This work studies the practicality of using finite-time Lyapunov exponents (FTLEs) to detect the inception of parametric resonance for vessels operating in irregular longitudinal seas. Parametrically excited roll motion is modelled as a single degree-of-freedom system, with nonlinear damping and restoring terms. FTLEs are numerically calculated at every integration time step. Using this numeric...

In this paper, we experimentally demonstrate non-degenerate parametric resonance in a torsional micro electro mechanical (MEM) oscillator with two interacting mechanical modes of oscillation. The parametric oscillation results from a displacement-dependent electrostatic force generated in both the modes of oscillation. There is a decoupling of the input and the output frequencies in this mode o...

We study parametric resonance of interacting waves having the same wave vector and frequency. In addition to the well-known period-doubling instability we show that under certain conditions the instability is caused by a Hopf bifurcation leading to quasiperiodic traveling waves. It occurs, for example, if the group velocities of both waves have different signs and the damping is weak. The dynam...

Multi-parametric magnetic resonance imaging is an emerging imaging modality for diagnosis, staging, characterization, and treatment planning of prostate cancer. In this report, we reviewed the literature for studies assessing the accuracy of multi-parametric magnetic resonance imaging in detecting clinically significant prostate cancer, and we critically examined the future role of this imaging...

This example is studied using Floquet theory. A classic example is k(t) = 1 + ε cosωt, where one finds regions of instability in the ε, ω plane for which there are solutions which grow exponentially in time. The instability regions are open and with closures touching ε = 0 at critical frequencies (see [A], [MW]). For any t, the constant coefficient problems with k frozen at k(t) is conservative...

We propose a new scenario to produce the superheavy dark matter based on the inflationary universe. In our scenario, the inflaton couples to both a boson and a stable fermion. Although the fermion is produced by the inflaton decay after inflation, almost energy density of the inflaton is transmitted into the radiation by parametric resonance which causes the explosively copious production of th...

The concept of combining ionization cooling with parametric resonances (PIC) was proposed earlier [1] in order to lead to an additional reduction of muon transverse emittances by an order of magnitude so that high luminosity in a collider can be achieved with fewer muons per bunch. After 6D cooling performed in a Helical Cooling Channel, the muon beam is injected in a channel with alternating d...

In this paper, we investigate the stability of a fluid-structure interaction problem in which a flexible elastic membrane immersed in a fluid is excited via periodic variations in the elastic stiffness parameter. This model can be viewed as a prototype for active biological tissues such as the basilar membrane in the inner ear, or heart muscle fibers immersed in blood. Problems such as this, in...

We perform a stability analysis for a fluid-structure interaction (FSI) problem in which a spherical elastic shell or membrane is immersed in a 3D viscous, incompressible fluid. The shell is an idealized structure having zero thickness, and has the same fluid lying both inside and outside. The problem is formulated mathematically using the immersed boundary framework in which Dirac delta functi...