The last few years have witnessed rapid developments in semiconductor
mathematical research including modeling, analysis and numerical simulations
of semiconductor device equations, ranging from the Schroedinger equation for
the evolution of the electron wave function to the drift-diffusion system for
the evolution of the 'electron gas' which is close to a Maxwellian equilibrium.
Like semiconductor devices, many proteins and biological systems are also devices
in exactly the engineering sense of the word. These devices have a definite function
described by an approximate device equation that is valid ONLY when the device is
working as designed. Devices have complex internal structure that allows them to
have a reasonably robust and simple equation and much of biological research is
really an inverse problem to determine the device equation.
The diversity of physical architectures for semiconductor devices and biological
ionic channels as well as the mathematical models they are based on has proven
to be a fruitful ground for interaction of researchers from different disciplines
in physics, biology, engineering, mathematics and scientific computation.
We plan to revisit existing intersections and to explore future directions in
modeling, analysis and numerics of classical and quantum transport in semiconductor
devices, and classical transport in biological ionic channels, and related topics.
The last two decades have seen an enormous amount of research activities in both
mathematical analysis and numerical simulations of the semiconductor device
equations as well as the ion transport equations for biological channels.
We can foresee even more activities in this area given the potential industrial
applications of semiconductor device and biological channel modeling.
This workshop will bring together experts representing a variety of different
approaches to semiconductor models as well as biological systems to report
their current research results in order to foster future collaborations and
strengthen existing ones between mathematicians and semiconductor/biological
This week-long workshop will consist of expository lectures by leaders in
different disciplines, regular research presentations and panel discussions
on future directions. Interactions between people from different communities
will be an important component of the workshop.
Classical & quantum transport in semiconductor devices
Semi-classical device modeling: hydrodynamic and kinetic models
Inverse problems in semiconductors and biological systems