Ekaterina Pavlovskaia

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We propose an archetypal system to investigate transitions from smooth to discontinuous dynamics. In the smooth regime, the system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. At the discontinuous limit, however, there(More)
In this work the strange behavior of an impact oscillator with a one-sided elastic constraint discovered experimentally is compared with the predictions obtained using its mathematical model. Extensive experimental investigations undertaken on the rig developed at the Aberdeen University reveal different bifurcation scenarios under varying excitation(More)
A physical model to examine impact oscillators has been developed and analyzed. The model accounts for the viscoelastic impacts and is capable to mimic the dynamics of a bounded progressive motion (a drift), which is important in practical applications. The system moves forward in stick-slip phases, and its behavior may vary from periodic to chaotic motion.(More)
The Invisalign orthodontic system (Align Technology, Inc, Santa Clara, CA) is a series of clear removable appliances that is worn by a patient to correct malocclusions. Introduced in 1999, it has been applied to successfully correct an increasingly wide variety of malocclusions. Part of the success of the system is because of the innovative technologies(More)
In a recent paper we examined a model of an arch bridge with viscous damping subjected to a sinusoidally varying central load. We showed how this yields a useful archetypal oscillator which can be used to study the transition from smooth to discontinuous dynamics as a parameter, alpha, tends to zero. Decreasing this smoothness parameter (a non-dimensional(More)
In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the(More)
An impact oscillator with drift is considered. The model accounts for viscoelastic impacts and is capable of mimicking the dynamics of progressive motion, which is important in many applications. To simplify the analysis of this system, a transformation decoupling the original coordinates is introduced. As a result, the bounded oscillations are separated(More)
We discovered a narrow band of chaos close to the grazing condition for a simple soft impact oscillator. The phenomenon was observed experimentally for a range of system parameters. Through numerical stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits, created at "invisible"(More)
Hemostatic changed induced by ozone therapy were studied in 81 patients with atherosclerosis of different vessels in 81 patients. It was found that use of ozone-oxygen mixtures leads to hypocoagulatory changes (diminution of platelet aggregation, lowering of fibrinogen concentration, prolongation of activated partial thromboplastin time, enhanced(More)