Supplementation of Male Pheromone on Rock Substrates Attracts Female Rock Lizards to the Territories of Males: A Field Experiment

Background: Many animals produce elaborated sexual signals to attract mates, among them are common chemical sexual signals (pheromones) with an attracting function. Lizards produce chemical secretions for scent marking that may have a role in sexual selection. In the laboratory, female rock lizards (Iberolacerta cyreni) prefer the scent of males with more ergosterol in their femoral secretions. However, it is not known whether the scent-marks of male rock lizards may actually attract females to male territories in the field. Methodology/Principal Findings: In the field, we added ergosterol to rocks inside the territories of male lizards, and found that this manipulation resulted in increased relative densities of females in these territories. Furthermore, a higher number of females were observed associated to males in manipulated plots, which probably increased mating opportunities for males in these areas. Conclusions/Significance: These and previous laboratory results suggest that female rock lizards may select to settle in home ranges based on the characteristics of scent-marks from conspecific males. Therefore, male rock lizards might attract more females and obtain more matings by increasing the proportion of ergosterol when scent-marking their territories. However, previous studies suggest that the allocation of ergosterol to secretions may be costly and only high quality male

An averaging theorem for time-periodic degree zero homogeneous differential equations

This paper considers the stability of the differential equation ẋ = εX(t,x, ε), x ∈ ℝn, where X(t,x, ε) is a time-periodic, degree zero homogeneous vector field and ε > 0 is a parameter. It is shown that asymptotic stability of the time-averaged equation implies asymptotic stability of the original system for ε sufficiently small. © 1997 Elsevier Science B.V

Spectral analysis of vibratory gyro noise

This paper presents analysis of the noise spectra of closed-loop mode-matched vibratory gyros. Closed-form expressions for the noise-equivalent angular rate spectrum as well as the integrated angular rate (angle) variance are derived to explore the effects of modal frequency mismatch, closed-loop bandwidth, and the spectra of noise sources appearing at the sensor's input and output. It is shown that noise sources located at the output of the sensor's electromechanical transfer function create angle white noise in the closed-loop sensor. The angle white noise dominates the integrated rate behavior until it crosses the angle random walk asymptote at integration times exceeding the sensor's open-loop time constant. Even though the closed-loop sensor asymptotically recovers the angle random walk figure associated with the mode-matched open-loop sensor, the results can be used to quantify the larger integrated rate variance that is produced as a consequence of extending the sensor's bandwidth through feedback. A parameter, called the effective bandwidth, is introduced to capture the relative importance of the input noise versus output noise in determining the noise-equivalent rate spectrum. It is shown that the rate noise spectrum is robust to frequency mismatch as long as it does not exceed the effective bandwidth parameter. Empirical data obtained with a high performance MEMS vibratory gyro shows excellent agreement with the model predictions for a variety of sensor configurations including frequency-matched, frequency-mismatched, modified bandwidth, and manipulated input noise intensity cases. © 2013 IEEE

A systematic method for tuning the dynamics of electrostatically actuated vibratory gyros

High-performance vibratory gyroscopes require two degenerate modal frequencies for maximizing the rate-induced signals relative to noise produced by signal conditioning electronics. The present paper introduces a systematic approach for tuning these modes in vibratory gyros that employ electrostatic actuation. The key contribution shows how a parametric model, which captures the dependence of the sensor dynamics on the bias electrodes' potentials, can be fit to empirical frequency response data by solving a generalized eigenvalue problem. The models typically have 20 to 30 parameters for which the frequency response data imposes up to several hundred constraints. Subsequent analysis of the identified model enables the direct computation of the bias potentials which yield degenerate modal frequencies. The results are illustrated on a JPL-Boeing MEMS gyro prototype. © 2006 IEEE

A systematic method for tuning the dynamics of electrostatically actuated vibratory gyros

