Home

(In the) News

Curriculum Vitae

Book*Algorithms with Julia*

CAIML

Research

START Project

Publications: Journals

Publications: Conferences

Invited Presentations

Teaching

(In the) News

Curriculum Vitae

Book

CAIML

Research

START Project

Publications: Journals

Publications: Conferences

Invited Presentations

Teaching

Welcome to

Clemens Heitzinger's

homepage!

Clemens Heitzinger's

homepage!

The project *PDE Models for Nanotechnology* started in 2013
and is currently scheduled to run till 2019. The subject are
**deterministic and stochastic partial differential
equations** (PDEs) with applications in nanoscience and
nanotechnology. The project is funded by the START
program of FWF.

In nanoscience and nanotechnology, there are many timely applications
that give rise to **multiscale problems** in a natural
manner. Therefore we also concern ourselves with the homogenization of
deterministic and stochastic PDEs.

Noise, fluctuations, process variations, and **uncertainty
quantification** in general are another area where stochastic
PDEs are essential. In short, we go beyond deterministic models and
consider more general model equations that include dependencies on
random variables.

The mathematical aspects include

proving existence and uniqueness,

deterministic and stochastic homogenization problems, and

developing numerical methods, especially for stochastic PDE.

Important model equations in this context include, e.g.,

the Boltzmann transport equation and derived transport equations,

linear and nonlinear elliptic (Poisson) equations, and

systems such as the stochastic drift-diffusion-Poisson system.

Both deterministic and stochastic homogenization problems occur naturally in nanoscience and nanotechnology due to the often vastly different length scales of whole devices and their microscopic structure. Multiscale problems also arise when modeling materials with a periodic or random microscopic structure.

The applications include, e.g.,

nanowire bio- and gas sensors as more general structures than nanoscale transistors,

nanopore sensors,

confined structures with large aspect ratios and hence posing multiscale problems, and

materials with a microscopic structure that is to be designed.

I believe that mathematical modeling and numerical simulations of real-world problems are an important contribution to the rational design of new devices and technologies.

The ultimate goals are

to provide new mathematical models for multiscale problems and uncertainty quantification,

to develop new simulation capabilities based on these mathematical models, and

to provide quantitative understanding for the development of new technologies.