# Registered Data

## [00545] Waves in complex and multiscale media

**Session Time & Room**:**Type**: Proposal of Minisymposium**Abstract**: Characterizing wave propagation in complex and multiple-scale media is important for modelling and simulating the propagation of acoustic, electromagnetic, elastic and water waves in heterogeneous media. This minisymposium demonstrates the ubiquity of mathematical techniques by bringing together researchers from all of these application areas. The talks will illustrate a variety of the current methods and the challenges that remain. The session will represent a cross section of applied mathematics, ranging from applied analysis to large-scale numerical simulation schemes. A central aim of the minisymposium is to promote the exchange of ideas and knowledge between the different application areas.**Organizer(s)**: Bryn Davies, Luke Bennetts**Classification**:__35J05__,__76B15__,__34M30__**Minisymposium Program**:- 00545 (1/3) :
__5B__@__G406__[Chair: Bryn Davies] **[03757] Effective waves in random particulate media: introduction and numerical validation****Format**: Talk at Waseda University**Author(s)**:**ARTUR LEWIS GOWER**(University of Sheffield)- Stuart Hawkins (Macquarie University)
- Gerhard Kristensson (Lund University)

**Abstract**: Describing how waves scattering between a large set of particles is challenging. There are accurate numerical methods, but they lack intuition and can be slow. Effective theory is a method to replace the particles with a homogeneous media which leads to greater intuition and is quick to calculate. One drawback is often that effective theory is only accurate for long wavelengths. In this talk, I will show how we overcame the challenges to extend effective theory for a large range of wavelengths (0 < k a < 2) and material properties (particle type and volume fractions) for waves in a random particulate material.

**[04234] Scattered wavefield in the stochastic homogenization regime****Format**: Talk at Waseda University**Author(s)**:**Laure Giovangigli**(ENSTA Paris)- Quentin Goepfert (ENSTA Paris)
- Pierre Millien (Institut Langevin, ESPCI)
- Josselin Garnier (Ecole Polytechnique)

**Abstract**: This work aims at modelling and studying the propagation and diffusion of ultrasounds in complex multi-scale media such as biological tissues or composite materials. We consider in the free space a homogeneous bounded medium in which lie randomly distributed inhomogeneities that are small compared to the wavelength. In order to characterize the response of this medium to an incident plane wave, we perform an asymptotic expansion of the scattered wave with respect to the size of the inhomogeneities using stochastic homogenisation techniques. The difficulties lie in the transmission conditions at the boundary of the medium. We derive quantitative error estimates given that the random distribution of inhomogeneities verifies mixing properties. Finally we present numerical simulations to illustrate and validate our results.

**[04262] Waves on Graphs****Format**: Talk at Waseda University**Author(s)**:**Gregor Tanner**(University of Nottingham)- Stephen C Creagh (University of Nottingham)
- Cerian Brewer (University of Nottingham)

**Abstract**: We consider the wave dynamics on networks or graphs carrying both propagating and evanescent modes on each edge. This is an extension of quantum graph theory and occurs naturally when considering networks of plates or beams with different mode types (flexural, longitudinal and shear waves) propagating on each connecting structure. The local vertex scattering matrices and the global transfer operator are no longer unitary with interesting consequences for secular equations and the Weyl law.

**[04615] Designing large-scale acoustic scattering systems using structural optimization and multiple scattering theory****Format**: Talk at Waseda University**Author(s)**:**Kei Matsushima**(The University of Tokyo)- Takayuki Yamada (The University of Tokyo)

**Abstract**: In this talk, we present a numerical scheme for designing large-scale acoustic scattering systems based on a multiple scattering theory and shape/topology optimization. We first solve exterior Helmholtz problems using the T-matrix method. This formulation allows us to evaluate a design sensitivity of multiple scattering systems using the adjoint variable method. We will demonstrate that the proposed scheme can design an omnidirectional acoustic cloak.

- 00545 (2/3) :
__5C__@__G406__[Chair: Luke Bennetts] **[04940] Bounds on the Quality-factor of Two-phase Quasi-static Metamaterial Resonators and Optimal Microstructure Designs****Format**: Talk at Waseda University**Author(s)**:- Kshiteej Deshmukh (University of Utah)
**Graeme Milton**(University of Utah)

**Abstract**: Material resonances are fundamentally important in the ﬁeld of nano-photonics and optics. So it is of great interest to know what are the limits to which they can be tuned. The bandwidth of the resonances in materials is an important feature which is commonly characterized by using the quality (Q) factor. We present bounds on the quality factor of two-phase quasi-static metamaterial resonators evaluated at a given resonant frequency by introducing an alternative definition for the Q-factor in terms of the complex effective permittivity of the composite material. Optimal metamaterial microstructure designs achieving points on these bounds are presented. The most interesting optimal microstructure, is a limiting case of doubly coated ellipsoids, consisting of a dilute suspension of ellipsoids near resonance sandwiched between layers. It attains points on the lower bound for the Q-factor. We also obtain bounds on Q for three dimensional, isotropic, and fixed volume fraction two-phase quasi-static metamaterials. Some almost optimal isotropic microstructure geometries are identified.

