Dynamics of filaments of scroll waves

This has been written as a chapter for "Engineering Chemical Complexity II", and as such does not have an abstract.Comment: 18 pages, 10 figure

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

Asymptotic properties of mathematical models of excitability

We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic timescales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially-extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for break-ups and self-termination of re-entrant waves in excitable media with Courtemanche et al. (1998) kinetics.Comment: 15 pages, 8 figures, to appear in Phil Trans Roy Soc London

Gendarmes and the modernization of local rule in Russia (research experience and prospects)

The article was submitted on 06.04.2015.The article explores the historiography of the secret police in the Russian Empire. Revealing the approaches of historians to this subject, the methods and manner of their work with historical sources, the author demonstrates the negative consequences that were a result of political topicality and the concealing of information about the state. A review of historiographic heritage enables the author to cleanse the perception of the topic from a number of “quasi-evident facts” created at various times and under different circumstances. Additionally, she pays attention to the existence of a vast number of documents of the police department which can still be found in state archives. Special attention needs to be paid to those ones that contain the reflections of gendarme officers on professional ethics and duties. The author reveals documental evidence of conflicts of interest between the local administration and the police officers controlling its activity. The approach used by the author bears a non-conventional character which consists in the study of creation of these documents and their functions in the police department. Preliminary results enable the author to claim that these certificates can provide information not only about the sphere of impact and peculiarities of the secret police, but also about the ways of implementation of the political concept of a regular, well-organized state in 19th century-Russia and the ways of self-improvement of government.Статья содержит анализ историографии тайной полиции в Российской империи. Выявляя подходы историков к данной теме и способы их работы с историческими свидетельствами, автор показывает негативные следствия политической актуальности и процесса герметизации знаний о государстве. Ревизия историографического наследия позволяет автору освободить восприятие темы от созданных в разные времена и в разных условиях «квазиочевидностей». Одновременно обращается внимание на наличие богатого комплекса делопроизводственных документов полицейского ведомства, сохранившихся в государственном архиве. Предлагая неоинституциональный подход к их анализу, автор показывает очевидные и латентные информационные возможности обнаруженных документов. Среди них особенный интерес представляют тексты, в которых зафиксировалась рефлексия жандармских офицеров о профессиональной этике и служебном долге, а также находятся свидетельства конфликтов интересов местной администрации и контролирующей ее деятельность полиции. Оригинальность предлагаемого подхода состоит в том, чтобы исследовать логику создания этих документов, их назначение в полицейском управлении. Предварительные результаты позволяют автору утверждать, что данные свидетельства могут рассказать не только о сфере полномочий и характере работы тайной полиции, но и о способах реализации политической концепции «регулярного, хорошо организованного» государства в России XIX в., о путях самоусовершенствования государственного аппарата.Исследование осуществлено в рамках программы «Научный фонд НИУ ВШЭ» в 2013–2014 гг. (проект № 12-01-0123)

Beatbox - a computer simulation environment for computational biology of the heart

Despite over a century’s study, the trigger mechanisms of cardiac arrhythmias are poorly understood. Even modern experimental methods do not provide sufficient temporal and spacial resolution to trace the development of fibrillation in samples of cardiac tissue, not to mention the heart in vivo. Advances in human genetics provide information on the impact of certain genes on cellular activity, but do not explain the resultant mechanisms by which fibrillation arises. Thus, for some genetic cardiac diseases, the first presenting symptom is death. Computer simulations of electrical activity in cardiac tissue offer increasingly detailed insight into these phenomena, providing a view of cellular-level activity on the scale of a whole tissue wall. Already, advances in this field have led to developments in our understanding of heart fibrillation and sudden cardiac death and their impact is expected to increase significantly as we approach the ultimate goal of whole-heart modelling. Modelling the propagation of Action Potential through cardiac tissue is computationally expensive due to the huge number of equations per cell and the vast spacial and temporal scales required. The complexity of the problem encompasses the description of ionic currents underlying excitation of a single cell through the inhomogeneity of the tissue to the complex geometry of the whole heart. The timely running of computational models of cardiac tissue is increasingly dependant on the effective use of High Performance Computing (HPC), i.e. systems with parallel processors. Current state of the art cardiac simulation tools are limited either by the availability of modern, detailed models, or by their hardware portability or ease of use. The miscellany of current model implementations leads many researchers to develop their own ad-hoc software, preventing them from both utilising the power of HPC effectively, and from collaborating fluidly. It is, arguably, impeding scientific progress. This paper presents a roadmap for the development of Beatbox, a computer simulation environment for computational biology of the heart—an adaptable and extensible framework with which High Performance Computing may be harnessed by researchers

Orbital movement of spiral waves

Spiral waves in active media react to small perturbations as particle-like objects. Here we apply the asymptotic theory to the interaction of spiral waves with a localized inhomogeneity, which leads to a novel prediction: drift of the spiral rotation centre along circular orbits around the inhomogeneity. The stationary orbits have alternating stability and fixed radii, determined by the properties of the bulk medium and the type of inhomogeneity, while the drift speed along an orbit depends on the strength of the inhomogeneity. Direct simulations confirm the validity and robustness of the theoretical predictions and show that these unexpected effects should be observable in experiment

Drift of scroll waves in thin layers caused by thickness features: asymptotic theory and numerical simulations

Copyright © 2015 American Physical SocietyA scroll wave in a very thin layer of excitable medium is similar to a spiral wave, but its behavior is affected by the layer geometry. We identify the effect of sharp variations of the layer thickness, which is separate from filament tension and curvature-induced drifts described earlier. We outline a two-step asymptotic theory describing this effect, including asymptotics in the layer thickness and calculation of the drift of so-perturbed spiral waves using response functions. As specific examples, we consider drift of scrolls along thickness steps, ridges, ditches, and disk-shaped thickness variations. Asymptotic predictions agree with numerical simulations.FWO-Flanders (Belgium)Engineering and Physical Sciences Research Council (EPSRC