**Seminar 25, ****Tuesday**** **** 19 ****January**** 2021, 14:00 (London Time)**

Speaker: **Ross McPhedran **(School of Physics, University of Sydney, Australia)

Title**: Resonant States for Scattering Problems: Killing Mie Softly**

**Abstract:** This talk deals with issues common to those addressed by David Bergman, in that the topic is certain difficulties associated with complex resonant states encountered in scattering problems. These difficulties arise when one wishes to evaluate normalisation integrals and inner products for these states, which have rapid oscillations and diverging amplitudes at large dis- tances from the scatterer. Rather than using numerical treatments, the method presented here is analytic in nature, and relies on results of distri- bution theory. The method can yield closed form expressions for integrals over an infinite range involving the product of two Bessel functions of the same or different types, combined with a power of the radial distance. The essential point is that for rapidly oscillating functions with mean zero, the contribution to the integrals from the infinite upper limit is zero, despite the diverging amplitudes (equivocation trumps exaggeration).

** Biography: **Ross McPhedran is an Emeritus Professor at the University of Sydney, a Fellow of the Australian Academy of Science and the Optical Society of America, the Institute of Physics UK and the Australian Institute of Physics and doctor honoris causa of Aix-Marseille University.He works on problems in mathematical physics and wave science. Notably, he has many contributions to the theory of composite materials, the theory of diffraction gratings, and the theory of photonic, phononic, and platonic crystals, the latter name being chosen by Ross, and he codiscovered anomalous localized resonance. He has published over 300 articles in offered scientific journals, has an h index of 64 and around 17,000 citations on Google Scholar. He is the founding president of the ETOPIM association. The topic will include plasmonic resonances of particles, and the mathematical background to effective medium theories (particularly Bergman-Milton bounds and multipole theories).

**Seminar 26, ****Tuesday 26 January 2021****, 14:00 (London Time)**

Speaker: **Emil V Prodan **(Physics Department, Yeshiva University, New York, USA)

Title**: Phason Engineering for Topological Wave Steering**

**Abstract: **A general principle discovered by Jean Bellissard says that every aperiodic pattern has an intrinsic global degree of freedom that lives on a topological space called the hull of a pattern. This concept generalizes the notion of phason found in the physics literature on quasicrystals. In this talk, I will describe various ways to characterize and compute the hull of quasi-periodic patterns (i.e. aperiodic perturbations of periodic lattices) and then I will turn to problem of generating patterns with prescribed hulls, a process that I call phason engineering. Specifically, I will describe the main philosophy and supply a very general algorithm that produces phason spaces that are d-tori with d arbitrarily large. If discrete resonators are placed according to such a pattern, I will show that the hull augments the physical space, hence opening a door to the physic of the Integer Quantum Hall Effect in arbitrary dimensions. In the second part, I will demonstrate laboratory implementations of the ideas with mechanical and acoustic metamaterials that exhibit 2D and 4D IQHE physics. Among these examples, is the first un-assisted dynamical edge-to-edge Thouless pumping achieved in a laboratory.

**Biography:** Emil received BS and MS degrees in theoretical and mathematical physics from University of Bucharest. His advisor for the MS degree was mathematical physicists Gheorghe Nenciu. He received another MS degree in theoretical physics from University of Houston and then he graduated with a PhD from Rice University in theoretical physics. His advisor at Rice University was Peter Nordlander and his doctoral thesis was on large-scale quantum simulations of the plasmon response of nano-particles. Emil received further postdoctoral training at University of California Santa Barbara under the direction of Walter Kohn, a Nobel Laureate in theoretical chemistry. He was a fellow of the Princeton Center for Complex Materials at Princeton University, where he was sponsored by Roberto Car (2009 Dirac Medal) and Duncan Haldane (2016 Nobel Prize in Physics). Emil joined the Physics Department of Yeshiva University in 2007 and now he is a full professor of physics. While at Princeton, Emil witnessed Haldane’s effort on extending the concept of topological modes to photonic crystals, and he start working on the mechanical analog of the concept. The outcome, published in 2009 and co-authored with Camelia Prodan, was that Lagrangian systems containing q-dot-p terms can host Chern physics, a prediction confirmed experimentally in 2015. In about the same time, Emil’s research was profoundly influenced by the works of Jean Bellissard, who pioneered methods of analysis based on operator algebras, K-theory and non-commutative geometry. These days, together with many other enthusiasts, Emil is using these methods for search-and-discovery in materials science. He is also advertising what he calls Mathematical Engineering, where deep and utterly abstract concepts from pure mathematics are made concrete and applied, with a focus on advancing the technological progress rather than on just explaining observed phenomena.

