On the Hybrid Minimum Principle On Lie Groups and the Exponential Gradient HMP Algorithm

This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups $(G,\star)$ which are left invariant under the controlled dynamics of the system, and whose switching manifolds are defined as smooth embedded time invariant submanifolds of $G$. The analysis is expressed in terms of extremal (i.e. optimal) trajectories on the cotangent bundle of the state manifold $G$. The Hybrid Maximum Principle (HMP) algorithm introduced in \cite{Shaikh} is extended to the so-called Exponential Gradient algorithm. The convergence analysis for the algorithm is based upon the LaSalle Invariance Principle and simulation results illustrate their efficacy

Schizophrenic molecules and materials with multiple personalities - how materials science could revolutionise how we do chemical sensing

Molecular photoswitches like spiropyrans derivatives offer exciting possibilities for the development of analytical platforms incorporating photo-responsive materials for functions such as light-activated guest uptake and release and optical reporting on status (passive form, free active form, guest bound to active form). In particular, these switchable materials hold tremendous promise for microflow-systems, in view of the fact that their behaviour can be controlled and interrogated remotely using light from LEDs, without the need for direct physical contact. We demonstrate the immobilisation of these materials on microbeads which can be incorporated into a microflow system to facilitate photoswitchable guest uptake and release. We also introduce novel hybrid materials based on spiropyrans derivatives grafted onto a polymer backbone which, in the presence of an ionic liquid, produces a gel-like material capable of significant photoactuation behaviour. We demonstrate how this material can be incorporated into microfluidic platforms to produce valve-like structures capable of controlling liquid movement using light

Large-amplitude non-linear normal modes of piecewise linear systems

International audienceA numerical method for constructing non-linear normal modes (NNMs) for piecewise linear autonomous systems is presented. These NNMs are based on the concept of invariant manifolds, and are obtained using a Galerkin-based solution of the invariant manifold's non-linear partial differential equations. The accuracy of the constructed non-linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution, in both time and frequency domains. It is found that thisconstruction approach can accurately capture the NNMs over a wide range of amplitudes, including those with strong non-linear effects. Several interesting dynamic characteristics of the non-linear modal motion are found and compared to those of linear modes. A two-degree-of-freedom example is used to illustrate the technique. The existence, stability and bifurcations of the NNMs for this example are investigated