Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

We consider a model of a Hopf bifurcation interacting as a codimension 2 bifurcation with a saddle-node on a limit cycle, motivated by a low-order model for magnetic activity in a stellar dynamo. This model consists of coupled interactions between a saddle-node and two Hopf bifurcations, where the saddle-node bifurcation is assumed to have global reinjection of trajectories. The model can produce chaotic behaviour within each of a pair of invariant subspaces, and also it can show attractors that are stuck-on to both of the invariant subspaces. We investigate the detailed intermittent dynamics for such an attractor, investigating the effect of breaking the symmetry between the two Hopf bifurcations, and observing that it can appear via blowout bifurcations from the invariant subspaces. We give a simple Markov chain model for the two-state intermittent dynamics that reproduces the time spent close to the invariant subspaces and the switching between the different possible invariant subspaces; this clarifies the observation that the proportion of time spent near the different subspaces depends on the average residence time and also on the probabilities of switching between the possible subspaces

Infinities of stable periodic orbits in systems of coupled oscillators

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor

Phosphorene-AsP Heterostructure as a Potential Excitonic Solar Cell Material - A First Principles Study

Solar energy conversion to produce electricity using photovoltaics is an emerging area in alternative energy research. Herein, we report on the basis of density functional calculations, phosphorene/AsP heterostructure could be a promising material for excitonic solar cells (XSCs). Our HSE06 functional calculations show that the band gap of both phosphorene and AsP fall exactly into the optimum value range according to XSCs requirement. The calculated effective mass of electrons and holes show anisotropic in nature with effective masses along ${\Gamma}$-X direction is lower than the ${\Gamma}$-Y direction and hence the charge transport will be faster along ${\Gamma}$-X direction. The wide energy range of light absorption confirms the potential use of these materials for solar cell applications. Interestingly, phosphorene and AsP monolayer forms a type-II band alignment which will enhance the separation of photogenerated charge carriers and hence the recombination rate will be lower which can further improve its photo-conversion efficiency if one use it in XSCs

Sociological Knowledge and Transformation at ‘Diversity University’, UK

This chapter is based on a case study of one UK university sociology department and shows how sociology knowledge can transform the lives of ‘non-traditional’ students. The research from which the case is drawn focused on four departments teaching sociology-related subjects in universities positioned differently in UK league tables. It explored the question of the relationship between university reputation, pedagogic quality and curriculum knowledge, challenging taken-for-granted judgements about ‘quality’ and in conceptualising ‘just’ university pedagogy by taking Basil Bernstein’s ideas about how ‘powerful’ knowledge is distributed in society to illuminate pedagogy and curriculum. The project took the view that ‘power’ lies in the acquisition of specific (inter)disciplinary knowledges which allows the formation of disciplinary identities by way of developing the means to think about and act in the world in specific ways. We chose to focus on sociology because (1) university sociology is taken up by all socio-economic classes in the UK and is increasingly taught in courses in which the discipline is applied to practice; (2) it is a discipline that historically pursues social and moral ambition which assists exploration of the contribution of pedagogic quality to individuals and society beyond economic goals; (3) the researchers teach and research sociology or sociology of education - an understanding of the subjects under discussion is essential to make judgements about quality. ‘Diversity’ was one of four case study universities. It ranks low in university league tables; is located in a large, multi-cultural English inner city; and, its students are likely to come from lower socio-economic and/or ethnic minority groups, as well as being the first in their families to attend university. To make a case for transformative teaching at Diversity, the chapter draws on longitudinal interviews with students, interviews with tutors, curriculum documents, recordings of teaching, examples of student work, and a survey. It establishes what we can learn from the case of sociology at Diversity, arguing that equality, quality and transformation for individuals and society are served by a university curriculum which is research led and challenging combined with pedagogical practices which give access to difficult-to-acquire and powerful knowledge

