arXiv subjects

Mark Walth

Publications and source records attributed to Mark Walth.

4 recordsLinked to original sources

arXiv2024

Lunar Power Grid: Network Structure and Spontaneous Synchronization

Achieving stable synchronized operation in an alternating current power network is critical to the continuity and reliability of energy delivery. In this paper, we study a dynamic model for synchronization in the proposed power network which the National Aeronautic and Space Agency plans to build on the lunar surface to support continuous human presence on the Moon and a lunar economy. This network is quite remarkable in the sense that it is expected to be the first power network to operate at the unprecedented operating frequency in the $\text{kHz}$ range. The particular structure of this network allows us to derive the necessary and sufficient conditions guaranteeing the existence of a unique locally stable synchronized mode, which will provide a passive control mechanism for the system. Furthermore, we study the bifurcation process leading to the loss of synchronization when the system parameters fall outside of the stable regime. Our results have broader implications for many complex networks with parametric heterogeneity to enhance stability and resilience.

eess.SY↗

arXiv2023

Learning the Delay Using Neural Delay Differential Equations

The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap between these fields. In this paper, we develop a continuous time neural network approach based on Delay Differential Equations (DDEs). Our model uses the adjoint sensitivity method to learn the model parameters and delay directly from data. Our approach is inspired by that of NODEs and extends earlier neural DDE models, which have assumed that the value of the delay is known a priori. We perform a sensitivity analysis on our proposed approach and demonstrate its ability to learn DDE parameters from benchmark systems. We conclude our discussion with potential future directions and applications.

math.OC↗

arXiv2022

Synchronization in pairs of opto-thermally driven mechanically coupled micro-oscillators

We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the oscillations using interferometry. Devices of different dimensions are used to introduce frequency detuning, and short silicon bridges connecting the micro-beams are used as mechanical coupling between the oscillators. The region of synchronization is plotted for the MEMS system in the detuning vs. coupling parameter space and compared with the numerical analysis of a corresponding, lumped-parameter model. Three states of oscillations are observed i.e. the drift state, quasi-periodic state, and the synchronized state. The numerical model also distinguishes between in-phase and out-of-phase synchronization where out-of-phase synchronization is observed at low coupling strengths and low frequency detuning.

nlin.PS↗

arXiv2021

Bistability in coupled opto-thermal micro-oscillators

In this work, we experimentally investigate the dynamics of pairs of opto-thermally driven, mechanically coupled, doubly clamped, silicon micromechanical oscillators, and numerically investigate the dynamics of the corresponding lumped-parameter model. Coupled limit cycle oscillators exhibit striking nonlinear dynamics and bifurcations in response to variations in system parameters. We show that the input laser power influences the frequency detuning between two non-identical oscillators. As the laser power is varied, different regimes of oscillations such as the synchronized state, the drift state, and the quasi-periodic state are mapped at minimal and high coupling strengths. For non-identical oscillators, coexistence of two states, the synchronized state and the quasi-periodic state, is demonstrated at high coupling and high laser power. Experimentally, this bistability manifests as irregular oscillations as the system rapidly switches between the two states due to the system's sensitive dependence on initial conditions in the presence of noise. We provide a qualitative comparison of the experimental and numerical results to elucidate the behavior of the system.

nlin.PS↗