M. Silber

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Through a linear stability analysis, we investigate the effectiveness of a noninvasive feedback control scheme aimed at stabilizing traveling wave solutions Re iKx+iωt of the one-dimensional complex Ginzburg Landau equation (CGLE) in the Benjamin-Feir unstable regime. The feedback control is a generalization of the time-delay method of Pyragas [1], which(More)
A recent Faraday wave experiment with two-frequency forcing reports two types of 'superlattice' patterns that display periodic spatial structures having two separate scales [1]. These patterns both arise as secondary states once the primary hexagonal pattern becomes unstable. In one of these patterns (so-called 'superlattice-two') the original hexagonal(More)
The Faraday wave experiment is a classic example of a system driven by paramet-ric forcing, and it produces a wide range of complex patterns, including superlattice patterns and quasipatterns. Nonlinear three-wave interactions between driven and weakly damped modes play a key role in determining which patterns are favoured. We use this idea to design single(More)
A mathematical model describing the coupling between two independent amplification mechanisms in auditory hair cells is proposed and analyzed. Hair cells are cells in the inner ear responsible for translating sound-induced mechanical stimuli into an electrical signal that can then be recorded by the auditory nerve. In nonmammals, two separate mechanisms(More)
We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single- and multifrequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically forced partial differential equation that shares some characteristics of the Faraday wave experiment. One mechanism,(More)
Motivated by experimental observations of exotic free surface standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the associated pattern-selection problem. With forcing frequency components in ratio m/n, where m and n are coprime integers that are not both odd, there is the possibility that(More)
Metabolome analyses by NMR spectroscopy can be used in quality control by generating unique fingerprints of different species. Hundreds of components and their variation between different samples can be analyzed in a few minutes/hours with high accuracy and low cost of sample preparation. Here, apple peel and pulp extracts of a variety of apple cultivars(More)
Three-wave interactions form the basis of our understanding of many pattern-forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the shorter wavelength to interact with one wave of the longer, as well as for two waves of the longer wavelength to(More)
Motivated by recent analytical and numerical work on two-and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic solutions of partial differential equations. Our approach is based on centre manifold reduction for maps, and is in the(More)
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