Rodolphe André Chabreyrie

Chaotic behavior has been observed both in nature and in the laboratory in a wide variety of systems including the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growths in ecology, the stock market, the dynamics of the action potentials in neurons, molecular vibration, electrical circuits, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices. Due to their omnipresence and the ever increasing demand of predictability in everyday life technology, chaotic systems present more and more challenges to the engineering community. One of today’s most formidable challenges is no longer to observe, but instead control, chaotic behavior in order to activate, increase, reduce or eliminate it as desired for particular applications. For instance, in systems where mixing is important chaotic behavior is highly desired. In contrast, in some electrical/electro-magnetic applications such as micro permanent magnet synchronous motors, chaotic behavior has to be eliminated. Our work deals with the elaboration and application, theoretically, computationally and experimentally, of strategies in order to control chaos. These strategies are applied to systems for which chaotic behavior plays a crucial role e.g., microfluidic devices, electrical and mechanical oscillators. 
Below are some descriptions of our main research activities.

Tailored Mixing Inside a Translating Droplet Using Resonance Strategy:

This work deals with the enhancing and control of chaotic advection or chaotic mixing within liquid droplets. We study Stokes flows corresponding to a translating spherical liquid droplet which we perturb by imposing a time-periodic rigid-body rotation. Using the tools of dynamical systems, we show that the rotation is not only able to create one or more three-dimensional chaotic mixing regions ... read more

Destabilizing Key Periodic Orbits for Complete Chaotic Mixing in an Electro-osmotic Mixer:

The ability to generate complete chaotic mixing (i.e., all initial conditions lead to chaotic pathlines) is of great interest in numerous applications, especially in microfluidic devices. In these devices, principally used as micro-chemical reactors, the presence of a complete chaotic mixing assures that all involved reactants are efficiently put into contact and blend together without leaving any clumps of isolated ... read more

Switching Chaos On/Off in an Inverted Pendulum by Bi-Chromic Forcing:

Monochromatic oscillatory forcing may result in the generation of chaotic behavior in dynamical systems. Such behavior, however, may be desired, as in microfluidic devices where mixing is required for heat transfer to take place or biochemical reactions to occur, or should be avoided as in a permanent magnet synchronous motor for which chaotic behavior has been observed to degrade the .... read more

 

Optimizing Chaotic Mixing in a Two-Inlet Microfluidic Channel by Out-of-Phase Pulsing:

D. Chang, J. He

Implementing chaotic mixing in microfluidic devices is a very difficult problem. Our approach to accomplishing complete chaotic mixing in the microfluidic T-Channel is through the use of out-of-phase inlet pulsing. The fluid velocities at oppositely faced inlets in the T-Channel are governed by identical sine curves with equal amplitudes and frequencies, only they are out of phase with ... read more