Research_interests

Nonlinear Dynamics and Chaos

My interest in nonlinear dynamics and chaos involves studying models governed by simple mathematical equations, yet possess complicated behaviours. The approaches to those systems include fixed-points analysis, Poincaré section and numerical simulation to investigate into the dynamics of the systems under different conditions and also the onset of chaos.

Fractals

My interest in fractals involves studying different methods of generating fractals, their properties and applications. These properties include tiling space, tuning dimension and universal generator. The applications include using fractals to model different natural processes and phenomena like coastline formation and terrain evolution.

Self-Organized Criticality

My interest in self-organized criticality involves studying cellular automaton models like sandpile. These studies can be either analytical or numerical. The analytical approaches include building a field theory for stochastic sandpile models, establishing scaling laws and transformations of the model for different structures to prove universality. The numerical approaches include reliable determination of the critical exponents, moment ratios and moment amplitudes, probing for finite-size corrections, and support for analytical approaches. The questions arising from those studies include universality class of different models and their behaviours against different structures. The ultimate question is, however, what the necessary and sufficient conditions for the occurrence of scale-invariant phenomena are.