Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales

We establish the oscillation criteria of Philos type for second-order half-linear neutral delay dynamic equations with damping on time scales by the generalized Riccati transformation and inequality technique. Our results are new even in the continuous and the discrete cases

Effects of noise on the internal resonance of a nonlinear oscillator

We numerically analyze the response to noise of a system formed by two coupled mechanical oscillators, one of them having Duffing and van der Pol nonlinearities, and being excited by a self-sustaining force proportional to its own velocity. This system models the internal resonance of two oscillation modes in a vibrating solid beam clamped at both ends. In applications to nano- and micromechanical devices, clamped-clamped beams are subjected to relatively large thermal and electronic noise, so that characterizing the fluctuations induced by these effects is an issue of both scientific and technological interest. We pay particular attention to the action of stochastic forces on the stability of internal-resonance motion, showing that resonant oscillations become more robust than other forms of periodic motion as the quality factor of the resonant mode increases. The dependence on other model parameters - in particular, on the coupling strength between the two oscillators - is also assessed.Fil: Zanette, Damian Horacio. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales

We use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation with damping on a time scale T(r(t)g(x(t), xΔ(t)))Δ+p(t)g(x(t), xΔ(t))  + q(t)f(x(τ(t)))=0, where r(t), p(t), and q(t) are positive right dense continuous (rd-continuous) functions on T. Our results improve and extend some results established by Zhang et al., 2011. Also, our results unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. Finally, we give some examples to illustrate our main results

Applying engineering feedback analysis tools to climate dynamics

The application of feedback analysis tools from engineering control theory to problems in climate dynamics is discussed through two examples. First, the feedback coupling between the thermohaline circulation and wind-driven circulation in the North Atlantic Ocean is analyzed with a relatively simple model, in order to better understand the coupled system dynamics. The simulation behavior is compared with analysis using root locus (in the linear regime) and describing functions (to predict limit cycle amplitude). The second example does not directly involve feedback, but rather uses simulation-based identification of low-order dynamics to understand parameter sensitivity in a model of El Nino/Southern Oscillation dynamics. The eigenvalue and eigenvector sensitivity can be used both to better understand physics and to tune more complex models. Finally, additional applications are discussed where control tools may be relevant to understand existing feedbacks in the climate system, or even to introduce new ones

Relaxation Tribometry: A Generic Method to Identify the Nature of Contact Forces

Recent years have witnessed the development of so-called relaxation tribometers, the free oscillation of which is altered by the presence of frictional stresses within the contact. So far, analysis of such oscillations has been restricted to the shape of their decaying envelope, to identify in particular solid or viscous friction components. Here, we present a more general expression of the forces possibly acting within the contact , and retain six possible, physically relevant terms. Two of them, which had never been proposed in the context of relaxation tribometry, only affect the oscillation frequency, not the amplitude of the signal. We demonstrate that each of those six terms has a unique signature in the time-evolution of the oscillation, which allows efficient identification of their respective weights in any experimental signal. We illustrate our methodology on a PDMS sphere/glass plate torsional contact

OSCILLATION OF SOLUTION TO SECOND-ORDER HALF-LINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES

This article concerns the oscillation of solutions to second-order half-linear dynamic equations with a variable delay. By using integral averaging techniques and generalized Riccati transformations, new oscillation criteria are obtained. Our results extend Kamenev-type, Philos-type and Li-type oscillation criteria. Several examples are given to illustrate our results