Waves in the Skyrme--Faddeev model and integrable reductions

In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging method has been exploited in order to describe slow deformation of periodic wave states, leading to a quasi-linear system. The reduction to general hydrodynamic systems have been considered and it is compared with other integrable reductions of the system.Comment: 16 pages, 5 figure

A normal form for excitable media

We present a normal form for travelling waves in one-dimensional excitable media in form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behaviour of single pulses in a periodic domain and also the richer behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.Comment: 22 pages, accepted for publication in Chao

Wave Instabilities in Excitable Media with Fast Inhibitor Diffusion

An excitable activator-inhibitor system with relatively fast inhibitor diffusion is considered. Numerical simulations of wave propagation inside long channels show transitions from stable flat traveling waves to folded waves and further to spreading spiral turbulence as the inhibitor diffusivity is increased. For sufficiently narrow channels the suppression of turbulence and the development of regular steadily propagating patterns is observed. The curvature dependence of the wave propagation velocity is derived and used to interpret the observed phenomena

Controlling Spiral Waves in Confined Geometries by Global Feedback

The evolution of spiral waves on a circular domain and on a spherical surface is studied by numerical integration of a reaction-diffusion system with a global feedback. It is shown that depending on intensity, sign, and/or time delay in the feedback loop a global coupling can be effectively used either to stabilize the rigid rotation of a spiral wave or to completely destroy spiral waves and to suppress self-sustained activity in a confined domain of an excitable medium. An explanation of the numerically observed effects is produced by a kinematical model of spiral wave propagation

Control of scroll wave turbulence using resonant perturbations

Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behaviour is believed to underlie fibrillation which, without intervention, precedes cardiac death. In this study we investigate suppression of the turbulence using stimulation of two different types, "modulation of excitability" and "extra transmembrane current". With cardiac defibrillation in mind, we used a single pulse as well as repetitive extra current with both constant and feedback controlled frequency. We show that turbulence can be terminated using either a resonant modulation of excitability or a resonant extra current. The turbulence is terminated with much higher probability using a resonant frequency perturbation than a non-resonant one. Suppression of the turbulence using a resonant frequency is up to fifty times faster than using a non-resonant frequency, in both the modulation of excitability and the extra current modes. We also demonstrate that resonant perturbation requires strength one order of magnitude lower than that of a single pulse, which is currently used in clinical practice to terminate cardiac fibrillation. Our results provide a robust method of controlling complex chaotic spatio-temporal processes. Resonant drift of spiral waves has been studied extensively in two dimensions, however, these results show for the first time that it also works in three dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last version: 2008/09/18, after revie

Characteristics of discharge in crossed ЕxН fields near breakdown curve in acceleration and plasma regime

In the present study the characteristics of discharge in crossed EH fields in acceleration and plasma regimes have been researched at low voltages near the breakdown curve. The new experimental data for current-voltage characteristic and their dependence on argon pressure and magnetic fields strength are presented. It is shown that initial stage of the current-voltage characteristic in acceleration and plasma regime are quite similar and correspond to regime with “oscillating” electrons. The theoretic model based on the energy balance of electrons in plasma regime is presented as well as the comparison of the theory with the experiment. The obtained results may be useful for further development of magnetron sputtering systems and plasma accelerators with closed electrons drift.Исследованы характеристики разряда в скрещенных ЕxН полях в ускорительном и плазменном режимах вблизи порога зажигания. Получены новые экспериментальные данные для вольт-амперных характеристик и их зависимости от давления и напряженности магнитного поля. Показано, что стартовые участки вольт- амперных характеристик в ускорительном и плазменном режимах идентичны и соответствуют режиму с «осциллирующими» электронами. Также представлена теоретическая модель на основе энергетического баланса электронов и проведено сравнение с экспериментом. Полученные результаты представляют интерес для дальнейшего развития магнетронных распылительных систем и плазменных ускорителей с замкнутым дрейфом электронов.Досліджено характеристики розряду в схрещених ЕxН полях у прискорювальному та плазмовому режимах поблизу порогу запалювання. Отримано нові експериментальні дані для вольт-амперних характеристик та їх залежності від тиску та сили магнітного поля. Показано, що стартові участки вольт- амперних характеристик у прискорювальному та плазмовому режимах ідентичні і відповідають режиму з «осцилюючими» електронами. Також представлено теоретичну модель на базі енергетичного балансу електронів та проведено порівняння з експериментом. Отримані дані будуть корисні для подальшого розвитку магнетронних розпилювальних систем та плазмових прискорювачів з замкнутим дрейфом електронів

Uncovering the (un-)occupied electronic structure of a buried hybrid interface

The energy level alignment at organic/inorganic (o/i) semiconductor interfaces is crucial for any light-emitting or -harvesting functionality. Essential is the access to both occupied and unoccupied electronic states directly at the interface, which is often deeply buried underneath thick organic films and challenging to characterize. We use several complementary experimental techniques to determine the electronic structure of p-quinquephenyl pyridine (5P-Py) adsorbed on ZnO(10-10). The parent anchoring group, pyridine, significantly lowers the work function by up to 2.9 eV and causes an occupied in-gap state (IGS) directly below the Fermi level $E_\text{F}$. Adsorption of upright-standing 5P-Py also leads to a strong work function reduction of up to 2.1 eV and to a similar IGS. The latter is then used as an initial state for the transient population of three normally unoccupied molecular levels through optical excitation and, due to its localization right at the o/i interface, provides interfacial sensitivity, even for thick 5P-Py films. We observe two final states above the vacuum level and one bound state at around 2 eV above $E_\text{F}$, which we attribute to the 5P-Py LUMO. By the separate study of anchoring group and organic dye combined with the exploitation of the occupied IGS for selective interfacial photoexcitation this work provides a new pathway for characterizing the electronic structure at buried o/i interfaces