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SUMMARY:The mathematics of charged liquid drops - Cyrill Muratov (New Jers
 ey Institute of Technology)
DTSTART:20190320T160000Z
DTEND:20190320T170000Z
UID:TALK121849@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk\, I will present an overview of recent analytical
  developments in the studies of equilibrium configurations of liquid drops
  in the presence of repulsive Coulombic forces. Due to the fundamental nat
 ure of Coulombic interaction\, these problems arise in systems of very dif
 ferent physical nature and on vastly different scales: from femtometer sca
 le of a single atomic nucleus to micrometer scale of droplets in electrosp
 rays to kilometer scale of neutron stars. Mathematically\, these problems 
 all share a common feature that the equilibrium shape of a charged drop is
  determined by an interplay of the cohesive action of surface tension and 
 the repulsive effect of long-range forces that favor drop fragmentation. M
 ore generally\, these problems present a prime example of problems of ener
 gy driven pattern formation via a competition of long-range attraction and
  long-range repulsion. In the talk\, I will focus on two classical models 
 - Gamow&#39\;s liquid drop model of an atomic nucleus and Rayleigh&#39\;s 
 model of perfectly conducting liquid drops. Surprisingly\, despite a very 
 similar physical background these two models exhibit drastically different
  mathematical properties. I will discuss the basic questions of existence 
 vs. non-existence\, as well as some qualitative properties of global energ
 y minimizers in these models\, and present the current state of the art fo
 r this class of geometric problems of calculus of variations.
LOCATION:Seminar Room 2\, Newton Institute
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