High-performance vibratory gyroscopes require two degenerate modal frequencies for maximizing the rate-induced signals relative to noise produced by signal conditioning electronics. The present paper introduces a systematic approach for tuning these modes in vibratory gyros that employ electrostatic actuation. The key contribution shows how a parametric model, which captures the dependence of the sensor dynamics on the bias electrodes' potentials, can be fit to empirical frequency response data by solving a generalized eigenvalue problem. The models typically have 20 to 30 parameters for which the frequency response data imposes up to several hundred constraints. Subsequent analysis of the identified model enables the direct computation of the bias potentials which yield degenerate modal frequencies. The results are illustrated on a JPL-Boeing MEMS gyro prototype. © 2006 IEEE

Decoupling of a disk resonator from linear acceleration via mass matrix perturbation

Axisymmetric microelectromechanical (MEM) vibratory rate gyroscopes are designed so the central post which attaches the resonator to the sensor case is a nodal point of the two Coriolis-coupled modes that are exploited for angular rate sensing. This configuration eliminates any coupling of linear acceleration to these modes. When the gyro resonators are fabricated, however, small mass and stiffness asymmetries cause coupling of these modes to linear acceleration of the sensor case. In a resonator postfabrication step, this coupling can be reduced by altering the mass distribution on the resonator so that its center of mass is stationary while the operational modes vibrate. In this paper, a scale model of the disk resonator gyroscope (DRG) is used to develop and test methods that significantly reduce linear acceleration coupling. © 2012 American Society of Mechanical Engineers

Phase compensation strategies for modulated-demodulated control with application to pulsed jet injection

Modulated-demodulated control is an effective method for asymptotic disturbance rejection and reference tracking of periodic signals, however, conventional static phase compensation often limits the loop gain in order to avoid sensitivity function peaking in a neighborhood of the frequencies targeted for rejection or tracking. This paper introduces dynamic phase compensation for modulated-demodulated control which improves disturbance rejection characteristics by inverting the plant phase in a neighborhood of the control frequency. Dynamic phase compensation is implemented at baseband which enables the use of low-bandwidth compensators to invert high frequency dynamics. Both static and dynamic phase compensation methods are used to demonstrate a novel application of repetitive control for pulsed jet injection. In this application pulsing an injectant has been shown to produce advantageous effects such as increased mixing in many energy generation and aerospace systems. The sharpness of the pulse can have a large impact on the effectiveness of control. Modulated-demodulated control is used to maximize the sharpness of a pulsed jet of air using active forcing by tracking a square wave in the jet's temporal velocity profile. © 2012 American Society of Mechanical Engineers

Real-time tuning of MEMS gyro dynamics

This paper reports real-time tuning of the JPL-Boeing micromachined vibratory rate sensor. The ideal sensor is designed to operate in a degenerate condition in which two modes of vibration have equal resonant frequencies. This condition achieves the best possible signal-to-noise ratio thereby maximizing sensor performance. A frequency split between the two modes, however, is inevitable in actual devices and leads to degraded performance. To modify the sensor dynamics to a desired condition, we have studied the bias potential effect on the sensor dynamics and successfully implemented a real-time tuning process via electrostatic forces to reduce the frequency split to less than 0.1 Hz when the nominal modal frequencies are near 4.4 kHz. A closed-loop identification method is employed for rapid and precise empirical frequency response estimates of the sensor dynamics. An LMI-based parameter estimation scheme produces an excellent fit of the model to the frequency response data and this enables the successful implementation of a steepest descent algorithm. Transformations for decoupling the MIMO sensor dynamics are also motivated and demonstrated. © 2005 AACC

Decoupling of a disk resonator from linear acceleration via mass matrix perturbation

Axisymmetric microelectromechanical (MEM) vibratory rate gyroscopes are designed so the central post which attaches the resonator to the sensor case is a nodal point of the two Coriolis-coupled modes that are exploited for angular rate sensing. This configuration eliminates any coupling of linear acceleration to these modes. When the gyro resonators are fabricated, however, small mass and stiffness asymmetries cause coupling of these modes to linear acceleration of the sensor case. In a resonator postfabrication step, this coupling can be reduced by altering the mass distribution on the resonator so that its center of mass is stationary while the operational modes vibrate. In this paper, a scale model of the disk resonator gyroscope (DRG) is used to develop and test methods that significantly reduce linear acceleration coupling. © 2012 American Society of Mechanical Engineers