Localization of response functions of spiral waves in the FitzHugh-Nagumo system

Dynamics of spiral waves in perturbed, e. g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spiral's Response Functions, which are eigenfunctions of the adjoint linearised problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh-Nagumo model, and show that they are effectively localised in the vicinity of the spiral core.Comment: 11 pages, 2 figure

Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator-prey pursuit and evasion example

We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the ``taxis'', represented by nonlinear ``cross-diffusion'' terms in the mathematical formulation. We have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms, ``parabolic'' and ``linear''. Transition from one form to the other correlates with changes in the shape of the wave profile. Dependence of the propagation velocity on diffusion in this system differs from the square-root dependence typical of reaction-diffusion waves. We demonstrate also that, for systems with negative and positive taxis, for example, pursuit and evasion, there typically exists a large region in the parameter space, where the waves demonstrate quasisoliton interaction: colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries.Comment: 15 pages, 18 figures, submitted to Physica

Pursuit-evasion predator-prey waves in two spatial dimensions

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wavetips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatio-temporal activity, unknown in reaction-diffusion population models.Comment: 15 pages, 15 figures, submitted to Chao

Localization of response functions of spiral waves in the FitzHugh-Nagumo system

Preprint of an article submitted for consideration and subsequently published in International Journal of Bifurcation and Chaos © 2005 copyright World Scientific Publishing Company. http://www.worldscientific.com/worldscinet/ijbcDynamics of spiral waves in perturbed, e. g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spiral's Response Functions, which are eigenfunctions of the adjoint linearised problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh-Nagumo model, and show that they are effectively localised in the vicinity of the spiral core

In-Plane Spectral Weight Shift of Charge Carriers in YBa2Cu3O6.9YBa_2Cu_3O_{6.9}

The temperature dependent redistribution of the spectral weight of the $CuO_2$ plane derived conduction band of the $YBa_2Cu_3O_{6.9}$ high temperature superconductor (T_c = 92.7 K) was studied with wide-band (from 0.01 to 5.6 eV) spectroscopic ellipsometry. A superconductivity - induced transfer of the spectral weight involving a high energy scale in excess of 1 eV was observed. Correspondingly, the charge carrier spectral weight was shown to decrease in the superconducting state. The ellipsometric data also provide detailed information about the evolution of the optical self-energy in the normal and superconducting states

Anomalous oxygen isotope effect on the in-plane FIR conductivity of detwinned YBa2Cu316,18^{16,18}O6.9_{6.9}

We observe an anomalous oxygen isotope effect on the a-axis component of the far-infrared electronic response of detwinned YBa2Cu3$^{16,18}$O$_{6.9}$. For $^{18}$O a pronounced low-energy electronic mode (LEM) appears around 240 cm$^{-1}$. This a-axis LEM exhibits a clear aging effect, after one year it is shifted to 190 cm$^{-1}$. For $^{16}$O we cannot resolve a corresponding a-axis LEM above 120 cm$^{-1}$. We interpret the LEM in terms of a collective electronic mode that is pinned by `isotopic defects', i.e. by the residual $^{16}$O in the matrix of $^{18}$O.Comment: 10 pages, 2 figure

Striving to practice what we preach: academics reflecting on teaching reflective practice.

That reflection is part of the HRD academics’ continuing professional development is a powerful rhetoric. But to what extent are we guilty of hypocrisy? Inspired by the title and theme of the conference ‘HRD: Reflecting upon the Past, Shaping the Future’ this paper seeks to make a critically reflective statement on our own practice as HRD academics teaching and researching reflective practice. Researching ‘practising what we preach’, in the context of reflective practice, raises difficult questions but offers the potential for valuable insight into the HRD academics’ professional practice

From reflective learning to reflective practice: assessing transfer

A key attribute of reflective practice is its capacity for on-going purposeful learning in relation to changing and demanding professional work. The teaching of reflective learning techniques in management education is intended to promote deep-level learning and the application of critical thinking to oneself, personal experience and the work environment. However, we lack empirical evidence that the teaching of reflective learning leads to enhanced reflective practice in professional work. This study provides an examination of reflection in work post formal education. It reports on interviews with 18 Human Resource professionals. Reflection does not get ‘left behind’ on completion of formal teaching but there is not an even or simple process of transfer to a work context. Likewise, there was not a slavish adherence to reflective techniques but rather some evidence that students were able to translate their learning into something meaningful for their practice. © 2016 Society for Research into Higher Educatio

Reflective practice: is there transfer from classroom to workplace?

Does HE based teaching of reflective practice transfer into management practice in the workplace? This paper reports on research addressing this question. Initially the research is set in context. Extensive theorising, conceptual debate and discussion on a problematic curriculum have not been matched with empirical data about reflection as part of managing. Interviews with eighteen HR professionals provide the data upon which initial findings are drawn. Management practice is influenced by their professional programme and, in the main, reflection is an important element of perceived change. For some transfer appears restricted to instrumental practice. For others, however, a more complex picture emerges; one where glimpses of criticality are evident but where the link to the formal teaching of reflection is less straightforward. This, together with factors influencing the reflective landscape observed, warrant further analysis as a precursor to consideration of curriculum implication