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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. 

Effective thermal management is critical to many engineering applications, yet identifying optimal heat-transfer designs remains challenging due to complex interactions among material, geometry, and structural parameters. Here, we use a full-factorial design combined with thermal physics finite element simulations to systematically evaluate the effects of five factors—material, fin configuration, geometry, spacing, and thickness—on the time to boil water (τb) in a heatsink-assisted system. Using data from just 32 treatment simulations and a statistically reduced categorical model, we resolve all main effects and interactions, revealing that sparse fin spacing, aluminum material, and thin fins significantly reduce τb. While radial configurations generally outperform linear ones, interaction effects demonstrate that optimum performance depends on specific factor combinations; for example, linear designs can outperform radial ones when paired with certain geometries and materials. Contrary to intuition, neither surface area nor surface-area-to-mass ratio reliably predicts performance due to confounding effects of mass. The best-performing design—an Al-linear-trapezoidal-sparse-thin heatsink—achieved τ^b=618±2s, while other optimal designs emerged under constraints such as reduced mass or manufacturing simplicity. This study underscores the value of factorial design in navigating complex design spaces and optimizing thermal performance, offering a powerful framework for the development of next-generation heat transfer systems. 

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. 

Arrays of coupled nanoelectromechanical resonators are a promising foundation for implementing large-scale network applications, such as mechanical-based information processing and computing, but their practical realization remains an outstanding challenge. In this work, we demonstrate a scalable platform of suspended graphene resonators, such that neighboring resonators are persistently coupled mechanically. We provide evidence of strong coupling between neighboring resonators using two different tuning methods. Additionally, we provide evidence of inter-resonator coupling of higher-order modes, demonstrating the rich dynamics that can be accessed with this platform. Our results establish this platform as a viable option for realizing large-scale programmable networks, enabling applications such as phononic circuits, tunable waveguides, and reconfigurable metamaterials.