Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams

Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics through the concepts of differential geometry can help to address the non-linear phenomena in their intrinsic qualities. This results in a field of research aimed at establishing and solving dynamic models purged of any artificial nonlinearity by taking advantage of symmetry properties underlying the use of Lie groups. The geometric constructions needed for reduction are presented in the context of the "covariant" approach.Comment: Submitted to GSI2013 - Geometric Science of Informatio

Frequency locking of modulated waves

We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be close to the modulation frequency of the modulated wave solution, while the wave frequency of the forcing is supposed to be far from that of the modulated wave solution. We describe the domain in the three-dimensional control parameter space (of frequencies and amplitude of the forcing) where stable locking of the modulation frequencies of the forcing and the modulated wave solution occurs. Our system is a simplest case scenario for the behavior of self-pulsating lasers under the influence of external periodically modulated optical signals

On the Dynamics of Elastic Strips.

The dynamics of elastic strips, i.e., long thin rods with noncircular cross section, is analyzed by studying the solutions of the appropriate Kirchhoff equations. First, it is shown that if a naturally straight strip is deformed into a helix, the only equilibrium helical configurations are those with no internal twist and whose principal bending direction is either along the normal or the binormal. Second, the linear stability of a straight twisted strip under tension is analyzed, showing the possibility of both pitchfork and Hopf bifurcations depending on the external and geometric constraints. Third, nonlinear amplitude equations are derived describing the dynamics close to the different bifurcation regimes. Finally, special analytical solutions to these equations are used to describe the buckling of strips. In particular, finite-length solutions with a variety of boundary conditions are considered

Stories in mental health reflection, inquiry, action

Mcallister, MM ORCiD: 0000-0003-1181-1610This is an extraordinary collection of personal stories from a range of mental health consumers, carers and mental health nurse clinicians who openly share their experiences. This is an important new mental health resource

Stories in mental health reflection, inquiry, action

This is an extraordinary collection of personal stories from a range of mental health consumers, carers and mental health nurse clinicians who openly share their experiences. This is an important new mental health resource

Bursting oscillations in optical parametric oscillators

Different forms of bursting oscillations with frequencies from a few MHz to hundreds of MHz separated by intervals of no activity have been observed experimentally for an optical parametric oscillator (OPO) system subject to thermal effects. These oscillations have been simulated numerically using previously derived equations for two interacting transverse modes. In this paper, we investigate one particular case in detail and show that a simple phase-plane analysis explains the bursting cycle. Furthermore, by taking advantage of the values of the parameters, we determine an approximation for the solution of the OPO equations, leading to estimates of the oscillation frequency and of the threshold of the bimode regime. © 2003 The American Physical Society.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Instabilités et chaos dans les oscillateurs paramétriques optiques

Nous discutons quelques mécanismes d'instabilité récemment observés dans un oscillateur paramétrique optique (OPO) : d'une part des instabilités opto-thermiques où le système oscille autour des courbes de résonance d'un ou plusieurs modes, d'autre part des oscillations rapides résultant de l'interaction de plusieurs modes transverses. La première observation expérimentale de chaos déterministe dans un OPO est également présentée