Control bifurcations

A parametrized nonlinear differential equation can have multiple equilibria as the parameter is varied. A local bifurcation of a parametrized differential equation occurs at an equilibrium where there is a change in the topological character of the nearby solution curves. This typically happens because some eigenvalues of the parametrized linear approximating differential equation cross the imaginary axis and there is a change in stability of the equilibrium. The topological nature of the solutions is unchanged by smooth changes of state coordinates so these may be used to bring the differential equation into Poincare/spl acute/ normal form. From this normal form, the type of the bifurcation can be determined. For differential equations depending on a single parameter, the typical ways that the system can bifurcate are fully understood, e.g., the fold (or saddle node), the transcritical and the Hopf bifurcation. A nonlinear control system has multiple equilibria typically parametrized by the set value of the control. A control bifurcation of a nonlinear system typically occurs when its linear approximation loses stabilizability. The ways in which this can happen are understood through the appropriate normal forms. We present the quadratic and cubic normal forms of a scalar input nonlinear control system around an equilibrium point. These are the normal forms under quadratic and cubic change of state coordinates and invertible state feedback. The system need not be linearly controllable. We study some important control bifurcations, the analogues of the classical fold, transcritical and Hopf bifurcations

A Quasi-Steady Model for the Lift on a Hovering Flexible Wing

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140422/1/6.2014-1114.pd

Modeling of Instantaneous Passive Pitch of Flexible Flapping Wings

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106449/1/AIAA2013-2469.pd

Passive Wing Rotation in Flexible Flapping Wing Aerodynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97083/1/AIAA2012-2763.pd

Effects of Flexibility on the Aerodynamics of a Hovering Flexible Airfoil at Reynolds Number of 100 to 1000

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97084/1/AIAA2012-1206.pd

Aromatherapy Benefits Autonomic Nervous System Regulation for Elementary School Faculty in Taiwan

Workplace stress-related illness is a serious issue, and consequently many stress reduction methods have been investigated. Aromatherapy is especially for populations that work under high stress. Elementary school teachers are a high-stress working population in Taiwan. In this study, fifty-four elementary school teachers were recruited to evaluate aromatherapy performance on stress reduction. Bergamot essential oil was used for aromatherapy spray for 10 minutes. Blood pressure and autonomic nervous system parameters were recorded 5 minutes before and after the application of the aroma spray. Results showed that there were significant decreases in blood pressure, heart rate, LF power percentage, and LF/HF while there were increases in heart rate variability and HF power percentage (P < .001∗∗∗) after application of the aromatherapy spray. Further analysis was investigated by dividing subjects into three background variables (position variables, age variables, gender variables) and anxiety degree groups. All parameters were significantly different for most subgroups, except for the substitute teachers and the light-anxiety group. Parasympathetic nervous system activation was measured after aromatherapy in this study. It encouraged further study for other stress working population by aromatherapy

CEO tenure and environmental fraud for listed family firms

This paper examines CEO tenure's impact on the environmental fraud committed by listed Chinese family firms from the year 2012 to 2019. Using a bivariate probit model, we provide robust evidence that CEO tenure is positively related to the environmental fraud commission, indicating that longer-serving CEOs are more likely to violate environmental regulations and to commit fraud in the family firms. Besides, when there is a higher proportion of independent directors, CEO tenure is negatively related to the environmental fraud commission but positively related to fraud detection. Moreover, when there is a greater proportion of family members in senior positions, CEOs with longer tenure are more likely to commit environmental fraud. Our additional analysis finds that compared to non-family professional CEOs, family CEOs are more likely to commit environmental fraud. Overall, our results call for the introduction of CEO tenure limits and the increased recruitment of independent directors in family firms

Transverse momentum broadening of vector boson production in high energy nuclear collisions

We calculate in perturbative QCD the transverse momentum broadening of vector boson production in high energy nuclear collisions. We evaluate the effect of initial-state parton multiple scattering for the production of the Drell-Yan virtual photon and $W/Z$ bosons. We calculate both the initial- and final-state multiple scattering effect for the production of heavy quarkonia and their transverse momentum broadening in both NRQCD and Color Evaporation model of quarkonium formation. We find that J/$\psi$ and $\Upsilon$ broadening in hadron-nucleus collision is close to $2C_A/C_F$ times the corresponding Drell-Yan broadening, which gives a good description of existing Fermilab data. Our calculations are also consistent with RHIC data on J/$\psi$ broadening in relativistic heavy ion collisions. We predict the transverse momentum broadening of vector boson (J/$\psi$, $\Upsilon$, and $W/Z$) production in relativistic heavy ion collisions at the LHC, and discuss the role of the vector boson broadening in diagnosing medium properties.Comment: 22 pages, 10 figures, revised version to appear in Phys. Rev.