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CATEGORIES:Applied and Computational Analysis Graduate Semina
r
SUMMARY:Homogenization and transport in confined structure
s for applications in nano-sensors - Dr Clemens He
itzinger (DAMTP)
DTSTART;TZID=Europe/London:20101119T160000
DTEND;TZID=Europe/London:20101119T170000
UID:TALK28069AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28069
DESCRIPTION:We present results for the mathematical modeling o
f nanotechnological field-effect sensors. First\,
we show how a homogenization problem for the elec
trostatics in these structures can be solved to fi
nd an effective equation with two jump conditions.
Based on this homogenized equation\, an existenc
e and uniqueness (around equilibrium) result and e
stimates for the solution of a 3d self-consistent
charge-transport model are given. This model has
been implemented as a parallelized 3d simulator t
hat can simulate realistic structures.\n\nIn order
to investigate noise in nanostructures\, we prese
nt a homogenization result for a stochastic ellipt
ic PDE that yields an effective equation for the (
co-)variance and a scaling law.\n\nFinally\, we pr
esent the derivation of a transport equation for 3
d structures that are confined in one or two dimen
sions from the Boltzmann transport equation. Exam
ples for these structures are nanowires\, ion chan
nels\, etc. In the case of confinement in two dir
ections (which corresponds to tubes) we find a dif
fusive transport equation. A crucial feature of t
his equation is that we can give explicit expressi
ons for the transport coefficients as functions of
the parabolic confinement potential. Computation
ally\, this means that\nwe have reduced the six-di
mensional problem to a 2d diffusion-type equation.
Entropy estimates are also given.\n\nNumerical s
imulation 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\, Wilberf
orce Road\, Cambridge
CONTACT:Dan Brinkman
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