On the Symmetry-Breaking Bifurcation of Chaotic Attractors
Symmetry breaking is a common phenomenon in nature. (1) In the field of dynamical systems, the symmetry-breaking bifurcation of attractors is a subject of special interest. For limit cycles this phenomenon has been studied extensively, (a) especially in the Lorenz model. (3) Less is known about the symmetry breaking of chaotic attractors. A symmetry-recovering crisis has been discovered experimentally and modeled in ref. 4. Here we consider the symmetry breaking of strange attractors from another point of view in a more general class of systems and we show that a new type of crisis (5) may exist leading to an anomalous band splitting (6) or to a symmetry-breaking transition of the strange attractor, depending on the actual values of the parameters. We investigate Lorenz-type systems characterized by the property that trajectories on the attractor pass close to a saddle point. This saddle has a two-dimensional stable and a one-dimensional unstable invariant manifold. Therefore, trajectories approaching the stable manifold may stay for an
Symmetry-breaking bifurcations in O(2) maps
Codimension-one bifurcations of O(2)-equivariant maps on Rn are analyzed. Steady-state and period-doubling bifurcations lead to reflection symmetric patterns; subsequent instabilities can lead to a slow phase precession. For Hopf bifurcation, the theory for steady-state bifurcation with D4-symmetry applies.
Application of infrared camera to bituminous concrete pavements: measuring vehicle
Infrared thermography (IR) has been used for decades in certain fields. However, the technological level of advancement of measuring devices has not been sufficient for some applications. Over the recent years, good quality thermal cameras with high resolution and very high thermal sensitivity have started to appear on the market. The development in the field of measuring technologies allowed the use of infrared thermography in new fields and for larger number of users. This article describes the research in progress in Transport Research Centre with a focus on the use of infrared thermography for diagnostics of bituminous road pavements. A measuring vehicle, equipped with a thermal camera, digital camera and GPS sensor, was designed for the diagnostics of pavements. New, highly sensitive, thermal cameras allow to measure very small temperature differences from the moving vehicle. This study shows the potential of a high-speed inspection without lane closures while using IR thermography.