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1. Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

   https://doi.org/10.1515/jiip-2020-0114  

   Nguyen, Dinh-Liem; Truong, Trung (November 2020, Journal of Inverse and Ill-posed Problems)

   null (Ed.)

   Abstract This paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures.The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency.The factorization method is studied as an analytical and numerical tool for solving the inverse problem.We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer.Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method. 

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2. Effect of defects and reinforcements on the mechanical behaviour of a bi-layered panel

   https://doi.org/10.1098/rspa.2022.0754  

   Wu, C. L.; Zhang, L. L.; Yin, H. M. (March 2023, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   This paper investigates the mechanical behaviour of a bi-layered panel containing many particles in one layer and demonstrates the size effect of particles on the deflection. The inclusion-based boundary element method (iBEM) considers a fully bounded bi-material system. The fundamental solution for two-jointed half spaces has been used to acquire elastic fields resulting from source fields over inclusions and boundary-avoiding multi-domain integral along the interface. Eshelby’s equivalent inclusion method is used to simulate the material mismatch with a continuously distributed eigenstrain field over the equivalent inclusion. The eigenstrain is expanded at the centre of the inclusion, which provides tailorable accuracy based on the order of the polynomial of the eigenstrain. As a single-domain approach, the iBEM algorithm is particularly suitable for conducting virtual experiments of bi-layered composites with many defects or reinforcements for both local analysis and homogenization purposes. The maximum deflection of solar panel coupons is studied under uniform vertical loading merged with inhomogeneities of different material properties, dimensions and volume fractions. The size of defects or reinforcements plays a significant role in the deflection of the panel, even with the same volume fraction, as the substrate is relatively thin. 

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3. Multiple scale method applied to homogenization of irrational metamaterials

   https://doi.org/10.1109/Metamaterials49557.2020.9284990  

   Guenneau, S.; Zolla, F.; Cherkaev, E.; Wellander, N. (September 2020, 2020 Fourteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials))

   null (Ed.)

   We adapt the multiple scale method introduced over 40 years ago for the homogenization of periodic structures [1], to the quasiperiodic (cut-and-projection) setting. We make use of partial differential operators (gradient, divergence and curl) acting on periodic functions of m variables in a higher-dimensional space that are projected onto operators acting on quasiperiodic functions in the n-dimensional physical space (m>n). We replace heterogeneous quasiperiodic structures, coined irrational metamaterials in [2], by homogeneous media with anisotropic permittivity and permeability tensors, obtained from the solution of annex problems of electrostatic type in a periodic cell in higher dimensional space. This approach is valid when the wavelength is much larger than the period of the higher dimensional elementary cell. 

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4. Laser additive manufacturing of powdered bismuth telluride

   https://doi.org/10.1557/jmr.2018.390  

   Zhang, Haidong; Hobbis, Dean; Nolas, George S.; LeBlanc, Saniya (December 2018, Journal of Materials Research)

   Traditional manufacturing methods restrict the expansion of thermoelectric technology. Here, we demonstrate a new manufacturing approach for thermoelectric materials. Selective laser melting, an additive manufacturing technique, is performed on loose thermoelectric powders for the first time. Layer-by-layer construction is realized with bismuth telluride, Bi 2 Te 3 , and an 88% relative density was achieved. Scanning electron microscopy results suggest good fusion between each layer although multiple pores exist within the melted region. X-ray diffraction results confirm that the Bi 2 Te 3 crystal structure is preserved after laser melting. Temperature-dependent absolute Seebeck coefficient, electrical conductivity, specific heat, thermal diffusivity, thermal conductivity, and dimensionless thermoelectric figure of merit ZT are characterized up to 500 °C, and the bulk thermoelectric material produced by this technique has comparable thermoelectric and electrical properties to those fabricated from traditional methods. The method shown here may be applicable to other thermoelectric materials and offers a novel manufacturing approach for thermoelectric devices. 

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5. Fourier series-based approximation of time-varying parameters in ordinary differential equations

   https://doi.org/10.1088/1361-6420/ad1fe5  

   Fitzpatrick, Anna; Folino, Molly; Arnold, Andrea (January 2024, Inverse Problems)

   Abstract Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some unobservable system parameters may vary with time without known evolution models. In this work, we propose a novel approximation method inspired by the Fourier series to estimate time-varying parameters in deterministic dynamical systems modeled with ordinary differential equations. Using ensemble Kalman filtering in conjunction with Fourier series-based approximation models, we detail two possible implementation schemes for sequentially updating the time-varying parameter estimates given noisy observations of the system states. We demonstrate the capabilities of the proposed approach in estimating periodic parameters, both when the period is known and unknown, as well as non-periodic time-varying parameters of different forms with several computed examples using a forced harmonic oscillator. Results emphasize the importance of the frequencies and number of approximation model terms on the time-varying parameter estimates and corresponding dynamical system predictions. 

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