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Abstract This study explains the role of economic uncertainty as a bridge between business cycles and investors’ herding behavior. Starting with a conventional stochastic differential equation representing the evolution of stock returns, we provide a simple theoretical model and empirically demonstrate it. Specifically, the growth rate of gross domestic product and the power law exponent are used as proxies for business cycles and herding behavior, respectively. We find stronger herding behavior during recessions than during booms. We attribute this to economic uncertainty, which leads to strong behavioral bias in the stock market. These findings are consistent with the predictions of the quantum model.

To enhance the accuracy of micro-Newton thrust measurements via a torsion pendulum, addressing microgravity coupling effects caused by platform tilt and pendulum mass eccentricity is crucial. This study focuses on analyzing and minimizing these effects by alleviating reference surface tilt and calibrating the center of mass during thrust measurements. The study introduced analysis techniques and compensation measures. It first examined the impact of reference tilt and center of mass eccentricity on the stiffness and compliance of the torsion pendulum by reconstructing its dynamic model. Simscape Multibody was initially employed for numerical analysis to assess the dynamic coupling effects of the tilted pendulum. The results showed the influence of reference tilt on the stiffness and compliance of the torsion pendulum through simulation. An inverted pendulum was developed to amplify the platform’s tilt angle for microgravity drag-free control. Center of mass calibration can identify the gravity coupling caused by the center of mass position. Based on the displacement signal from the capacitive sensor located at the end of the inverted pendulum, which represents the platform’s tilt angle, the pendulum’s vibration at 0.1 mHz was reduced from 5.7 μm/Hz1/2 to 0.28 μm/Hz1/2 by adjusting the voltage of piezoelectric actuator. Finally, a new two-stage torsion pendulum structure was proposed to decouple the tilt coupling buried in both pitch and roll angle. The study utilized theoretical models, numerical analysis, and experimental testing to validate the analysis methods and compensation measures for microgravity coupling effects in torsion pendulums. This led to a reduction in low-frequency noise caused by ground vibrations and thermal strains, ultimately improving the micro-Newton thrust measurement accuracy of the torsion pendulum through the platform’s drag-free control.

The space gravitational wave detection and drag free control requires the micro-thruster to have ultra-low thrust noise within 0.1 mHz–0.1 Hz, which brings a great challenge to calibration on the ground because it is impossible to shield any spurious couplings due to the asymmetry of torsion balance. Most thrusters dissipate heat during the test, making the rotation axis tilt and components undergo thermal drift, which is hysteretic and asymmetric for micro-Newton thrust measurement. With reference to LISA’s research and coming up with ideas inspired from proportional-integral-derivative (PID) control and multi-timescale (MTS), this paper proposes to expand the state space of temperature to be applied on the thrust prediction based on fine tree regression (FTR) and to subtract the thermal noise filtered by transfer function fitted with z-domain vector fitting (ZDVF). The results show that thrust variation of diurnal asymmetry in temperature is decoupled from 24 μN/Hz1/2 to 4.9 μN/Hz1/2 at 0.11 mHz. Additionally, 1 μN square wave modulation of electrostatic force is extracted from the ambiguous thermal drift background of positive temperature coefficient (PTC) heater. The PID-FTR validation is performed with experimental data in thermal noise decoupling, which can guide the design of thermal control and be extended to other physical quantities for noise decoupling.