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The manipulation of mechanical waves is a long-standing challenge for scientists and engineers, as numerous devices require their control. The current forefront of research in the control of classical waves has emerged from a seemingly unrelated field, namely, non-Hermitian quantum mechanics. By drawing analogies between this theory and those of classical systems, researchers have discovered phenomena that defy conventional intuition and have exploited them to control light, sound, and elastic waves. Here, we provide a brief perspective on recent developments, challenges and intricacies that distinguish non-Hermitian elastodynamics from optics and acoustics. We close this perspective with an outlook on potential directions such as topological phases in non-Hermitian elastodynamics and broken Hermitian symmetry in materials with electromomentum couplings.

Algorithmic materials discovery is a multi-disciplinary domain that integrates insights from specialists in alloy design, synthesis, characterization, experimental methodologies, computational modeling, and optimization. Central to this effort is a robust data management system paired with an interactive work platform. This platform should empower users to not only access others data but also integrate their analyses, paving the way for sophisticated data pipelines. To realize this vision, there is a need for an integrative collaboration platform, streamlined data sharing and analysis tools, and efficient communication channels. Such a collaborative mechanism should transcend geographical barriers, facilitating remote interaction and fostering a challenge-response dynamic. In this paper, we present our ongoing efforts in addressing the critical challenges related to an accelerated Materials Discovery Framework as a part of the High-Throughput Materials Discovery for Extreme Conditions Initiative. Our BIRDSHOT Center has successfully harnessed various tools and strategies, including the utilization of cloud-based storage, a standardized sample naming convention, a structured file system, the implementation of sample travelers, a robust sample tracking method, and the incorporation of knowledge graphs for efficient data management. Additionally, we present the development of a data collection platform, reinforcing seamless collaboration among our team members. In summary, this paper provides an illustration and insight into the various elements of an efficient and effective workflow within an accelerated materials discovery framework while highlighting the dynamic and adaptable nature of the data management tools and sharing platforms., Comment: 28 pages, 9 figures, 2 tables, with appendix that has 8 pages, accepted for publication at IMMI

In this study, we introduce a groundbreaking framework for materials discovery, we efficiently navigate a vast phase space of material compositions by leveraging Batch Bayesian statistics in order to achieve specific performance objectives. This approach addresses the challenge of identifying optimal materials from an untenably large array of possibilities in a reasonable timeframe with high confidence. Crucially, our batchwise methods align seamlessly with existing material processing infrastructure for synthesizing and characterizing materials. By applying this framework to a specific high entropy alloy system, we demonstrate its versatility and robustness in optimizing properties like strain hardening, hardness, and strain rate sensitivity. The fact that the Bayesian model is adept in refining and expanding the property Pareto front highlights its broad applicability across various materials, including steels, shape memory alloys, ceramics, and composites. This study advances the field of materials science and sets a new benchmark for material discovery methodologies. By proving the effectiveness of Bayesian optimization, we showcase its potential to redefine the landscape of materials discovery., Comment: 12 pages, 6 figures, with Supplementary Appendix that has 17 pages, 9 figures

This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via proper orthogonal decomposition (POD), both by using all velocity components, and after separating the streamwise and secondary components of the flow. The causal relations between the mode coefficients are analysed using pairwise-conditional Granger causality analysis. We also formulate a nonlinear Granger causality analysis that can account for nonlinear interactions between modes. Focusing on streamwise-constant structures within a duct of short streamwise extent, we show that the causal relationships are highly sensitive to whether the mode coefficients or their squared values are considered, whether nonlinear effects are explicitly accounted for, and whether streamwise and secondary flow structures are separated prior to causality analyses. We leverage these sensitivities to determine that linear mechanisms underpin causal relationships between modes that share the same symmetry or anti-symmetry properties about the corner bisector, while nonlinear effects govern the causal interactions between symmetric and antisymmetric modes. In all cases, we find that the secondary flow fluctuations (manifesting as streamwise vorticial structures) are the primary cause of both the presence and movement of near-wall streaks towards and away from the duct corners.

In this paper, we introduce a new approach for soft robot shape formation and morphing using approximate distance fields. The method uses concepts from constructive solid geometry, R-functions, to construct an approximate distance function to the boundary of a domain in $\Re^d$. The gradients of the R-functions can then be used to generate control algorithms for shape formation tasks for soft robots. By construction, R-functions are smooth and convex everywhere, possess precise differential properties, and easily extend from $\Re^2$ to $\Re^3$ if needed. Furthermore, R-function theory provides a straightforward method to creating composite distance functions for any desired shape by combining subsets of distance functions. The process is highly efficient since the shape description is an analytical expression, and in this sense, it is better than competing control algorithms such as those based on potential fields. Although the method could also apply to swarm robots, in this paper it is applied to soft robots to demonstrate shape formation and morphing in 2-D (simulation and experimentation) and 3-D (simulation).