**Seminar 27, ****Tuesday 02 **Februar**y**** 2021****, 14:00 (London Time)**

Speaker: **Nader Engheta **(Department of Electrical and Systems Engineering, University of Pennsylvania, USA)

Title**: TBA**

**Abstract: **TBA.

**Seminar 28, ****Tuesday 09 **Februar**y**** 2021****, 14:00 (London Time)**

Speaker: **Vincent Tournat **(Laboratoire d’acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique – Graduate School, France)

Title**: Nonlinear Waves and Flexible Elastic Metamaterials**

**Abstract: **Flexible elastic metamaterials can be described as artificial structures, designed to be highly compliant and capable of withstanding large elastic deformations. Their current significance lies in the fact that they possess a number of unusual properties that can be controlled and, in addition, they belong to an extremely large design space. While their static character has been widely studied, their dynamic properties are still in their early stages, especially with regard to their non-linear dynamics. Nevertheless, we recall here that these non-linear properties can be designed in a rational way, allowing the development of metamaterials for the control of large amplitude elastic waves [1-5]. In this context, I synthesize in this talk a set of our recent results on the propagation of nonlinear waves in these flexible elastic metamaterials [1-10], and I will draw up possible perspectives from these initiated directions, ranging from vibration control, toy models for fundamental wave physics, to possible practical applications.

[1] B. Deng, J.R. Raney, V. Tournat, K. Bertoldi, **Elastic vector solitons in soft architected materials**, Phys. Rev. Lett. 118(20), 204102 (2017). **PDF** **Supp. Mat.**

[2] B. Deng, P. Wang. Q. He, V. Tournat, K. Bertoldi, **Metamaterials with amplitude gaps for elastic solitons**, Nature Communications 9, 3410 (2018). **PDF** **Supp. Mat.**

[3] B. Deng, V. Tournat, K. Bertoldi, **Effect of predeformation on the propagation of vector solitons in flexible mechanical metamaterials**, Phys. Rev. E 98, 053001 (2018). **PDF**

[4] B. Deng, V. Tournat, P. Wang, K. Bertoldi, **Anomalous collisions of elastic vector solitons in mechanical metamaterial**, Phys. Rev. Lett. 122, 044101 (2019). **PDF** **Supp. Mat.**

[5] X. Guo, V.E. Gusev, V. Tournat, B. Deng, K. Bertoldi, **Frequency-doubling effect in acoustic reflection by a nonlinear, architected rotating-square metasurface**, Phys. Rev. E 99, 052209 (2019). **PDF**

[6] B. Deng, C. Mo, V. Tournat, K. Bertoldi, J.R. Raney, **Focusing and Mode Separation of Elastic Vector Solitons in a 2D Soft Mechanical Metamaterial**, Phys. Rev. Lett. 123(2), 024101 (2019). **PDF** **Supp. Mat.**

[7] L. Jin, R. Khajehtourian, J. Mueller, A. Rafsanjani, V. Tournat, K. Bertoldi, D. M. Kochmann, **Guided transition waves in multistable mechanical metamaterials**, Proc. Natl. Acad. Sci. 201913228 (2020). **PDF**

[8] B. Deng, P. Wang, V. Tournat, K. Bertoldi, **Nonlinear Transition Waves in Free-standing Bistable Chains**, J. Mech. Phys. Sol. 136, 103661 (2020). **PDF**

[9] B. Deng, S. Yu, A. E. Forte, V. Tournat, K. Bertoldi, **Characterization, stability, and application of domain walls in flexible mechanical metamaterials**, Proc. Natl. Acad. Sci. 202015847 (2020). **PDF** **Supp. Mat**.

[10] B. Deng, J. Li, V. Tournat, P. Purohit, K. Bertoldi, **Dynamics of mechanical metamaterials: A framework to connect phonons, nonlinear periodic waves and solitons**, J. Mech. Phys. Sol. 147, 104233 (2021). **PDF**

**Biography:** Vincent TOURNAT (VT) is currently a Research Director at CNRS and is the director of Institut d’Acoustique – Graduate School. VT conducts research activities in the field of acoustics and nonlinear waves at the Laboratoire d’Acoustique de l’Université du Mans in France (LAUM UMR CNRS 6613). He graduated with a major in fundamental physics and acoustics and defended his PhD thesis on nonlinear acoustics in granular materials in 2003. His research ranges from elastic waves in complex solids (granular media and crystals, cracked solids, metamaterials) to audible range acoustics of metamaterials, nonlinear ultrasonics in liquids, nonlinear ultrasonic NDT of solids and laser ultrasonics. His main current research activities combine theoretical, computational and experimental methods for the study of nonlinear elastic and acoustic waves in metamaterials.

**Seminar 29, ****Tuesday 16 **Februar**y**** 2021****, 14:00 (London Time)**

Speaker: **Angela Madeo **(GEOMAS Laboratory of the Institut National des Sciences Appliquées de Lyon, France)

Title**: Towards the engineering design of metamaterials’ structures through micromorphic enriched continuum modeling**

**Abstract: **In this talk, I will show how enriched continuum models of the micromorphic type can be used to describe the dynamical behavior of anisotropic mechanical metamaterials. I will show to which extent one of the the proposed models, that I contributed to pioneer, is able to capture all the main microscopic and macroscopic characteristics of the targeted metamaterials, namely, stiffness, anisotropy, dispersion and band-gaps. The simple structure of our material model, which simultaneously lives on a micro-, a meso- and a macroscopic scale, requires only the identification of a limited number of frequency-independent parameters thus allowing the introduction of pertinent boundary conditions to be imposed at metamaterials’ boundaries when the model is framed in the context of Variational Principles. I will show how this model can be applied to the study of the scattering properties of finite-size metamaterials’ structures thus opening new perspectives for metastructural engineering design.

