Paroxysmal starting and stopping of circulating waves in excitable media

Levels of intracellular Ca2+ were monitored using fluorescence from Ca2+-sensitive dyes in chick embryonic heart cells cultured in an annular geometry. There was spontaneous starting and stopping of reentrant waves of activity. The results are modeled using modified FitzHugh-Nagumo equations representing pacemakers embedded in a conducting medium. These results provide a potential mechanism for spontaneous abnormal cardiac rhythms in which there are rapid heart beats (tachycardias) that repetitively start and stop.     

Free Groups from Fields

In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, ‘The circle cannot be squared’ by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators.     

Local Exact Controllability for the One-Dimensional Compressible Navier–Stokes Equation

In this paper we deal with the isentropic (compressible) Navier-Stokes equation in one space dimension and we adress the problem of the boundary controllability for this system. We prove that we can drive initial conditions which are sufficiently close to some constant states to those constant states. This is done under some natural hypotheses on the time of control and on the regularity on the initial conditions.     

Spiral wave generation in heterogeneous excitable media

As the coupling in a heterogeneous excitable medium is reduced, three different types of behavior are encountered: plane waves propagate without breaking up, plane waves break up into spiral waves, and plane waves block. We illustrate these phenomena in monolayers of chick embryonic heart cells using calcium sensitive fluorescent dyes. Following the addition of heptanol, an agent that reduces the electrical coupling between cells, we observe breakup of spiral waves. These results are modeled in a heterogeneous cellular automaton model in which the neighborhood of interaction is modified.     

Introduction: Mapping and control of complex cardiac arrhythmias

This paper serves as an introduction to the Focus Issue on mapping and control of complex cardiac arrhythmias. We first introduce basic concepts of cardiac electrophysiology and describe the main clinical methods being used to treat arrhythmia. We then provide a brief summary of the main themes contained in the articles in this Focus Issue. In recent years there have been important advances in the ability to map the spread of excitation in intact hearts and in laboratory settings. This work has been combined with simulations that use increasingly realistic geometry and physiology. Waves of excitation and contraction in the heart do not always propagate with constant velocity but are often subject to instabilities that may lead to fluctuations in velocity and cycle time. Such instabilities are often treated best in the context of simple one- or two-dimensional geometries. An understanding of the mechanisms of propagation and wave stability is leading to the implementation of different stimulation protocols in an effort to modify or eliminate abnormal rhythms. (c) 2002 American Institute of Physics.     

The absence of dipolar ferromagnetism in a simple cubic array

By using the Bogoliubov inequality à la Mermin and Wagner, it is shown that dipolar ferromagnetism cannot exist for a large, simple cubic array.     

Highly stereoselective reductions of α-alkoxy-β-keto esters. Aspects of the mechanism of sodium borohydride reduction of ketones in 2-propanol

Reduction of α-alkoxy-β-keto esters with sodium borohydride in 2-propanol proceeds with high stereoselectivity via a five-membered ring chelated sodium ion.     

Pressures inside a room subjected to simulated sonic booms

The pressure variations inside a room of plaster-wood construction subjected to sonic boom loadings were investigated both analytically and experimentally to study the problems of dynamic structural response. The N-wave pressure signatures were generated in the UTIAS (University of Toronto Institute for Aerospace Studies) Travelling Wave Horn-Type Sonic Boom Simulator. The room overpressures in some cases were found to be twice as great as that in the incident sonic boom. The analysis and experimental data can be useful in assessing structural damage caused by supersonic aircraft overfligths.