Brownian Noise and Temperature Sensitivity of Long-Period Lunar Seismometers

ABSTRACT As long-period ground motion holds the key to understanding the interior of the Earth’s Moon, reducing long-period noise sources will be an essential area of focus in the design of future lunar seismometers. For the proposed Lunar Geophysical Network (LGN), the International Lunar Network (ILN) Science Definition Team specifies that an LGN enabling seismometer will need to be more sensitive than any previous seismometer at frequencies below 1 Hz. In an effort toward lowering the seismometer noise floor for lunar geophysical missions, we evaluate the 1/f Brownian noise and the temperature sensitivity of a seismometer. Temperature sensitivity of a seismometer is related to an important component of the seismometer output noise that is proportional to the temperature noise in the environment. The implications of the ILN requirement are presented in the context of the state-of-the-art InSight Seismic Experiment for Interior Structure (SEIS) Very Broad Band (VBB) planetary seismometer. Brownian noise due to internal friction was estimated for future lunar operation after accounting for the rebalance of the product of mass and distance to the center of gravity of the pendulum for the SEIS-VBB sensor. We find that Brownian noise could be a limiting factor in meeting the ILN requirement for lunar seismometers. Further, we have developed a formalism to understand the temperature sensitivity of a seismometer, relating it quantitatively to the local gravity, the thermoelastic coefficient of the spring, change in center of gravity, and the coefficient of thermal expansion of the mechanical structures. We found that in general the temperature sensitivity of a seismometer is proportional to the local gravity, and so the temperature sensitivity can be reduced when operating on a planetary body with lower gravity. Our Brownian noise and temperature sensitivity models will be useful in the design of the next generation of planetary seismometers.

Colored Levy Noise Induced Stochastic Dynamics in a Tri-Stable Hybrid Energy Harvester

The piezoelectric and electromagnetic hybrid vibration energy harvester (HVEH) has proven to be a favorable option to deal with the low power generation issue and overcome the drawbacks of each individual transduction mechanism. Besides, colored Lévy noise consisting of small perturbations, large jumps and correlation time turns out to be a relatively suitable tool for describing the complex environments. For the purpose of enhancing the harvesting performance of HVEH, the stochastic dynamics induced by colored Lévy noise in a tri-stable HVEH is mainly investigated in this paper. The stationary probability density, the largest Lyapunov exponent, the signal-to-noise ratio and the mean harvested power are calculated to explore the stochastic dynamics of system, such as the stochastic response, the stochastic stability, the stochastic resonance (SR) and the energy harvesting performance. Results show that the colored Lévy noise can induce stochastic P-bifurcation, D-bifurcation and SR phenomenon. In particular, the comparisons between colored Lévy noise and colored Brownian noise in dynamics and harvesting performance are also discussed in detail. It is found that the colored Lévy noise can make a greater contribution than colored Brownian noise in the effective voltage and help to improve the mean harvested power through the SR effect.

Orientation of motion of a flat folding nano-swimmer in soft matter

It is well established that anisotropic molecules do have a preferential direction of motion at short time scales that is washed out at larger times by Brownian noise. Anisotropic molecular...

An Actuarial Approach for Modeling Pandemic Risk

In this article, a model for pandemic risk and two stochastic extensions is proposed. It is designed for actuarial valuation of insurance plans providing healthcare and death benefits. The core of our approach relies on a deterministic model that is an efficient alternative to the susceptible-infected-recovered (SIR) method. This model explains the evolution of the first waves of COVID-19 in Belgium, Germany, Italy and Spain. Furthermore, it is analytically tractable for fair pure premium calculation. In a first extension, we replace the time by a gamma stochastic clock. This approach randomizes the timing of the epidemic peak. A second extension consists of adding a Brownian noise and a jump process to explain the erratic evolution of the population of confirmed cases. The jump component allows for local resurgences of the epidemic.

Generation of acoustic-Brownian noise in nuclear magnetic resonance under non-equilibrium thermal fluctuations

We present an analytical study on generation of acoustic-Brownian noise in nuclear magnetic resonance (NMR) induced as a result of thermal fluctuations of the magnetic moments under non-equilibrium thermal interactions which has not been explored independent of Nyquist–Johnson noise until now. The mechanism of physical coupling between non-equilibrium thermal fluctuations and magnetic moments is illustrated using Lighthill’s formulation on suspension dynamics. We discover that unlike Nyquist–Johnson noise which has a uniform spectral density across a range of frequencies, the spectral dependence of acoustic-Brownian noise decreases with an increase in frequency and resembles Brownian noise associated with a particle in a potential well. The results have applications in the field of image enhancement algorithm as well as noise reduction instrumentation in NMR systems.

Typical dynamics and fluctuation analysis of slow–fast systems driven by fractional Brownian motion

This paper studies typical dynamics and fluctuations for a slow–fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we characterize the asymptotic dynamics of the slow component to two orders (i.e. the typical dynamics and the fluctuations). The limiting distribution of the fluctuations turns out to depend upon the manner in which the small-noise parameter is taken to zero relative to the scale-separation parameter. We study also an extension of the original model in which the relationship between the two small parameters leads to a qualitative difference in limiting behavior. The results of this paper provide an approximation, to two orders, to dynamical systems perturbed by small fractional Brownian noise and incorporating multiscale effects.