Qualitative System Identification from Imperfect Data

Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as differential equations. Quantitative modelling works best when the structure of the model (i.e., the form of the equations) is known; and the primary concern is one of estimating the values of the parameters in the model. For complex biological systems, the model-structure is rarely known and the modeler has to deal with both model-identification and parameter-estimation. In this paper we are concerned with providing automated assistance to the first of these problems. Specifically, we examine the identification by machine of the structural relationships between experimentally observed variables. These relationship will be expressed in the form of qualitative abstractions of a quantitative model. Such qualitative models may not only provide clues to the precise quantitative model, but also assist in understanding the essence of that model. Our position in this paper is that background knowledge incorporating system modelling principles can be used to constrain effectively the set of good qualitative models. Utilising the model-identification framework provided by Inductive Logic Programming (ILP) we present empirical support for this position using a series of increasingly complex artificial datasets. The results are obtained with qualitative and quantitative data subject to varying amounts of noise and different degrees of sparsity. The results also point to the presence of a set of qualitative states, which we term kernel subsets, that may be necessary for a qualitative model-learner to learn correct models. We demonstrate scalability of the method to biological system modelling by identification of the glycolysis metabolic pathway from data

CampProf: A Visual Performance Analysis Tool for Memory Bound GPU Kernels

Current GPU tools and performance models provide some common architectural insights that guide the programmers to write optimal code. We challenge these performance models, by modeling and analyzing a lesser known, but very severe performance pitfall, called 'Partition Camping', in NVIDIA GPUs. Partition Camping is caused by memory accesses that are skewed towards a subset of the available memory partitions, which may degrade the performance of memory-bound CUDA kernels by up to seven-times. No existing tool can detect the partition camping effect in CUDA kernels. We complement the existing tools by developing 'CampProf', a spreadsheet based, visual analysis tool, that detects the degree to which any memory-bound kernel suffers from partition camping. In addition, CampProf also predicts the kernel's performance at all execution configurations, if its performance parameters are known at any one of them. To demonstrate the utility of CampProf, we analyze three different applications using our tool, and demonstrate how it can be used to discover partition camping. We also demonstrate how CampProf can be used to monitor the performance improvements in the kernels, as the partition camping effect is being removed. The performance model that drives CampProf was developed by applying multiple linear regression techniques over a set of specific micro-benchmarks that simulated the partition camping behavior. Our results show that the geometric mean of errors in our prediction model is within 12% of the actual execution times. In summary, CampProf is a new, accurate, and easy-to-use tool that can be used in conjunction with the existing tools to analyze and improve the overall performance of memory-bound CUDA kernels

Phase resetting effects for robust cycles between chaotic sets

In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena including that of robust attractors showing chaotic itinerancy. At the simplest level this is an attracting heteroclinic cycle between equilibria, but cycles between more general invariant sets are also possible. This paper introduces and discusses an instructive example of an ODE where one can observe and analyse robust cycling behaviour. By design, we can show that there is a robust cycle between invariant sets that may be chaotic saddles (whose internal dynamics correspond to a Rossler system), and/or saddle equilibria. For this model, we distinguish between cycling that include phase resetting connections (where there is only one connecting trajectory) and more general non-phase resetting cases where there may be an infinite number (even a continuum) of connections. In the non-phase resetting case there is a question of connection selection: which connections are observed for typical attracted trajectories? We discuss the instability of this cycling to resonances of Lyapunov exponents and relate this to a conjecture that phase resetting cycles typically lead to stable periodic orbits at instability whereas more general cases may give rise to `stuck on' cycling. Finally, we discuss how the presence of positive Lyapunov exponents of the chaotic saddle mean that we need to be very careful in interpreting numerical simulations where the return times become long; this can critically influence the simulation of phase-resetting and connection selection

Chaos in Symmetric Phase Oscillator Networks

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos, i.e., nonlinear interactions of phases give rise to the necessary instabilities.Comment: 4 pages; Accepted by Physical Review Letter

Transverse instability for non-normal parameters

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as ``non-normal''. If there is chaos in the invariant subspace that is not structurally stable, this has the effect of ``blurring out'' blowout bifurcations over a range of parameter values that we show can have positive measure in parameter space. Associated with such blowout bifurcations are bifurcations to attractors displaying a new type of intermittency that is phenomenologically similar to on-off intermittency, but where the intersection of the attractor by the invariant subspace is larger than a minimal attractor. The presence of distinct repelling and attracting invariant sets leads us to refer to this as ``in-out'' intermittency. Such behaviour cannot appear in systems where the transverse dynamics is a skew product over the system on the invariant subspace. We characterise in-out intermittency in terms of its structure in phase space and in terms of invariants of the dynamics obtained from a Markov model of the attractor. This model predicts a scaling of the length of laminar phases that is similar to that for on-off intermittency but which has some differences.Comment: 15 figures, submitted to Nonlinearity, the full paper available at http://www.maths.qmw.ac.uk/~eo