In this paper, we present a powerful method (Atomistic Green's Function, AGF) for calculating the effective Hamiltonian of acoustic and elastic wave-scatterers. The ability to calculate the effective Hamiltonian allows for the study of scattering problems in infinite systems without the introduction of any artificial truncating boundaries such as perfectly matched layers or Dirichlet to Neumann (DtN) maps. Furthermore, the AGF formalism also allows for the efficient calculation of the Green's function of the scatterer as well as all relevant scattering metrics including reflection and transmission ratios. The formalism presented here is especially suited to scattering problems involving waveguides, phononic crystals, metamaterials, and metasurfaces. We show the application of the method to three scattering problems: scattering from a slab (1D), scattering from a finite phononic crystal (1D), and scattering from defects in a waveguide (2D).

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in their loss function. While PINNs are successfully used for solving forward and inverse problems, their accuracy decreases significantly for parameterized systems. PINNs also have a soft implementation of boundary conditions resulting in boundary conditions not being exactly imposed everywhere on the boundary. With these challenges at hand, we present first-order physics-informed neural networks (FO-PINNs). These are PINNs that are trained using a first-order formulation of the PDE loss function. We show that, compared to standard PINNs, FO-PINNs offer significantly higher accuracy in solving parameterized systems, and reduce time-per-iteration by removing the extra backpropagations needed to compute the second or higher-order derivatives. Additionally, FO-PINNs can enable exact imposition of boundary conditions using approximate distance functions, which pose challenges when applied on high-order PDEs. Through three examples, we demonstrate the advantages of FO-PINNs over standard PINNs in terms of accuracy and training speedup., Comment: 16 pages, 11 figures, Selected for ML4PS workshop at NeurIPS 2022

The aim of this work is to analyse the formation mechanisms of large-scale coherent structures in the flow around a wall-mounted square cylinder, due to their impact on pollutant transport within cities. To this end, we assess causal relations between the modes of a reduced-order model obtained by applying proper-orthogonal decomposition to high-fidelity-simulation data of the flow case under study. The causal relations are identified using conditional transfer entropy, which is an information-theoretical quantity that estimates the amount of information contained in the past of one variable about another. This allows for an understanding of the origins and evolution of different phenomena in the flow, with the aim of identifying the modes responsible for the formation of the main vortical structures. Our approach unveils that vortex-breaker modes are the most causal modes, in particular, over higher-order modes, and no significant causal relationships were found for vortex-generator modes. We validate this technique by determining the causal relations present in the nine-equation model of near-wall turbulence developed by Moehlis et al. (New J. Phys, vol. 6, 2004, p. 56), which are in good agreement with literature results for turbulent channel flows., Comment: 19 pages, 10 figures

In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at specific locations and how these locations connect to the vibrational properties of the scatterer. The resonance locations are connected to the eigenvalues of a finite dimensional effective operator, $H_{eff}$, corresponding to the scatterer. The developments are presented from the perspective of open systems, which seeks to convert the infinite dimensional scattering problem (scatterer+environment) into a finite dimensional effective problem involving only the finite scatterer. This is achieved through a projection operator formalism which allows us to formally calculate $H_{eff}$. An interesting corollary of our analysis is the deep connection between resonance locations in the scattering spectrum and the eigenfrequencies of the scatterer under Neumann boundary condition. We bring out this point further by considering 3D scattering from an elastic shell, connecting our results to classical results in acousto-elastic scattering theory.

In this work, a parameterized eigenvalue problem is analyzed for a phononic array in a 2D stress wave scattering setup, and a corresponding sensing application of this system is proposed to achieve source angle localization. The phononic domain consists of a periodic micro-structured medium, of which the eigen-wavevector band structure and the eigen-modes are exploited. The eigen-modes are naturally angle dependent due to changes in phases and periodic mode shapes determined by the incident angle. Intriguingly, the band exhibits angle-dependent transitions at the exceptional points (EPs) and critical angles (CAs), where the eigenvalues coincide or vanish. Coupled with these transitions, it is found that the eigen-modes switch their energy characteristics and symmetry patterns at these branch points, leading to enhanced angle dependence. Moreover, these eigen-modes also serve as the basis functions of the scattered waves. Therefore, the scattering response of the medium inherently possesses the angle-dependent properties, making this system naturally suitable for sensing applications. An artificial neural network (ANN) is trained with randomly weighted eigen-modes to achieve deep learning of the eigen features and angle dependence. The training data is derived only based on the eigen-modes of the unit cells. Nevertheless, the trained ANN can accurately identify the incident angle of an unknown scattering signal, with minimal side lobe levels and suppressed main lobe width. The ANN shows superior performance in comparison with standard delay-and-sum technique of estimating angle of arrival. The proposed application of ANN and micro-structured media highlights the physical importance of band structure topology and eigen-modes to a technological application, adds extra strength to the existing localization methods, and can be easily enhanced with the fast-growing data-driven techniques.