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Showing 1 to 7 of 7 for “"amplitude equation"”.
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Asymptotic analysis of the parametrically driven damped nonlinear evolution equation
Singular perturbation methods are used to obtain amplitude equations for the parametrically driven damped linear and nonlinear oscillator, the linear and nonlinear Klein-Gordon equations in the small-amplitude limit in various frequency regimes. In the case of the parametrically driven linear …
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Localised solutions of the parametrically driven Ginzburg-Landau and nonlinear Schrӧdinger equations
… of the parametrically driven Ginzburg-Landau equation and its nonlinear Schrӧdinger limit. We begin with a detailed analysis of the Faraday Resonance experiment, in which the driven complex Ginzburg-Landau equation (CGLE) arises, and an examination of how the CGLE appears as the amplitude …
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Axisymmetric Rayleigh-Benard convection
… 2, a numerical solution of the linearised equations which govern the non-rotating fluid with rigid boundaries, is presented. In Chapter 3, the non-rotating layer is perturbed by making the elevation of the lower plane a small slowly varying function .1 of the radial coordinate. The modified …
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Spreading behavior of molten metal microdroplets
… because of time-dependent coefficients in the amplitude equation. A large impact inertia, associated with a high Weber number, promotes interface instability and prefers high wave number for maximum instability. The next stage investigates the oscillations of liquid droplets upon collision with …
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Shear flow instabilities in stratified magnetohydrodynamics
… case. Using weakly nonlinear theory, we derive amplitude equations for the two cases of Pe,Rm∼O(1) and Pe,Rm»1, where Pe (the ratio between thermal convection and thermal diffusion) and Rm (the ratio between magnetic induction and magnetic diffusion) denote the Péclet and magnetic Reynolds …
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Surface Deformations of Magnetic Continua in Homogeneous Fields
… for the growth and decay of the pattern at small amplitudes is extracted from the measurements and compared with an existing theoretical model. In addition, the measurement technique provides the reconstruction of a fully nonlinear amplitude equation, which is qualitatively compared to model …
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Analysis of pattern dynamics for a nonlinear model of the human cortex via bifurcation theories
… The linear stability analysis of the model equations predict the emergence of a Turing instability (in which separated areas of the cortex become activated) when gap-junction diffusivity is increased above a critical level. In addition, a Hopf bifurcation (oscillation) occurs when the …