Uncertainty quantification, systems biology, fluid and solid mechanics, scientific computing, numerical analysis
Research projects
I am interested in the development, analysis and application of numerical methods for partial
differential equations with
stochastic parameters or forcing. Applications that I have studied
include modeling the effects of uncertain material properties and loading
on 3D elastic structures. Currently I am applying
these techniques to systems biology, where many parameters such as
reaction rates and protein concentrations are uncertain. Specifically, I
am studying the effects of variability in the location and rate of protein
synthesis on pattern formation in the dorso-ventral axis of the drosophila
embryo.
Previous projects include:
Numerical studies of fluid flow past rigid cylinders subject to vortex-induced vibrations (VIV)
at low mass-damping parameter. Specific considerations include vortex mode selection in the wake,
correlation length and force phasing.
Development and implementation of a hybrid particle/continuum method for Burgers' equation with a stochastic forcing term.
This algorithm couples an asymmetric excluded random walk model with a viscous Burgers' equation that represents the mean field
approximation to the dynamics. (summer work at LBNL)
Refereed Publications:
Foo, J., Wan, X., Karniadakis, G. `A Multi-Element Probabilistic
Collocation Method for PDEs with Parametric Uncertainty: Error Analysis
and Simulation' (submitted)
Foo, J., Yosibash, Z., Karniadakis, G. `Stochastic Simulation of
Riser-Sections with Uncertain Measured Pressure Loads and/or Uncertain
Material Properties.' Computer Methods in Applied Mechanics and
Engineering (2007) Vol 196: 4250-4271.
Bell, J., Foo, J., and Garcia, A. `Algorithm Refinement for the
Stochastic Burgers Equation.' Journal of Computational Physics
(2007) Vol 223 : 451-468.
Lucor, D., Foo, J., and Karniadakis, G. `Vortex mode selection of a
rigid cylinder subject to VIV at low mass-damping.' Journal of Fluids and
Structures (2005) Vol 20: 485-503.
Lucor, D., Foo, J., and Karniadakis, G. `Vortex mode selection of a
rigid cylinder subject to VIV at low mass-damping.' Proceedings Flow
Induced Vibrations. Eds. de Langre and Axisa. Ecole Polytechnique, Paris
(2004).
Lucor, D., Foo, J., and Karniadakis, G. `Correlation Length and
Force Phasing of a Rigid Cylinder Subject to VIV of Fully Coupled Fluid
Structure Interactions.' IUTAM Symposium on Integrated Modeling. Eds.
Benaroya, H., Weil, T. Dordrecht: Kluwer Academic Press, (2004) Vol. 75
: 187-199.
Publications in preparation:
Foo, J., Sindi, S., and Karniadakis, G. `Using the
Multi-Element Probabilistic Collocation Method for Sensitivity Analysis
in Cellular Signaling Networks.'
