The ODEN group for Applied Mathematics (AMG) is an interdisciplinary research effort from departments including Mathematics, Statistics, Physics and Computer Science.
We focus our research on the modeling, classical and statistical analysis and numerical simulations of non-linear phenomena.
Some of the current research projects include a wide range of theoretical and computational aspects of mathematical models from non-linear dynamics for classical and semi classical fluid systems as well as quantum and statistical transport dynamics in biological systems.
In particular, we study:
- some aspects of collisional and collision-less plasmas
- integral diffusion (Levy) processes; multi-scale modeling in high frequency wave propagation, visibility optimization and image processing
- non-linear elasticity in periodically or randomly heterogeneous media
- multi-scale non-linear flows with applications to dispersive wave propagation, hydrodynamics; transport in porous media, macroscopic/mesoscopic and phenomenological models for phase transitions in spatial-temporal periodic and randomly heterogeneous media
- geomechanics, aerodynamics, biological and molecular dynamics
- charged particle transport emphasizing the linking of quantum, statistical and fluid mechanical states
- premixed and non-premixed turbulent combustion models in spatial-temporal periodic and randomly heterogeneous media
- statistical methods in nonparametric Bayes, optimal design and decision problems and clinical trial design
- mathematical epidemiology by network-based for spread prediction of infectious diseases and theoretical evolutionary dynamics in biology
- computational number theory and combinatorics.
The research has direct applications to the formulation, interpretation, and assessment of model non-linear phenomena on multiple dimensional spatial and temporal scales in very diverse geometrical configurations, and to their accurate and efficient approximation using high-performance computing.