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Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical modeling, nonlinearity, and high dimensionality. In this work, we introduce a data-driven computational framework to derive low-dimensional linear models for nonlinear dynamical systems directly from raw experimental data. This framework enables global stability analysis through interpretable linear models that capture the underlying system structure. Our approach employs time-delay embedding, physics-informed deep autoencoders, and annealing-based regularization to identify novel low-dimensional coordinate representations, unlocking insights across a variety of simulated and previously unstudied experimental dynamical systems. These new coordinate representations enable accurate long-horizon predictions and automatic identification of intricate invariant sets while providing empirical stability guarantees. Our method offers a promising pathway to analyze complex dynamical behaviors across fields such as physics, climate science, and engineering, with broad implications for understanding nonlinear systems in the real world., Comment: http://generalroboticslab.com/AutomatedGlobalAnalysis

Moir\'e superlattices in twisted two-dimensional materials have generated tremendous excitement as a platform for achieving quantum properties on demand. However, the moir\'e pattern is highly sensitive to the interlayer atomic registry, and current assembly techniques suffer from imprecise control of the average twist angle, spatial inhomogeneity in the local twist angle, and distortions due to random strain. Here, we demonstrate a new way to manipulate the moir\'e patterns in hetero- and homo-bilayers through in-plane bending of monolayer ribbons, using the tip of an atomic force microscope. This technique achieves continuous variation of twist angles with improved twist-angle homogeneity and reduced random strain, resulting in moir\'e patterns with highly tunable wavelength and ultra-low disorder. Our results pave the way for detailed studies of ultra-low disorder moir\'e systems and the realization of precise strain-engineered devices.

Manipulating the nanostructure of materials is critical for numerous applications in electronics, magnetics, and photonics. However, conventional methods such as lithography and laser-writing require cleanroom facilities or leave residue. Here, we describe a new approach to create atomically sharp line defects in hexagonal boron nitride (hBN) at room temperature by direct optical phonon excitation in the mid-infrared (mid-IR). We term this phenomenon "unzipping" to describe the rapid formation and growth of a <30-nm-wide crack from a point within the laser-driven region. The formation of these features is attributed to large atomic displacements and high local bond strain from driving the crystal at a natural resonance. This process is distinguished by (i) occurring only under resonant phonon excitation, (ii) producing highly sub-wavelength features, and (iii) sensitivity to crystal orientation and pump laser polarization. Its cleanliness, directionality, and sharpness enable applications in in-situ flake cleaving and phonon-wave-coupling via free space optical excitation., Comment: 11 pages, 4 figures

Broken symmetries induce strong nonlinear optical responses in materials and at interfaces. Twist angle can give complete control over the presence or lack of inversion symmetry at a crystal interface, and is thus an appealing knob for tuning nonlinear optical systems. In contrast to conventional nonlinear crystals with rigid lattices, the weak interlayer coupling in van der Waals (vdW) heterostructures allows for arbitrary selection of twist angle, making nanomechanical manipulation of fundamental interfacial symmetry possible within a single device. Here we report highly tunable second harmonic generation (SHG) from nanomechanically rotatable stacks of bulk hexagonal boron nitride (BN) crystals, and introduce the term twistoptics to describe studies of optical properties in dynamically twistable vdW systems. We observe SHG intensity modulated by a factor of more than 50, polarization patterns determined by moir\'e interface symmetry, and enhanced conversion efficiency for bulk crystals by stacking multiple pieces of BN joined by symmetry-broken interfaces. Our study provides a foundation for compact twistoptics architectures aimed at efficient, scalable, and tunable frequency-conversion, and demonstrates SHG as a robust probe of buried vdW interfaces., Comment: 23 Pages, 17 Figures

Understanding the basins of attraction (BoA) is often a paramount consideration for nonlinear systems. Most existing approaches to determining a high-resolution BoA require prior knowledge of the system's dynamical model (e.g., differential equation or point mapping for continuous systems, cell mapping for discrete systems, etc.), which allows derivation of approximate analytical solutions or parallel computing on a multi-core computer to find the BoA efficiently. However, these methods are typically impractical when the BoA must be determined experimentally or when the system's model is unknown. This paper introduces a model-free sampling method for BoA. The proposed method is based upon hybrid active learning (HAL) and is designed to find and label the "informative" samples, which efficiently determine the boundary of BoA. It consists of three primary parts: 1) additional sampling on trajectories (AST) to maximize the number of samples obtained from each simulation or experiment; 2) an active learning (AL) algorithm to exploit the local boundary of BoA; and 3) a density-based sampling (DBS) method to explore the global boundary of BoA. An example of estimating the BoA for a bistable nonlinear system is presented to show the high efficiency of our HAL sampling method., Comment: Update: 1) add time trajectory of additional sampling

Additive Manufacturing (AM), a.k.a. 3D Printing, is increasingly used to manufacture functional parts of safety-critical systems. AM's dependence on computerization raises the concern that the AM process can be tampered with, and a part's mechanical properties sabotaged. This can lead to the destruction of a system employing the sabotaged part, causing loss of life, financial damage, and reputation loss. To address this threat, we propose a novel approach for detecting sabotage attacks. Our approach is based on continuous monitoring of the current delivered to all actuators during the manufacturing process and detection of deviations from a provable benign process. The proposed approach has numerous advantages: (i) it is non-invasive in a time-critical process, (ii) it can be retrofitted in legacy systems, and (iii) it is airgapped from the computerized components of the AM process, preventing simultaneous compromise. Evaluation on a desktop 3D Printer detects all attacks involving a modification of X or Y motor movement, with false positives at 0%., Comment: Accepted as poster at RAID 2017