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1. A machine learning based Bayesian optimization solution to non-linear responses in dusty plasmas

   https://doi.org/10.1088/2632-2153/abe7b7  

   Ding, Zhiyue; Matthews, Lorin S; Hyde, Truell W (June 2021, Machine Learning: Science and Technology)

   Abstract Nonlinear frequency response analysis is a widely used method for determining system dynamics in the presence of nonlinearities. In dusty plasmas, the plasma–grain interaction (e.g. grain charging fluctuations) can be characterized by a single-particle non-linear response analysis, while grain–grain non-linear interactions can be determined by a multi-particle non-linear response analysis. Here a machine learning-based method to determine the equation of motion in the non-linear response analysis for dust particles in plasmas is presented. Searching the parameter space in a Bayesian manner allows an efficient optimization of the parameters needed to match simulated non-linear response curves to experimentally measured non-linear response curves. 

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2. Rateless Codes for Distributed Non-linear Computations

   https://doi.org/10.1109/ISTC49272.2021.9594268  

   Mallick, Ankur; Smith, Sophie; Joshi, Gauri (October 2021, 11th International Symposium on Topics in Coding)

   Machine learning today involves massive distributed computations running on cloud servers, which are highly susceptible to slowdown or straggling. Recent work has demonstrated the effectiveness of erasure codes in mitigating such slowdown for linear computations, by adding redundant computations such that the entire computation can be recovered as long as a subset of nodes finish their assigned tasks. However, most machine learning algorithms typically involve non-linear computations that cannot be directly handled by these coded computing approaches. In this work, we propose a coded computing strategy for mitigating the effect of stragglers on non-linear distributed computations. Our strategy relies on the observation that many expensive non-linear functions can be decomposed into sums of cheap non-linear functions. We show that erasure codes, specifically rateless codes can be used to generate and compute random linear combinations of these functions at the nodes such that the original function can be computed as long as a subset of nodes return their computations. Simulations and experiments on AWS Lambda demonstrate the superiority of our approach over various uncoded baselines. 

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3. Linear response theory of open systems with exceptional points

   https://doi.org/10.1038/s41467-022-30715-8  

   Hashemi, A.; Busch, K.; Christodoulides, D. N.; Ozdemir, S. K.; El-Ganainy, R. (December 2022, Nature Communications)

   Abstract Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order M s with M s  = 2, 3, …,  M , depending on the choice of input and output channels. 

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4. Evaluation of the parallel coupling constitutive model for biomaterials using a fully coupled network-matrix model

   https://doi.org/10.1016/j.jmbbm.2024.106583  

   Dey, MK; Merson, J; Picu, RC (July 2024, Journal of the Mechanical Behavior of Biomedical Materials)

   In this article we discuss the effective properties of composites containing a crosslinked athermal fiber network embedded in a continuum elastic matrix, which are representative for a broad range of biological materials. The goal is to evaluate the accuracy of the widely used biomechanics parallel coupling model in which the tissue response is defined as the additive superposition of the network and matrix contributions, and the interaction of the two components is neglected. To this end, explicit, fully coupled models are used to evaluate the linear and non-linear response of the composite. It is observed that in the small strain, linear regime the parallel model leads to errors when the ratio of the individual stiffnesses of the two components is in the range 0.1–10, and the error increases as the matrix approaches the incompressible limit. The data presented can be used to correct the parallel model to improve the accuracy of the overall stiffness prediction. In the non-linear large deformation regime linear superposition does not apply. The data shows that the matrix reduces the stiffening rate of the network, and the response is softer than that predicted by the parallel model. The correction proposed for the linear regime mitigates to a large extent the error in the non-linear regime as well, provided the matrix Poisson ratio is not close to 0.5. The special case in which the matrix is rendered auxetic is also evaluated and it is seen that the auxeticity of the matrix may compensate the stiffening introduced by the network, leading to a composite with linear elastic response over a broad range of strains. 

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5. Barotropic Instability during Eyewall Replacement

   https://doi.org/10.3390/meteorology2020013  

   Slocum, Christopher J.; Taft, Richard K.; Kossin, James P.; Schubert, Wayne H. (June 2023, Meteorology)

   Just before making landfall in Puerto Rico, Hurricane Maria (2017) underwent a concentric eyewall cycle in which the outer convective ring appeared robust while the inner ring first distorted into an ellipse and then disintegrated. The present work offers further support for the simple interpretation of this event in terms of the non-divergent barotropic model, which serves as the basis for a linear stability analysis and for non-linear numerical simulations. For the linear stability analysis the model’s axisymmetric basic state vorticity distribution is piece-wise uniform in five regions: the eye, the inner eyewall, the moat, the outer eyewall, and the far field. The stability of such structures is investigated by solving a simple eigenvalue/eigenvector problem and, in the case of instability, the non-linear evolution into a more stable structure is simulated using the non-linear barotropic model. Three types of instability and vorticity rearrangement are identified: (1) instability across the outer ring of enhanced vorticity; (2) instability across the low vorticity moat; and (3) instability across the inner ring of enhanced vorticity. The first and third types of instability occur when the rings of enhanced vorticity are sufficiently narrow, with non-linear mixing resulting in broader and weaker vorticity rings. The second type of instability, most relevant to Hurricane Maria, occurs when the radial extent of the moat is sufficiently narrow that unstable interactions occur between the outer edge of the primary eyewall and the inner edge of the secondary eyewall. The non-linear dynamics of this type of instability distort the inner eyewall into an ellipse that splits and later recombines, resulting in a vorticity tripole. This type of instability may occur near the end of a concentric eyewall cycle. 

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