We present a novel twinned-square periodic structure for ultrasonic wave bending and splitting that does not require the existence of a complete band gap and plays the role of an ultrasonic wedge. The device allows 45° bending of waves and by adequately switching the twinned structure to an ultrasonic crystal 90° bending is achieved. An extreme refraction law at the grain boundaries is experimentally observed.

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems.

We present extended heterogeneous oscillator model of cardiac conduction system for generation of realistic 12 lead ECG waveforms. The model consists of main natural pacemakers represented by modified van der Pol equations, and atrial and ventricular muscles, in which the depolarization and repolarization processes are described by modified FitzHugh-Nagumo equations. We incorporate an artificial RR-tachogram with the specific statistics of a heart rate, the frequency-domain characteristics of heart rate variability produced by Mayer and respiratory sinus arrhythmia waves, normally distributed additive noise and a baseline wander that couple the respiratory frequency. The standard 12 lead ECG is calculated by means of a weighted linear combination of atria and ventricle signals and thus can be fitted to clinical ECG of real subject. The model is capable to simulate accurately realistic ECG characteristics including local pathological phenomena accounting for biophysical properties of the human heart. All these features provide significant advantages over existing nonlinear cardiac models. The proposed model constitutes a useful tool for medical education and for assessment and testing of ECG signal processing software and hardware systems.

We propose a model to generate electrocardiogram signals based on a discretized reaction-diffusion system to produce a set of three nonlinear oscillators that simulate the main pacemakers in the heart. The model reproduces electrocardiograms from healthy hearts and from patients suffering various well-known rhythm disorders. In particular, it is shown that under ventricular fibrillation, the electrocardiogram signal is chaotic and the transition from sinus rhythm to chaos is consistent with the Ruelle-Takens-Newhouse route to chaos, as experimental studies indicate. The proposed model constitutes a useful tool for research, medical education, and clinical testing purposes. An electronic device based on the model was built for these purposes

We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of disk sizes, offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids. Using this pattern as a seed, more complex biological structures can be mimicked, such as the pigmentation pattern of sea urchins and the plate arrangements of the calyxes of primitive camerate crinoids.