We study experimentally the interaction between two solitary waves that approach one another in a linear chain of spheres interacting via the Hertz potential. When these counterpropagating waves collide, they cross each other and a phase shift in respect to the noninteracting waves is introduced as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and is shown to be independent of viscoelastic dissipation at the bead contact. In addition, when the collision of equal amplitude and synchronized counterpropagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of the secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with an even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitudes are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the bead contact during solitary wave propagation.

The magnetic cannon is a simple device that converts magnetic energy into kinetic energy: when a steel ball with low initial velocity impacts a chain made of a magnet followed by a few other steel balls, the last ball of the chain is ejected at a much larger velocity. The analysis of this spectacular device involves understanding of advanced magnetostatics, energy conversion and collision of solids. In this article, the phenomena at each step of the process are modeled to predict the final kinetic energy of the ejected ball as a function of a few parameters which can all be experimentally measured.

Abstract. -We study experimentally and numerically the dynamics of the director of a liquid crystal driven by an electric field close to the critical point of the Fréedericksz Transition (FT). We show that the Landau-Ginzburg (LG) equation, although it describes correctly the stationary features of FT in a rather large range of the control parameter, cannot be used to describe the dynamics in the same range.The reasons of this discrepancy are related not only to the approximations done to obtain this equation but most importantly to the finite value of the anchoring energy and to small asymmetries on boundary conditions. The difference between static and dynamics is discussed.These results are useful in all of the cases where FT is used as an example for other orientational transitions.Transitions between different orientational orders appear in several systems characterized by strong anisotropy such as for example biological systems [1,2], anisotropic phase in superfluids [3,4], ferromagnetic [5] and elastic media [6]. Liquid crystals (LC), being constituted by elongated molecules, have a strong anisotropy of their physical properties, and are certainly the most common and general system where such a kind of transitions can be observed [7,8]. For example, a nematic liquid crystal, whose molecules are initially homogeneously aligned between two parallel plates, undergoes a transition to an elastically deformed state when a sufficiently high external electric, magnetic or optical field E is appropriately applied. This is the Fréedericksz transition (FT) characterized by its critical field E c ; this transition is very important, not only for its obvious industrial applications, but also because it is used as an example to understand other systems. The relevant order parameter of the FT is the unit pseudo vector n (the director) which defines the local direction of alignment of the molecules. A stability analysis at the mean-field level of FT shows that the transition is of second order and that the dynamics of the order parameter can be described by a Landau-Ginzburg The purpose of this letter is to show (experimentally and numerically) that although the static equilibrium measurements seem to agree with the LG, the experimental study of the fluctuations and the dynamics of n demonstrates that such a model does not describe correctly the time dependent behavior. This is a useful information because, even if the purpose of the LG is to give the threshold of the instability, it is often used in literature to predict the dynamics close to the critical point of the FT.We consider in this letter the dynamics of the FT of a nematic liquid crystal (NLC), subjected to an electric field E [7,8], but the results are general enough to be applied to other systems where FT is used as a reference of orientational instability. In order to fix the framework of this letter, let us recall that FT must not be confused with electroconvective instabilities because in FT, no stationary fluid motion exists. However time dependent hydro...