**[04245] Band structure and Dirac points of real-space quantum optics in periodic media****Format**: Talk at Waseda University**Author(s)**:**Erik Orvehed Hiltunen**(Yale University)- John Schotland (Yale University)
- Michael Weinstein (Columbia University)
- Joseph Kraisler (Columbia University)

**Abstract**: The field of photonic crystals is almost exclusively based on a Maxwell model of light. While often an effective model, it is natural to study such systems under a quantum-mechanical photon model instead. In the real-space parametrization, interacting photon-atom systems are governed by a system of \emph{nonlocal} partial differential equations. In this talk, we study resonant phenomena of such systems. Using integral equations, we phrase the resonant problem as a nonlinear eigenvalue problem. In a setting of high-contrast atom inclusions, we obtain fully explicit characterizations of resonances, band structure, and Dirac cones. Additionally, we present a strikingly simple relation between the Green's function of the nonlocal equation and that of the local (Helmholtz) equation. Based on this, we are able to achieve highly efficient numerical calculations of band structures of interacting photon-atom systems.

**[03889] Mathematics of in-gap interface modes in photonic/phononic structures in one dimension****Format**: Talk at Waseda University**Author(s)**:**Hai Zhang**(HKUST)- Junshan Lin (Auburn University)

**Abstract**: The developments of topological insulators have provided a new avenue for creating interface modes (or edge modes) in photonic/phononic structures. Such created modes have the distinct property of being topologically protected and are stable with respect to perturbations in certain classes. In this talk, we will report recent results on the existence of an in-gap interface mode that is bifurcated from a Dirac point in a photonic/phononic structure in one dimension.

**[04807] Recent advances in the theory of field patterns****Format**: Talk at Waseda University**Author(s)**:**Ornella Mattei**(San Francisco State University)- Vincenzo Gulizzi (University of Palermo)

**Abstract**: Field pattern materials are spatial composites whose properties are modulated in time in such a way that disturbances propagate along locally periodic networks of characteristic lines, called field patterns. Depending on the material properties, modes can be propagating or can blow up (decay) in time. Here we show how to design the spatial geometry of one- and two-dimensional field pattern materials, so that modes are always stable.

- 00545 (3/3) :
__5D__@__G406__[Chair: Bryn Davies] **[05192] Water wave resonances between floating vessels: fundamentals to applications****Format**: Talk at Waseda University**Author(s)**:**Hugh Wolgamot**(University of Western Australia)- Wenhua Zhao (University of Western Australia)

**Abstract**: The narrow gap formed between floating vessels in close proximity supports resonances. This leads to a variety of problems of both theoretical and practical interest. In this talk the resonant structure of the coupled motion of the vessels and fluid is first investigated using linear potential flow theory for simple geometries. The interaction of prismatic vessels spanning a channel (a common experimental set-up) is then considered. Interaction with practical mechanical constraints (mooring) is discussed.

**[03152] Broadband energy capture by an array of heaving buoys****Format**: Talk at Waseda University**Author(s)**:**Amy-Rose Westcott**(The University of Adelaide)- Luke Bennetts (The University of Adelaide)
- Benjamin Cazzolato (The University of Adelaide)
- Nataliia Sergiienko (The University of Adelaide)

**Abstract**: Broadband energy capture is sought by grading the resonant properties of an array of heaving buoy-type wave energy converters (WECs) in 2D. Linear potential-flow theory is applied and WEC interactions are modelled using multiple-wave scattering theory. The resonant properties of WECs are tuned via a linear spring-damper power take-off mechanism to manipulate the complex-frequency zeros. The resulting graded array captures near-perfect absorption (>97% of incident energy) from a targeted band of wavelengths spanning 1.5 times the array's length.

**[04111] Graded arrays for spatial frequency separation and amplification of water waves****Format**: Talk at Waseda University**Author(s)**:**Malte A Peter**(University of Augsburg)- Luke G Bennetts (University of Adelaide)
- Richard V Craster (Imperial College London)

**Abstract**: Wave-energy converters extracting energy from ocean waves are known to suffer from poor efficiency. We propose structures substantially amplifying water waves over a broad range of frequencies at selected locations, with the idea of enhanced energy extraction. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified locations. Transfer-matrix analysis is used for the analysis and results from wave-flume experiments confirm the amplification in practice.

**[05656] Unstable Wave Dynamics in Sea Ice****Author(s)**:**Amin Chabchoub**(Kyoto University )- Alberto Alberello (University of East Anglia)
- Emilian Parau (University of East Anglia)

**Abstract**: Wave and sea ice properties in the Arctic and Southern Oceans are linked by feedback mechanisms. Therefore, the understanding of wave propagation in these regions is essential to model this key component of the Earth climate system. The most-striking effect of sea ice is the attenuation of waves at a rate proportional to their frequency. The nonlinear Schrödinger equation (NLS), a fundamental model for unidirectional and narrowband ocean waves, describes the full growth-decay cycles of unstable modes, a mechanism also known as modulational instability (MI). Here, a dissipative NLS (d-NLS) with characteristic sea ice attenuation is used to model the evolution of unstable waves. The MI in sea ice is preserved, however, in its phase-shifted form. Moreover, the frequency-dependent dissipation breaks the symmetry between the dominant left and right sideband.

- 00545 (1/3) :