Search results for "Marginal stability"
showing 5 items of 5 documents
Analysing the effects of power swing on wind farms using instantaneous impedances
2020
Abstract Most of the grid disturbances happen due to the presence of faults and power swing. This article focuses on power swing in view of the amount of penetration of renewable energy resources especially the wind farms. There are two sections. First section approached power swing by deriving a mathematical expression which would be able to track the locus of impedance in time domain and subsequently analyze resistance and reactance simultaneously with respect to time. It used a grid comprising of generator, transmission line and load. The derived expression was compared with a power swing generated using RTDS model and the results were analyzed in R-X plane. Second section analyses the i…
Optical bullets and double bullet complexes in dissipative systems
2006
We show that optical light bullets can coexist with double bullet complexes in nonlinear dissipative systems. Coexistence occurs for a relatively large range of the system parameters, and is associated with either marginal stability or bistable existence of the two dissipative soliton species. In the case of marginal stability, spontaneous transformations of single bullets into double bullet complexes are observed. Among the bistable cases, we show how both clockwise and anticlockwise rotating double bullet complexes can be formed out of the phase-controlled interaction of two single bullets. The internal dynamics of pulsating double bullet complexes, with oscillations in both the spatial s…
Thermally unstable throughflow of a power–law fluid in a vertical porous cylinder with arbitrary cross–section
2021
Abstract The present paper investigates how the cross–sectional shape of a vertical porous cylinder affects the onset of thermoconvective instability of the Rayleigh–Benard type. The fluid saturating the porous medium is assumed to be a non–Newtonian power–law fluid. A linear stability analysis of the vertical thorughflow is carried out. Three special shapes of the cylinder cross–section are analysed: square, circular and elliptical. The effect of changing the power–law index is investigated. The stability of a steady base state with vertical throughflow is analysed. The resulting stability problem is a differential eigenvalue problem that is solved numerically through the shooting method. …
Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion
2012
In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through a weakly nonlinear analysis, we are able to predict the shape and the amplitude of the pattern. For the amplitude, in the supercritical and in the subcritical case, we derive the cubic and the quintic Stuart–Landau equation respectively. When the size of the spatial domain is large, and the initial perturbation is localized, the pattern is formed sequentially and invades the whole domain as a travelin…
Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion
2013
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a trave…