Waves get messy when they meet messy materials. Light in a cloud, sound in a slurry, ultrasound in tissue, seismic waves in the ground, and every metamaterial that comes out of a real fabrication line with real imperfections. We have lots of clever tools for this: homogenisation, multiple scattering and multipole methods, diagrammatic expansions, random matrices, transmission matrices, reduced order models, multiscale numerics, inverse scattering. The catch is that each community tends to build its own tools separately.
This workshop is about bringing together mathematicians, physicists, and engineers for a week to work out together what the big open problems are, and work out viable directions to solve them. The workshop will be interactive with plenty of discussion, and will be an ideal event to get to know the broader community.
The structure of the week will likely be:
• Introductory talks, allowing everyone gets a working grip on the main approaches.
• Agree on the challenges and then debate and agree on the biggest challenges. Before the workshop the organisers will draw up a list of concrete challenges with input from the community, and you’re welcome to suggest some.
• Get stuck in. Small groups will tackle specific challenges. Each group will have a facilitator and a mix of senior and early-career people.
• Wrap up. All groups report back, and plan the next steps together.
Among the questions to be discussed:
• How stable are designed wave effects when the structure has random imperfections?
• Where do our approximations for natural materials break down, and can we put hard numbers on it?
• How do we get microstructure out of wave measurements, and go from microstructure to overall wave (or radiative) properties?
• How can we connect approaches like the Dyson equation and explicit multiple scattering, so results carry over from one to the other?
• Can we design broadband stop bands with disorder instead of despite it?
Who is the workshop for?
Anyone working on the maths of waves in complex, random or multiscale media, whether you specialize in: numerics, analysis, theoretical physicist or engineering mathematics. People in the functional materials community who care about how microstructure controls radiative properties are very welcome too. We particularly encourage early-career researchers to apply, including PhD students, postdocs and new lecturers.
Applications for participation will open in due course.
