Probabilistic response and rare events in Mathieu׳s equation under correlated parametric excitation

Sound Wave Propagation in a Multiferroic Thermo Elastic Nano Fiber Under the Influence of Surface Effect and Parametric Excitation

This study investigates that the sound wave propagation of multiferroic thermo elastic Nanofibers under the influence of surface effect and parametric excitation via Timoshenko form of beam equations. The equation of analytical model is obtained for Nanofiber through shear and rotation effect. The solution of the problem is reached through the coupled time harmonic equations in flexural directi...

Probabilistic Proofs of Existence of Rare Events

Statistical Monitoring of Rare Events in Healthcare

  There are miscellaneous quality characteristics in healthcare which are interested to be monitored. However, monitoring each characteristic needs a special statistical method. There are some characteristics with very small incidence rates that it’s usually considered not to be necessary to monitoring them, since their incidence rates are so small that p and np charts are not able to monitor t...

Parametric autoresonant excitation of the nonlinear Schrödinger equation.

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the dr...

Study on van der Pol Oscillator under Noisy Parametric Excitation

We calculated Eq. (4) by using the Runge-Kutta method. The attractors obtained by the simulations are shown in Fig. 3(a). We can confirm the generation of periodic and chaotic attractors. In order to investigate the attractors in van der Pol oscillator under noisy parametric excitation in detail, we consider the Poincaré map. The result of the Poincaré map are shown in Fig. 3(b). We can see tha...