Research Group for Mathematical and Numerical Analysis of Dynamical Systems

NONLINEAR DYNAMICAL SYSTEMS

• Nonlinear dynamics of different scientific and engineering systems:
  Particle in a field of propagating waves. Particle on the surface of Rayleigh wave. Angular motion transfer mechanisms. Conveyance of thin films. Manipulation of bioparticles using travelling wave dielectrophoresis. Drives without stages.

• Control of coexisting attractors:
  Attractor control based on small external impulses. Strategies for motion control in the field of propagating waves. Non-Newtonian fluid flow control. Synchronization of dendritic neural networks.

• Identification of systems:
  Effect of self-orientation; its applicability for identification of systems’ parameters. Separation and identification of flows.

  

EXPERIMENTAL TECHNIQUES FOR DYNAMICAL SYSTEMS

• Development of new optical full-field fringe-based experimental techniques and adaptation of existing experimental techniques for analysis of dynamical systems. Hybrid numerical-experimental techniques.

• Time average moiré – adaptations for macro, micro and nano scale dynamical systems:

• New experimental methods – time average stochastic geometric moiré exploiting natural micro irregularities as moiré gratings, geometric moiré for identification of nano scale oscillations measured by atomic force microscopy, time average super moiré for geometric differentiation of time averaged images. Adaptations of time average reflection and shadow moiré for analysis of dynamical systems. Applicability of moiré based techniques for chaotic oscillations.  

• Time average photoelasticity – new experimental technique for analysis of dynamic stress fields. New method for visualisation of discontinuous stress fields.

• Applications of time average holography for analysis of micro and nano scale dynamical systems, MEMS, NOEMS. New method for identification of defects in oscillating microstructures.

 

 NUMERICAL METHODS FOR DYNAMICAL SYSTEMS

• New algorithms for computation of definite integrals. Applicable for real-time holography analysis.

• Development of cryptographic hash functions based on optical experimental time averaging techniques. Algorithms for image encryption based on optical moiré techniques.  

• Development of FEM based algorithms for conjugate smoothing of discontinuous fields. Applicable for visualisation of photoelastic and reflection moiré fringes.

• Algorithms for visualisation of patterns of fringes from dynamic FEM results.

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