Symmetry-Breaking Bifurcation: When the drop hits the surface of the glass filled with milk, the circular symmetry of the surface is broken creating a crown-like structure with less symmetry, Dihedral symmetry.


Research Projects

My research interests are in Modeling Complex Nonlinear Systems. In particular, multidisciplinary problems in science and industry that lie at the interface between Nonlinear Science and other disciplines such as Physics, Engineering, and Biology. Current and previous projects include:

  • Advanced Dynamical Magnetic Sensors (SPAWAR SSC San Diego)
    In collaboration with the Applied Chaos Group at the Space and Naval Warfare Systems Center (SPAWAR) in San Diego, we are develping techniques that exploit the inherent nonlinearity of coupled ferromagnetic elements to construct the next generation of highly-sensitive, low-cost, magnetic sensors. Applications of this work include: biomedical detection of magnetic-field particles, e.g., MRI machines, Homeland Defense, e.g., detection of weapons, terrorist targets, and surveillance on land and sea.

  • Multi-frequency Oscillations for Antenna Systems (SPAWAR SSC San Diego)
    Also in collaboration with SPAWAR, we are investigating, mathematically and computationally, practical mechanisms for real-time broad frequency switching in commercial and military communication systems. Of particular interest are antenna and radar systems.Current work includes building a prototype for comparison against theoretical results.

  • Spatio-Temporal Flame Patterns in Combustion Systems
    In collaboration with Peter Blomgren (Nonlinear Dynamical Systems Group at SDSU), we are studdying the mechanisms that lead to various types of nonstationary cellular flame patterns. In particular, we are investigating the effects of noise near points of bifurcation.

  • Bubble Dynamics in Fluidization Processes (Oak Ridge National Laboratory)
    In collaboration with Stuart Daw (ORNL), we are using ideas and methods from nonlinear dynamics, and computational techniques, to understand the bifurcations that govern the formation and evolution of gas-fluid bubbles in fluidization processes.
 
 
Milk Splash