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SUMMARY:Elasticity and (dis)orders in networks and cellular patterns - Dr 
 Marc Durand\, Université Paris Diderot
DTSTART:20121019T130000Z
DTEND:20121019T140000Z
UID:TALK39477@talks.cam.ac.uk
CONTACT:Ms Helen Gardner
DESCRIPTION:Networks are heterogeneous materials whose continuous phase is
  assembled into slender objects - the links - that are connected to each o
 ther at nodes.\nThe macroscopic properties (elasticity\, transport\,...) o
 f such systems crucially depend on the specific arrangements of their comp
 onents. In the first part of this talk\, I will study the conditions for e
 xistence of "optimal networks"\, i.e. isotropic networks with highest elas
 tic moduli (and electrical conductivity) for a given density. Using a vari
 ational approach in an unconventional way\, I will show that a simple set 
 of rules can be established on the geometry and topology of the nodes in s
 uch networks. Networks that satisfy these rules can effectively be built a
 nd I will provide examples at two and three dimensions. The elastic moduli
  (and electrical conductivity) of these optimal networks constitute upper-
 bounds which compete or\nimprove the well-known Hashin-Shtrikman bounds.\n
 The second part of the talk will be devoted to the description of disorder
 s in two-dimensional cellular patterns\, such as dry foams: the macroscopi
 c properties of these systems are affected by two kinds of disorders: the 
 first one is the geometrical disorder\, defined as the relative width of t
 he distribution of cell sizes\, and the second one is the topological diso
 rder\, defined as the relative width of the distribution of the number of 
 sides of a cell. I will show that in fact these two quantities are strongl
 y correlated: a monodisperse foam contains mostly hexagonal cells\, while 
 in a polydisperse foam\, larger bubbles have more sides. A model\, based o
 n the formalism of statistical mechanics\, has been eveloped to explain th
 e quasi-linear dependence of the two disorders.
LOCATION:Oatley Seminar Room\, Department of Engineering
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