses. It includes a well-defined Simulated LISA Data Product (SLDP), which provides a clean interface between the communities that have developed to model and to analyze the LISA science data stream; a web-based clearinghouse (at ) providing SLDP software libraries, relevant software, papers and other documentation, and a repository for SLDP data sets; a set of mailing lists for communication between and among LISA simulators and LISA science analysts; a problem tracking system for SLDP support; and a program of workshops to allow the burgeoning LISA science community to further refine the SLDP definition, define specific LISA science analysis challenges, and report their results. This note describes the TLA Project, the resources it provides immediately, its future plans, and invites the participation of the broader community in the furtherance of its goals.Comment: 5 pages, no figure

Addressing LISA Science Analysis Challenges

The principal goal of the \emph{LISA Science Analysis Workshop} is to encourage the development and maturation of science analysis technology in preparation for LISA science operations. Exactly because LISA is a pathfinder for a new scientific discipline -- gravitational wave astronomy -- LISA data processing and science analysis methodologies are in their infancy and require considerable maturation if they are to be ready to take advantage of LISA data. Here we offer some thoughts, in anticipation of the LISA Science Analysis Workshop, on analysis research problems that demonstrate the capabilities of different proposed analysis methodologies and, simultaneously, help to push those techniques toward greater maturity. Particular emphasis is placed on formulating questions that can be turned into well-posed problems involving tests run on specific data sets, which can be shared among different groups to enable the comparison of techniques on a well-defined platform.Comment: 7 page

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