Global Stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers

In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping term, the Benjamin-Bona-Mahony-Burgers equation and the KdV-Burgers equation. This algorithm capitalizes on the fact that such infinite-dimensional dissipative dynamical systems posses finite-dimensional long-time behavior which is represented by, for instance, the finitely many determining parameters of their long-time dynamics, such as determining Fourier modes, determining volume elements, determining nodes , etc..The algorithm utilizes these finite parameters in the form of feedback control to stabilize the relevant solutions. For the sake of clarity, and in order to fix ideas, we focus in this work on the case of low Fourier modes feedback controller, however, our results and tools are equally valid for using other feedback controllers employing other spatial coarse mesh interpolants

Alterations in electrodermal activity and cardiac parasympathetic tone during hypnosis

Exploring autonomic nervous system (ANS) changes during hypnosis is critical for understanding the nature and extent of the hypnotic phenomenon and for identifying the mechanisms underlying the effects of hypnosis in different medical conditions. To assess ANS changes during hypnosis, electrodermal activity and pulse rate variability (PRV) were measured in 121 young adults. Participants either received hypnotic induction (hypnosis condition) or listened to music (control condition), and both groups were exposed to test suggestions. Blocks of silence and experimental sound stimuli were presented at baseline, after induction, and after de-induction. Skin conductance level (SCL) and high frequency (HF) power of PRV measured at each phase were compared between groups. Hypnosis decreased SCL compared to the control condition; however, there were no group differences in HF power. Furthermore, hypnotic suggestibility did not moderate ANS changes in the hypnosis group. These findings indicate that hypnosis reduces tonic sympathetic nervous system activity, which might explain why hypnosis is effective in the treatment of disorders with strong sympathetic nervous system involvement, such as rheumatoid arthritis, hot flashes, hypertension, and chronic pain. Further studies with different control conditions are required to examine the specificity of the sympathetic effects of hypnosis