**Biography:** Angela Madeo is currently Full Professor at the GEOMAS Laboratory of the Institut National des Sciences Appliquées de Lyon. She obtained a Master of Science in Civil Engineering at the University of Rome “La Sapienza” (Italy) in 2005 and a second one in Engineering Science and Mechanichs at the Virginia Polytechnic Institute and State University (USA) in 2006. She obtained her PhD in Theoretical and Applied Mechanics at the University of Rome “La Sapienza” in 2009. She has been Associate Professor at INSA Lyon from 2010 to 2017. Her research expertise seats on the study of Enriched Models in Continuum Mechanics and their applications to mechanical metamaterials, as well as to other materials with heterogeneous microstructures. She is recipient of the ERC Consolidator Grant META-LEGO (2021-2026). She is member of the prestigious Institut Universitaire de France since 2016, when she was nominated asjunior IUF member for her ground-breaking research on enriched continuum modeling of metamaterials. She was recipient of the CNRS Bronze medal in 2015. She coordinates several research projects funded with National French grants (ANR), as well as European grants (ERC, RIA, Horizon 2020). She gives lectures in the Civil Engineering Departement of INSA-Lyon, mainly in the field of Applied Math- ematics, Continuum Mechanics and Mechanical Behavior of Materials with Microstructure. She co-authored more than 60 papers in high-level international journals, she is author of a book on Generalized Continuum Mechanics and Engineering Applications, edited by ISTE Editions in 2015 and she has an H-index of 30 (according to Google Scholar). She is member of the Editorial board of 3 high level international journals in the field of Theorethical and Applied Mechanics.

**Seminar 30, ****Tuesday 23 **Februar**y**** 2021****, 14:00 (London Time)**

Speaker: **Patrick Sebbah **(Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, Israel)

Title**: TBA**

**Abstract: **TBA.

**Seminar 32, Tuesday 09 **March** 2021, 14:00 (London Time)**

Speaker:** Gengkai Hu **(School of Aerospace Engineering, Beijing Institute of Technology, Beijing, China)

Title**: Elastic Metamaterials and Their Applications to Wave Control**

**Abstract: **Wave property of materials is intimately related to their microstructures. By carefully designing the microstructure, different wave functions not available for traditional materials can be envisaged. In this talk, I will demonstrated through three examples the elastic wave control by the design of elastic metamaterials. The first is elastic negative refraction by designing an elastic metamaterial with both negative effective mass and modulus. The second example focuses on elastic wave filtering, we show that solids with only single polarization mode (either transverse wave or longitudinal wave) can be designed with pentamode materials. Finally I will explain the principle to make an asymmetric metamaterials which breaks the property of symmetric stress, and apply it to design elastic wave cloak. These results demonstrate a great capacity of elastic wave tailoring by elastic metamaterials and will surely find engineering applications in the near future.

**Biography:** Gengkai Hu is currently the Chair Professor of solid mechanics at Beijing Institute of Technology (BIT). He received his Ph.D. in mechanics and materials from Ecole Centrale de Paris (France) in 1991 and spent two years at the same university as a postdoctoral research associate before joining BIT. He has written or coauthored more than 170 papers in refereed journals, and received the Award of National Outstanding Youth Scientist by National Natural Science Foundation of China in 2003, and National Outstanding Teacher Award in 2004. He and his research group led some of the early works on elastic metamaterials. His current research interests include: dynamic homogenization of composite materials, metamaterials for controlling elastic wave propagation

**Seminar 33, Tuesday 16 **March** 2021, 14:00 (London Time)**

Speaker:** William Parnell **(University of Manchester, UK)

Title**: TBA**

**Abstract: **TBA.

**Seminar 34, Tuesday 23 **March** 2021, 14:00 (London Time)**

Speakers:** Agnes Maurel **(Langevin Institute, ESPCI Paris, CNRS) **& Kim Pham** (IMSIA, ENSTA Paris, Institut Polytechnique de Paris, France)

Title**: TBA**

**Abstract: **TBA.

**Seminar 35, Tuesday 30 **March** 2021, 14:00 (London Time)**

Speakers:** Natalia Movchan **(Department of Mathematical Sciences University of Liverpool, UK)

Title**: TBA**

**Abstract: **TBA.

**Seminar 36, Tuesday 06 **April** 2021, 14:00 (London Time)**

Speaker:** Mahmoud I. Hussein **(Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder, USA)

Title**: TBA**

**Abstract: **TBA.

**Seminar 37, Wednesday 14 **April** 2021, 14:00 (London Time)**

Speaker:** Alexandra Boltasseva **(Purdue University, USA)

Title**: TBA**

**Abstract: **TBA.