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Molecular Random Tilings

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  • UserProfessor Juan P. Garrahan, UoN
  • ClockThursday 05 December 2013, 13:45-15:00
  • HouseTheory Library.

If you have a question about this talk, please contact Kevin Ralley.

The tiling of surfaces with simple polygons has fascinated scientists, mathematicians and artists over the years. The rules that govern the formation of periodic tilings provide the foundation for the classification of crystalline materials. More recently, the discovery of quasicrystals has inspired great interest in aperiodic tilings. A class of tilings in which translational symmetry is absent is obtained by using simple tile shapes like dominoes or regular rhombi. Such tilings problems, or the associated ones of dimer coverings, are of interest both in mathematics (for example in applied probability in connection to perfect sampling and mixing algorithms) and in physics (in connection to antiferromagnetism or to entropic models of quasi-crystals). In this talk I will describe recent theoretical/experimental work on molecular networks of surface adsorbed small organic molecules which spontaneously assemble into two-dimensional random tilings. This is a rare, if not unique, experimental realisation of such ideal systems. These molecular networks display structural features anticipated by theory for model tilings, such as so-called Coulomb phase behaviour and fractional excitations. The molecular networks we study, however, are intrinsically non-equilibrium, as they are dynamically arrested and present many similarities to glasses. I will also show how in these systems we can explore the phase behaviour of interacting planar tilings and dimer coverings, including predicted transitions between multiple random and ordered tiling phases.

This talk is part of the Theoretical Physics Seminars series.

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