News regarding the theory of field patterns:
Field patterns are a new type of wave propagating along orderly patterns of characteristic lines which arise in specific space-time materials, that we call filed pattern materials. These are space-time microstructures whose geometry in one special dimension plus time is somehow commensurate with the slope of the characteristic lines.
In this video you can see the disturbances as time evolves (see the plot on the left), in a checkerboard space-time geometry in which the two phases have the same wave speed (the disturbances are the points marked by blue dots in the right plot). Every time the disturbance hits a space-time boundary it splits into two waves, giving rise to an orderly pattern of characteristic lines, the field pattern.
For further information, read the following papers:
G.W. Milton, O. Mattei, 2017. Field patterns: A new mathematical object. Proc. R. Soc. A 20160819. DOI: http://dx.doi.org/10.1098/rspa.2016.0819.
O. Mattei, G.W. Milton, 2017. Field patterns without blow up. To appear in New J. Phys..
O. Mattei, G.W. Milton, 2017. Field patterns: a new type of wave with infinitely degenerate band
See also the news release by Paul Gabrielsen, "Field patterns" as a new mathematical object, describing our work on this brand-new theory.
I am a Postdoctoral Research Fellow at the Department of Mathematics at the University of Utah, where I work in collaboration with Prof. Graeme W. Milton . I completed my doctoral studies at the Department of Civil, Environmental, Architectural Engineering and Mathematics of the University of Brescia in Italy, where I was enrolled in the PhD course in Methods and Mathematical Modeling for Engineering. I earned my Phd title in February 2016, on completion of the defense of my thesis, titled On bounding the response of linear viscoelastic composites in the time domain: The variational approach and the analytic method, advised by Prof. Angelo Carini and co-advised by Prof. Graeme W. Milton .
Last update: August 29, 2017