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Abstract Resonator networks are ubiquitous in natural and engineered systems, such as solid-state materials, electrical circuits, quantum processors, and even neural tissue. To understand and manipulate these networks it is essential to characterize their building blocks, which include the mechanical analogs of mass, elasticity, damping, and coupling of each resonator element. While these mechanical parameters are typically obtained from response spectra using least-squares fitting, this approach requires a priori knowledge of all parameters and is susceptible to large error due to convergence to local minima. Here we validate an alternative algebraic means to characterize resonator networks with no or minimal a priori knowledge. Our approach recasts the equations of motion of the network into a linear homogeneous algebraic equation and solves the equation with a set of discrete measured network response vectors. For validation, we employ our approach on noisy simulated data from a single resonator and a coupled resonator pair, and we characterize the accuracy of the recovered parameters using high-dimension factorial simulations. Generally, we find that the error is inversely proportional to the signal-to-noise ratio, that measurements at two frequencies are sufficient to recover all parameters, and that sampling near the resonant peaks is optimal. Our simple, powerful tool will enable future efforts to ascertain network properties and control resonator networks in diverse physical domains.
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This content will become publicly available on November 14, 2026
A minimal-data approach for spatially resolved parameter analysis of coupled graphene nanomechanical resonators
Networks of nanoelectromechanical (NEMS) resonators are useful analogs for a variety of many-body systems and enable applications in sensing, phononics, and mechanical information processing. A challenge toward realizing practical NEMS networks is the ability to characterize the constituent resonator building blocks and their coupling. Here, we spatially map graphene NEMS networks and introduce an efficient algebraic formalism to quantify the site-specific elasticity, mass, damping, and coupling parameters of network clusters. In a departure from multiple regression, our algebraic analysis uses minimal measurements to fully characterize the network parameters without a priori parameter estimates or iterative computation. We apply this suite of techniques to single-resonator and coupled-pair clusters and find excellent agreement with expected parameter values and broader spectral response. Our approach provides a nonregressive framework for accurately characterizing a range of classical and quantum resonator systems, offering a versatile modeling tool applicable across multiple disciplines and advancing the development of programmable NEMS networks.
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- Award ID(s):
- 2128671
- PAR ID:
- 10651351
- Publisher / Repository:
- American Association for the Advancement of Science
- Date Published:
- Journal Name:
- Science Advances
- Volume:
- 11
- Issue:
- 46
- ISSN:
- 2375-2548
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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