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1. Generative Design of Statistically Self-Similar Mechanical Structures

   https://doi.org/10.1115/DETC2023-117063  

   Hill, Noah; Ebert, Matthew; Maurice, Mena; Krishnamurthy, Vinayak (August 2023, American Society of Mechanical Engineers)

   Abstract We present a novel methodology to generate mechanical structures based on the idea of fractal geometry as described by the chaos game. Chaos game is an iterative method that generates self-similar point-sets in the limiting case within a polygonal domain. By computing Voronoi tessellations on these point-sets, our method generates mechanical structures that adopts the self-similarity of the point-sets resulting in fractal distribution of local stiffness. The motivation behind our approach comes from the observation that a typical generative structural design workflow requires the ability to generate families of structures that possess shared behavioral (e.g. thermal, mechanical, etc.) characteristics making each structure distinct but feasible. However, the generation of the alternatives, almost always, requires solving an inverse structural problem which is both conceptually and computationally challenging. The objective of our work is to develop and investigate a forward-design methodology for generating families of structures that, while not identical, exhibit similar mechanical behavior in a statistical sense. To this end, the central hypothesis of our work is that structures generated using the chaos game can generate families of self-similar structures that, while not identical, exhibit similar mechanical behavior in a statistical sense. Furthermore, each family is uniquely identifiable from the parameters of the chaos game, namely, the polygonal domain, fractional distance, and number of samples. We present a systematic study of these self-similar structures through modal analysis and demonstrate a preliminary confirmation of our hypothesis. 

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2. Applications of Polynomial Chaos-Based Cokriging to Simulation-Based Analysis and Design Under Uncertainty

   https://doi.org/10.1115/DETC2020-22369  

   Nagawkar, Jethro; Leifsson, Leifur (August 2020, Proceedings of the ASME 2020 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2020)

   null (Ed.)

   Abstract This paper demonstrates the use of the polynomial chaos-based Cokriging (PC-Cokriging) on various simulation-based problems, namely an analytical borehole function, an ultrasonic testing (UT) case and a robust design optimization of an airfoil case. This metamodel is compared to Kriging, polynomial chaos expansion (PCE), polynomial chaos-based Kriging (PC-Kriging) and Cokriging. The PC-Cokriging model is a multi-variate variant of PC-Kriging and its construction is similar to Cokriging. For the borehole function, the PC-Cokriging requires only three high-fidelity samples to accurately capture the global accuracy of the function. For the UT case, it requires 20 points. Sensitivity analysis is performed for the UT case showing that the F-number has negligible effect on the output response. For the robust design case, a 75 and 31 drag count reduction is reported on the mean and standard deviation of the drag coefficient, respectively, when compared to the baseline shape. 

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3. Chaos and Thermalization in the Spin-Boson Dicke Model

   https://doi.org/10.3390/e25010008  

   Villaseñor, David; Pilatowsky-Cameo, Saúl; Bastarrachea-Magnani, Miguel A.; Lerma-Hernández, Sergio; Santos, Lea F.; Hirsch, Jorge G. (January 2023, Entropy)

   We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called “efficient basis” over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis. 

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4. A simple method for detecting chaos in nature

   https://doi.org/10.1038/s42003-019-0715-9  

   Toker, Daniel Sommer (January 2020, Communications biology)

   null (Ed.)

   Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist’s toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available. 

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5. Hybrid Geometry/Property Autoencoders for Multi-Lattice Transitions

   Baldwin, M; Meisel, N. A.; McComb, C. (October 2023, 2023 International Solid Freeform Fabrication Symposium)

   Additive manufacturing has revolutionized structural optimization by enhancing component strength and reducing material requirements. One approach used to achieve these improvements is the application of multi-lattice structures. The performance of these structures heavily relies on the detailed design of mesostructural elements. Many current approaches use data-driven design to generate multi-lattice transition regions, making use of models that jointly address the geometry and properties of the mesostructures. However, it remains unclear whether the integration of mechanical properties into the data set for generating multi-lattice interpolations is beneficial beyond geometry alone. To address this issue, this work implements and evaluates a hybrid geometry/property machine learning model for generating multi-lattice transition regions. We compare the results of this hybrid model to results obtained using a geometry-only model. Our research determined that incorporating physical properties decreased the number of variables to address in the latent space, and therefore improves the ability of generative models for developing transition regions of multi-lattice structures. 

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