Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities

In this article, a general geometric singular perturbation framework is developed to study the impact of strong, spatially localized, nonlinear impurities on the existence, stability and bifurcations of localized structures in systems of linear reaction–diffusion equations. By taking advantage of the multiple-scale nature of the problem, we derive algebraic conditions determining the existence and stability of pinned single- and multi-pulse solutions. Our methods enable us to explicitly control the spectrum associated with a (multi-)pulse solution. In the scalar case, we show how eigenvalues may move in and out of the essential spectrum and that Hopf bifurcations cannot occur. By contrast, even a pinned 1-pulse solution can undergo a Hopf bifurcation in a two-component system of linear reaction–diffusion equations with (only) one impurity. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

Orthogonal Pulse Design Based on Sinusoidal and Cosinusoidal Functions

In order to improve the bandwidth efficiency for the communication system effectively, a designing method for orthogonal pulse based sinusoidal and cosinusoidal functions is put forward. The orthogonal pulse is designed by parameter setting, sub-band division, parameter solution and pulse solution from the point signal character. The orthogonal pulse’s spectrum is mixed or overlapped in frequency domain. It can not only be formed little relative bandwidth signal, but also large relative bandwidth signal. The system bandwidth efficiency can reach 2Baud/Hz when the orthogonal pulse is used in information transmission.

Short-term Pulsing Improves Postharvest Leaf Quality of Cut Oriental Lilies

Several pulse solutions were tested for their effectiveness in preventing leaf senescence on four cut oriental lily cultivars (Lilium sp. `Acapulco', `Kissproof', `Noblesse' and `Star Gazer'). Stems were pulsed 24 hours after harvest for 1 hour, stored in boxes in the dark for 5 days at 3 °C (37.4 °F) then evaluated in postharvest conditions. A new commercial product called Chrysal BVB, a proprietary mixture manufactured by Pokon & Chrysal (Miami) containing cytokinine and gibberellic acids, was the most effective product tested. Chrysal BVB [1 mL·L–1 (0.1%)] prevented leaf chlorosis and abscission on `Acapulco' and `Noblesse' and significantly reduced it by 82% on `Star Gazer' and by 69% on `Kissproof'. Stems pulsed in Fascination, a commercial mixture containing 1.8% gibberellins (GA4+7) and 1.8% benzyladenine [5.4 mg·L–1 (ppm) each], virtually prevented leaf chlorosis on `Noblesse', reduced it by 50% or more on `Acapulco' and `Star Gazer', and significantly delayed it 8 days on `Kissproof'. A 10 μm (2 ppm) pulse in thidiazuron, a substituted phenylurea with cytokinin-like properties, delayed leaf chlorosis on `Star Gazer' but to a lesser extent compared to BVB and Fascination. Chrysal SVB, a propri-etary mixture manufactured by Pokon & Chrysal containing gibberellic acid, had no effect on reducing leaf chlorosis on `Star Gazer'. None of the pulse solutions had adverse effects on bud opening, flower quality or vase life. Maintaining stems in a bulb flower preservative significantly reduced leaf chlorosis and abscission in all cultivars when stems were not pretreated with a pulse solution or when a pulse solution was ineffective.

Supersonic Rupture Pulses in an Earthquake Model

In this work, I study the supersonicrupturepulse in a two dimensionalelastic sheet. There is a friction force acting at the edge of the sheet which is composed of a term that dependson the local displacement at the edge and a viscous dissipation term. I consider the case where the sheet is driven forward by a force acting in the bulk, but is held back by the interfacial friction. I present the equations which describe such a system and then look for solutions which describe a slip pulse propagatingthough a region which is uniformly stressed. Such a pulse will allow the entire interface to move forward and partially relieve the stress. I present the integral equation that such a pulse solution must satisfy, and then discuss the behavior observed in numericalsolutions of this equation.