Building mathematical models, applying numerical analysis and using computer programming to simulate complex non-linear dynamical systems.

The multi-group diffusion equation, both steady-state and unsteady state. These equations describe the distribution of neutronics in space, time and energy (more accurate descriptions of neutron transport based on the Boltzmann transport equation also take into account the angular neutron distribution). In steady-state this equation consists of G non-linear PDEs, where is the number of neutron energy groups. In the unsteady case these G PDEs are coupled to typically 6 PDEs describing the production of delayed neutrons.

Single- and two-phase fluid conservation equations. In the general unsteady case a set of 3 non-linear PDEs coupled to a number of algebraic equations (for void fraction, wall shear stress and sub-cooled boiling).

1-D Fluid conservations for stratified multi-component flows consisting of I+2 coupled non-linear PDEs, where I is the number of fluid components. The equations are solved in the Lagrangian frame to accommodate the near-discontinuous flow field of the stratified fluid.

I am also interested in financial mathematical modeling, mostly financial derivatives pricing models.

I have extensive knowledge, experience and interest in building large computer codes for simulation purposes.

I have built a complete coupled neutronics thermal-hydraulics model of a natural circulation BWR. To simulate reactor behavior with this model, I implemented a C code with more than 20,000 lines of well-commented and well-structured source code.

More recently I have done extensive modeling and simulation efforts addressing nuclear reactor containment responses. For this modeling effort, I have switched to C++ as my preferred programming language because of the clear advantages that object-oriented programming has to offer. The resulting C++ code has more than 50,000 lines of well-commented highly advanced C++ source code.

I spent a considerable effort applying state-of-the-art object-oriented analysis and design, including the use of Use Cases, CRC cards, and class interaction diagrams and class diagrams in UML. The resulting C++ code utilizes numerous design patterns both standard and new ones coined during the design phase of the project.