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SUMMARY:Nearly Isostatic Periodic Lattices - Prof. Tom Lubensky\, Departme
 nt of Physics and Astronomy\, University of Pennsylvania
DTSTART:20100603T130000Z
DTEND:20100603T140000Z
UID:TALK25091@talks.cam.ac.uk
CONTACT:Ms Helen Gardner
DESCRIPTION:In 1864\, James Clerk Maxwell showed that a system of N spheri
 cal particles in d-dimensions is mechanically stable only if the number\, 
 z\, of two-point contacts between particles exceeds z_c = 2d.  Systems wit
 h z=z_c are isostatic. Recent work confirms that randomly packed spheres a
 re isostatic at the point J where the volume fraction \\phi reaches the cr
 itical value \\phi_c necessary to support shear and that the mechanics of 
 this isostatic state determine behavior at volume fractions above \\phi_c.
   The square and kagome lattice with nearest neighbor springs are isostati
 c.  This talk will discuss the mechanical properties and phonon spectrum o
 f nearly isostatic versions of these lattices in which next-nearest-neighb
 or springs with a variable spring constant are added either homogeneously 
 or randomly.  In particular\, it will show that these lattices exhibit cha
 racteristic lengths that diverge as 1/(z-z_c) and frequencies that vanish 
 as (z-z_c) in agreement with general arguments by the Chicago group.  The 
 shear elastic modulus depends on the geometry of the isostatic network and
  is not universal.  Response near z=z_c in the random case is highly nonaf
 fine. This talk will also discuss an isostatic chiral variant of the kagom
 e lattice that has a vanishing bulk modulus and a negative Poisson ratio f
 or which diverging length and  vanishing frequency scales have not been id
 entified. Finally\, if time permits\, the application of some of these ide
 as to networks of semi-flexible polymers will be discussed.\n\n\nSouslov\,
  A.\, Liu\, A.J.\, and Lubensky\, T.C.\, Elasticity and Response in Nearly
  Isostatic Periodic Lattices\, Phys. Rev. Lett. 103\, 205503 (2009)\;   Ma
 o X.M.\, Xu N.\, Lubensky T.C. Soft Modes and Elasticity of Nearly Isostat
 ic Lattices: Randomness and Dissipation\, Phys. Rev. Lett. 104\, 085504 (2
 010).
LOCATION:Oatley Seminar Room\, Department of Engineering
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