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Sharing experience across physics silos: The Laplacian and Wave Mechanics

In every topic branch of physics, and in every sector of society where physics is encountered, we encounter mathematical models.  In almost every case, we see either the Laplacian or the wave equation.  What those equations represent varies from specialism to specialism, but our initial approach is fundamental and forms a significant part of the physics taught in schools.

So, I would like to pose a series of questions:

  1. How do we present those concepts, in the outreach context, at school, at university, in industry, and to researchers in the field?
  2. What is the significance of these concepts in different physics specialisms?  What must be measured, modelled, or represented?
  3. What other awkward mathematical terms appear in the equations for different specialisms, and what impact does that have on the methods of solving the equations?
  4. How is this significant within the sector?  Is this progress towards physics discovery, to improve a product or capability, or to develop and improve lives?  What would the value be to society in making such an advance?

The event will comprise talks given by specialists in different fields, giving an overview of how they would answer these questions in their context.  This would be followed by a discussion session, with a view to sharing experiences and developing ideas.  During the discussion session, afternoon tea will be served.