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SUMMARY:Modeling and analysis of chromonic liquid crystal condensates - Ca
 rme Calderer (University of Minnesota)
DTSTART:20190514T105000Z
DTEND:20190514T113000Z
UID:TALK124387@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The discovery of the liquid crystal phases of DNA and their st
 udy has attracted the attention of many scientists\, for several decades. 
 These include the contributions by soft matter physicists such as Professo
 r F. Livolant\, that began in the mid-1970&rsquo\;s. On the other hand\, t
 he observation of clustering phenomena in lyotropic liquid crystals\, anal
 ogous to that formed by DNA condensates and bacteriophage viral genome in 
 a capsid domain\, led John Lyndon to coin the chromonic denomination of th
 e liquid crystals formed by plank-like molecules (2013). All these liquid 
 crystals are found to form hexagonal columnar chromonic phases\, although 
 they differ in order of magnitude by a factor of 106. This presentation ad
 dresses modeling and analysis of bacteriophage viruses\, the toroidal stru
 ctures formed by condensed DNA in free solutions\, and the analogous pheno
 mena observed in lyotropic chromonic liquid crystals phases of materials w
 ith plank-like molecular shapes. Part of the presentation will focus on th
 e experiments performed by ProfessorLavrentovich&rsquo\;s group on materia
 ls such as food dyes--sunset yellow--and anti-asthmatic drugs. A special f
 eature determining the arrangement of DNA in a capsid is the dominant cont
 ribution of the elastic energy penalizing distortion of the cross sections
  perpendicular to the column axis. The central mathematical problem is for
 mulated as a free boundary problem for the Oseen-Frank and Ericksen&rsquo\
 ;s energies\, where the domain and the vector (or tensor) field are unknow
 n. The admissible set includes volume constraints as well as those express
 ing the high resistance of the chromonic structures to splay and twist def
 ormation. The first part of the presentation will involve general geometri
 es of the domain\, resorting to earlier analyses of liquid crystal droplet
 s. We will subsequently show that minimizers of the bending dominated cons
 trained energy have toroidal shapes. Moreover\, we will show that axisymme
 tric configurations lead to families of polyconvex energies for which mini
 mization can be established by standard methods of calculus of variations.
  Moreover\, in the case of bacteriophage viruses\, we will identify the ab
 solute minimizer as the coiling DNA configuration. We will conclude the pr
 esentation with the discussion of a numerical algorithm aimed at the desig
 n of viruses for applications to drug delivery and nanotransport.
LOCATION:Seminar Room 1\, Newton Institute
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