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SUMMARY:Homogenization and transport in confined structures for applicatio
 ns in nano-sensors - Dr Clemens Heitzinger (DAMTP)
DTSTART:20101119T160000Z
DTEND:20101119T170000Z
UID:TALK28069@talks.cam.ac.uk
CONTACT:Dan Brinkman
DESCRIPTION:We present results for the mathematical modeling of nanotechno
 logical field-effect sensors.  First\, we show how a homogenization proble
 m for the electrostatics in these structures can be solved to find an effe
 ctive equation with two jump conditions.  Based on this homogenized equati
 on\, an existence and uniqueness (around equilibrium) result and estimates
  for the  solution of a 3d self-consistent charge-transport model are give
 n.  This model has been implemented as a parallelized 3d simulator that ca
 n simulate realistic structures.\n\nIn order to investigate noise in nanos
 tructures\, we present a homogenization result for a stochastic elliptic P
 DE that yields an effective equation for the (co-)variance and a scaling l
 aw.\n\nFinally\, we present the derivation of a transport equation for 3d 
 structures that are confined in one or two dimensions from the Boltzmann t
 ransport equation.  Examples for these structures are nanowires\, ion chan
 nels\, etc.  In the case of confinement in two directions (which correspon
 ds to tubes) we find a diffusive transport equation.  A crucial feature of
  this equation is that we can give explicit expressions for the transport 
 coefficients as functions of the parabolic confinement potential.  Computa
 tionally\, this means that\nwe have reduced the six-dimensional problem to
  a 2d diffusion-type equation.  Entropy estimates are also given.\n\nNumer
 ical simulation results are presented for all the models as well\, as are 
 comparisons to experimental data (field-effect biosensors\, ion channels).
 \n
LOCATION:MR13\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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