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\begin{document}
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 \centerline{\large \bf Modeling, Simulation and Optimization of Surface}
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 \centerline{\large \bf Acoustic Wave Driven Microfluidic Biochips}
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 \centerline{Ronald H.W. Hoppe $^{1,2}$}
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 \centerline{$^1$ Dept. of Math., Univ. of Houston, Houston, TX 77204-3008,
 U.S.A.} \\
 \centerline{$^2$ Inst. of Math., Univ. of Augsburg, D-86159 Augsburg, Germany}
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\centerline{\bf Abstract}
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Biochips, of the microarray type, are fast becoming the default tool
for combinatorial chemical and biological analysis in environmental
and medical studies. Programmable biochips are miniaturized labs
that are physically and/or electronically controllable. The
technology combines digital photolithography, microfluidics and
chemistry. The precise positioning of the samples (e.g., DNA or
proteins) on the surface of the chip in picoliter to nanoliter
volumes can be done either by means of external forces (active
devices) or by specific geometric patterns (passive devices). The
active devices which will be considered here are nanoliter fluidic
biochips where the core of the technology are nanopumps featuring
surface acoustic waves generated by electric pulses of high
frequency. These waves propagate like a miniaturized  earthquake
(nanoscale earthquake), enter the fluid filled channels on top of
the chip and cause an acoustic streaming in the fluid which provides
the transport of the samples. The mathematical model represents a
multiphysics problem consisting of the piezoelectric equations
coupled with multiscale compressible Navier-Stokes equations that
have to be treated by an appropriate homogenization. We discuss the
modeling approach, present algorithmic tools for the numerical
simulation and address optimal design issues as well.
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