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. A unifying theme of my research work is to study the model-independent features that transcend the intrinsic properties (physics, biology, or engineering related) of a given phenomenon. One such property, which is a central theme on my work, is symmetry. Representative examples of current and previous research projects include:

  • Biologically-inspired Sensor Devices
    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. The new sensor devices are up to four times more sensitive than conventional sensors. The work has been supported by NSF, ONR, DoD, and has lead to internships for students, manuscripts, and multiple U.S. patents, please see vitae.


  • Microwave Signal Generator at the Nano-scale
    The 2007 Nobel prize in Physics was awarded jointly to Albert Fert and Peter Grunberg for their discovery of the Giant Magnetoresistance Effect (GMR). The GMR effect can convert the magnetic precession of an electron into microwave voltage signals and turn the oscillator into a Spin Torque Nano-Oscillator (STNO) but its power output, about 1 nW, is too small for practical applications. A possible solution is to synchronize several STNOs so that a coherent signal with a common frequency and phase can be extracted from the ensemble to produce a more powerful microwave signal. Supported by NSF, I am currently studying and classifying the various coherent statesthat an ensemble of STNOs can produce, finding conditions for the existence and stability of such coherent states, determining the effects of different couplings and connection topologies.

  • Superconductivity
    Supported by NSA Tactical SIGINT Technology Program, I have conducted extensive analysis and computer simulations of the collective voltage response of arrays of superconducting quantum interference devices. The goal is the development of a sensitive, low noise, significantly lower Size, Weight and Power (SWaP) antenna, capable of meeting all requirements for certain class ships for Information Operations/Signals Intelligence (IO/SIGINT) applications in Very High Frequency/Ultra High Frequency (V/UHF) bands. The device will increase the listening capability of receivers by moving technology into a new regime of energy detection allowing wider band, smaller sized, more sensitive, more stealth systems.

  • Basins of Attraction
    We have developed computational methods to visualize basins of attractions for coupled bistable systems. Code is available under this folder: CCFM_Manifolds.
 
 
Milk Splash