Season 5
Seminar 2: Nonlinear Waves in Active Non-Hermitian Metamaterials
Speaker: dr. Bertin Many Manda
Abstract: I will address nonlinear waves in non-reciprocal metamaterials, a class of non-Hermitian systems characterised by active elements that produce constant asymmetric couplings between their components. In the linear regime, these systems exhibit both real and complex energy spectra, as well as out-of-equilibrium phenomena such as unidirectional wave amplification, known as the non-Hermitian skin effect. I will first extend this effect into the nonlinear regime, demonstrating the emergence of nonlinear skin states that evolve from their linear counterparts. Next, I will explore the interplay between the skin effect, topology, and nonlinearity, highlighting how this interaction can lead to nonlinear edge states with behaviours distinct from those of nonlinear skin modes. These nonlinear edge and skin states belong to a class of spatially localised, standing nonlinear solutions that appear at the system’s interface. Finally, I will discuss how the formation mechanisms, stability, and dynamics of these solutions differ from, and sometimes surpass, what is typically achievable with Hermitian systems. This work is in collaboration with Vassos Achilleos.
Biography: I am currently a Postdoctoral Researcher at the Acoustics Laboratory of Le Mans University (LAUM), where my research focuses on the role of nonlinearity in active non-Hermitian metamaterials and its potential for advanced wave control. This is my second postdoctoral position at LAUM; in my first, I concentrated on the interplay between topology, nonlinearity, and disorder, exploring how these phenomena can be simultaneously harnessed for wave manipulation in mechanical metamaterials. Prior to this, I completed my PhD in 2021 at the University of Cape Town (UCT) in South Africa, where I investigated the dynamical behavior of Anderson localization in disordered nonlinear media. Consequently my research interests encompass disorder, nonlinearity, and topology, with applications in both Hermitian and non-Hermitian systems.
Seminar 1: Predicting and optimizing wave motion in spatially graded structures
Speaker: Prof. Dennis M. Kochmann
Abstract: Periodic metamaterials and architected materials have emerged as powerful tools for, among others, controlling or suppressing elastic waves by bandgap engineering. However, wave guidance can also be achieved without bandgaps. Moreover, the manufacturable design space extends far beyond periodic structures. Spatially graded architectures with smoothly varying unit cell designs have hardly been explored for wave manipulation but offer a rich playground for wave manipulation. We here present a combined experimental-computational study into this rich design space at the example of spatially graded beam lattices. We confirm experimentally that Bloch-Floquet theory is an accurate approximation, as long as the grading in unit cell design is smooth. We further introduce ray tracing for dispersive elastic media as a convenient numerical approach to predict and optimize wave motion in graded structures. As an example, we demonstrate how conformal mappings can be exploited to create spatially graded structures which are capable of low-pass wave attenuation and wave guidance. Moreover, we discuss how computational design optimization can lead to interesting and peculiar wave motion in graded structural networks.
Biography: Dennis M. Kochmann received his education at Ruhr-University Bochum in Germany and at the University of Wisconsin-Madison. After postdoc positions at Wisconsin and Caltech, he joined the Aerospace Department at Caltech as Assistant Professor in 2011. In 2016 he was promoted to Professor of Aerospace, a position he held through 2019. Since April 2017 he has been Professor of Mechanics and Materials at ETH Zürich, where he served as Head of the Institute of Mechanical Systems and as Deputy Head of Department. His research focuses on the link between microstructure and properties of natural and architected materials, which includes the development of theoretical, computational, and experimental methods to bridge across scales from nano to macro. His research has been recognized by, among others, IUTAM’s Bureau Prize in Solid Mechanics, GAMM’s Richard von Mises Prize, ASME’s T.J.R. Hughes Young Investigator Award, an ERC Consolidator Grant, and recently IACM’s John Argyris Award. He is on the Board of Directors of the Society of Engineering Science, and serves as Associate Editor for Archive of Applied Mechanics and Applied Mechanics Reviews.