University of Liverpool Research Centre in Mathematics and Modelling - Wave scattering and Solid Mechanics
These seminars are organised by Stewart Haslinger, University of Liverpool
These seminars take place bi-weekly on Tuesdays at 16:00 – 17:15 (GMT).
To sign up to participate in these seminars, please complete this registration form
The University of Liverpool Research Centre in Mathematics and Modelling (RCMM) seminar series will cover a wide range of topics in the theory of partial differential equations that describe the propagation of waves in non-uniform media (both periodic and non-periodic), asymptotic analysis and solid mechanics.
Tuesday 24th November
Alexander Movchan (University of Liverpool) Waves in Chiral Discrete Systems
Abstract: The talk will provide an overview of modelling for time harmonic vibrations of solids with systems of chiral resonators. As well as models for finite-sized structures, the presentation will include infinite periodic systems and Floquet-Bloch waves in both continuous and discrete systems.
Tuesday 8th December
Anastasia Kisil, (The University of Manchester) Edges and Point Scatterers: solving Helmholtz equation with complicated boundary conditions
Abstract: coming soon
Tuesday 10th November
Artur Gower, University of Sheffield (Lecturer in Dynamics, Department of Mechanical Engineering)
Ensemble average waves in random materials of any geometry
Which is more useful: knowing the effective properties of a material, or its effective wavenumbers? In a low frequency regime these are essentially the same, but when the wavelength becomes comparable to the microstructure’s size, they are not. Using a broad range of frequencies is needed to characterize materials and to design for broad wave speed control and attenuation.
Suppose we perform an experiment that measures the scattered field from a material with a random microstructure. We could then find what effective properties would lead to the same scattered field we measured. So far so good. But what if we took that same microstructure and molded it into a different geometry and then repeated the experiment? The bad news is that even when using the same frequency we would potentially find a different set of effective properties. In contrast, in this talk I show how effective wavenumbers are inherently related to the material microstructure and not its geometry. I will also show how to calculate the average scattered field, including the field scattered from a pipe geometry filled with particles and a spherical droplet filled with particles.