Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnold tongues open regions of multistability exist, and the parameter dependency of the dynamics becomes rather complex. This paper discusses the bifurcation structure inside the Arnold tongue with zero rotation number and includes a study of nonsmooth bifurcations that happen for large nonlinearity in the region with strange nonchaotic attractors.Comment: 25 pages, 22 colored figures in reduced quality, submitted to Int. J. of Bifurcation and Chaos, a supplementary website (http://www.mpipks-dresden.mpg.de/eprint/jwiersig/0004003/) is provide

Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.Comment: 8 pages, 5 figures, 30 reference

Soil stabilisation using alkaline activation of fly ash for self-compacting rammed earth construction

This paper studies the effectiveness of alkaline activation of low-calcium fly ash on the improvement of residual granitic soils to be used on rammed-earth construction. Different liquid:solid ratios, alkali concentrations and Na2O : ash ratios were tested. Effect of calcium hidroxide, sodium chloride and concrete superplasticiser is also reported. Compressive strength up to 7 days at 60ºC was determined. Results show that, in terms of mechanical strength, there is an optimum value for the activator:solids ratio and the alkali concentration, and that a decrease in the Na2O:ash ratio results in strength increase. No improvement was observed with the sodium chloride or the superplasticiser, while the calcium produced only a short term increase in strength. SEM/EDS analysis were used to analyse microstructural development, showing that strength is fairly related to the Si:Al and Na:Si ratios

Analysis of the shearing instability in nonlinear convection and magnetoconvection

Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations. Steady rolls can develop a shearing instability, in which rolls turning over in one direction grow at the expense of rolls turning over in the other, resulting in a net shear across the layer. As the temperature difference across the fluid is increased, two-dimensional pulsating waves occur, in which the direction of shear alternates. We analyse the nonlinear dynamics of this behaviour by first constructing appropriate low-order sets of ordinary differential equations, which show the same behaviour, and then analysing the global bifurcations that lead to these oscillations by constructing one-dimensional return maps. We compare the behaviour of the partial differential equations, the models and the maps in systematic two-parameter studies of both the magnetic and the non-magnetic cases, emphasising how the symmetries of periodic solutions change as a result of global bifurcations. Much of the interesting behaviour is associated with a discontinuous change in the leading direction of a fixed point at a global bifurcation; this change occurs when the magnetic field is introduced

Phase-space structure of two-dimensional excitable localized structures

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.Comment: 10 pages, 9 figure