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

Irish Dairy Farming: Effects of Introducing a Maize Component on Grassland Management Over the Next 50 Years

Typical management of Irish dairy units is based on a low-cost spring-calving strategy with 90% of annual feed derived from grass grown on the farm. Almost 70% of feed is from grazed grass managed by rotational grazing, the remainder is conserved forage and concentrates. The objectives of the work were to examine how the management system has to be modified when part of the dairy unit land is allocated to maize silage instead of grass silage production, and to examine how climate change over the next 50 years will impact on grass and maize management within the production system

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

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

Controls on the spatial distribution of oceanic <i>δ</i>¹³C_DIC

We describe the design and evaluation of a large ensemble of coupled climate–carbon cycle simulations with the Earth system model of intermediate complexity GENIE. This ensemble has been designed for application to a range of carbon cycle questions, including the causes of late- Quaternary fluctuations in atmospheric CO2. Here we evaluate the ensemble by applying it to a transient experiment over the recent industrial era (1858 to 2008 AD). We employ singular vector decomposition and principal component emulation to investigate the spatial modes of ensemble variability of oceanic dissolved inorganic carbon (DIC) δ13C, considering both the spun-up pre-industrial state and the transient change. These analyses allow us to separate the natural (preindustrial) and anthropogenic controls on the δ13CDIC distribution. We apply the same dimensionally reduced emulation techniques to consider the drivers of the spatial uncertainty in anthropogenic DIC. We show that the sources of uncertainty related to the uptake of anthropogenic δ13CDIC and DIC are quite distinct. Uncertainty in anthropogenic δ13C uptake is controlled by air–sea gas exchange, which explains 63% of modelled variance. This mode of variability is largely absent from the ensemble variability in CO2 uptake, which is rather driven by uncertainties in thermocline ventilation rates. Although the need to account for air–sea gas exchange is well known, these results suggest that, to leading order, uncertainties in the ocean uptake of anthropogenic 13C and CO2 are governed by very different processes. This illustrates the difficulties in reconstructing one from the other, and furthermore highlights the need for careful targeting of both δ13CDIC and DIC observations to better constrain the ocean sink of anthropogenic CO2

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

Building professional discourse in emerging markets: Language, context and the challenge of sensemaking

Using ethnographic evidence from the former Soviet republics, this article examines a relatively new and mainly unobserved in the International Business (IB) literature phenomenon of communication disengagement that manifests itself in many emerging markets. We link it to the deficiencies of the local professional business discourse rooted in language limitations reflecting lack of experience with the market economy. This hampers cognitive coherence between foreign and local business entities, adding to the liability of foreignness as certain instances of professional experience fail to find adequate linguistic expression, and complicates cross-cultural adjustments causing multi-national companies (MNCs) financial losses. We contribute to the IB literature by examining cross-border semantic sensemaking through a retrospectively constructed observational study. We argue that a relative inadequacy of the national professional idiom is likely to remain a feature of business environment in post-communist economies for some time and therefore should be factored into business strategies of MNCs. Consequently, we recommend including discursive hazards in the risk evaluation of international projects

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

A Method For Relating GPS Performance To Forest Canopy

This paper describes the development of a quantitative method of classifying forest canopy that can be related to degradation in Differential GPS (DGPS) performance. Using digital images taken vertically skywards at 20 sites within a forest on the east coast of Ireland, canopy cover was described using percentage sky obstruction (Op), largest hole (DTmax), and the fragmentation of sky view (DTp) using pixel count and distance transform data. Statistical methods were used to produce three clusters which related to canopy cover in stands of Picea sitkensis and Picea contorta. DGPS data were then collected on 10 separate dates at the 20 sites, every two seconds for five minutes, and the two-dimensional standard deviation of the position fix was used to represent DGPS precision. The standard deviations ranged from 0.5 m to 9.7 m (compared to the manufacturer's specification of approximately 1 m in the horizontal). Precision was found to be related to the total obstruction, the size of the largest hole in the canopy, and the fragmentation of the sky view. Where there was little obstruction (less than 20%) or fragmentation, the DGPS performance was effectively the same as outside the forest, open canopy caused a 2-3 fold degradation in precision, and closed canopy a 5-7 fold degradation. It is suggested that the methods presented could be used to rapidly relate DGPS performance to forest canopy, and therefore may be useful in pre-planning inventory mapping and future machine operations using guidance systems