I will discuss recent investigatations of highly nonlinear solitary waves in granular chains using numerical computations, analytical calculations, and experiments. I will provide an introduction to granular chains, and then I will focus on the dynamics of intrinsic localized modes (aka, discrete breathers) in diatomic chains and chains with defects.
Molecular monolayers are playing an ever increasing role in technology as they allow manipulation of contact properties of materials in a precise and controlled manner. In order to derive simplified models of such systems, we consider the dynamics of monolayers of rolling self-interacting particles with an off-set center of mass and a non-isotropic inertia tensor. For the purpose of this work, we assume the properties of the particles (mass, inertia tensor etc) to be the same as water molecules. The perfect rolling constraint is considered as a simplied model of a very strong, but rapidly decaying bond with the surface. Since the rolling constraint is non-holonomic, it prevents the application of the standard tools of statistical mechanics. We show the existence and nonlinear stability of ordered lattice states. We also investigate the effect of rolling on the disturbance propagation through a crystalline lattice , and study the chaotic vibrations of the crystalline states. Finally, we investigate the dynamics of disordered gas states and show that there is a surprising and robust linear connection between distributions of angular and linear velocity for both lattice and gas states, allowing to define the concept of temperature. B. Kim and V. Putkaradze, Phys. Rev. Lett. 105, 244302 (2010)
The first part of the talk focuses on the locomotion of a specific organism, namely, a water snail, that exhibits a striking ability to "crawl" beneath the free surface. By modeling the foot of the snail as undergoing a simple sinusoidal motion, we apply lubrication approximations for small deformations to rationalize this peculiar mode of transport and its dependency on surface tension. While the first part is a theoretical investigation of low Reynolds locomotion, the second part of the talk features an experimental study of the flow field inside a water drop held stationary in a flowing external oil. The droplet is anchored in place by introducing a local variation in the channel height which reduces the free surface energy. Two contrasting flow regions are visible inside the drop: a fast recirculation flow is observed near the droplet boundary, while a slower flow takes place in the central region. In particular, the flow near the droplet edge displays strong three-dimensional recirculation, which requires further investigation.
The Starling resistor is a laboratory setup in which a length of elastic tube is mounted on two rigid tubes and the collapsible part of the system is usually contained within a pressurized chamber. A fluid is driven through the tubes either by imposing some flow rate upstream from the collapsible segment or by controlling a pressure difference along the tubes. Experiments with this apparatus, initially used for studying various physiological flows, yield an interesting fluid-structure interaction problem - in almost all such collapsible tubes experiment with Re > 200 a variety of spontaneous self-exited oscillations is observed. There are several possible mechanisms in the domain of flowstructure interactions for these oscillations and it is unclear which is operative in any particular experiment. It is very likely that different mechanisms operate in different parameter regimes. Although this problem is an intrinsically three-dimensional nonlinear fluid-structure interaction problem, physical insight can nevertheless be obtained from studying lower-dimensional models. In our work we focus on a 2D analogy of the Starling resistor - a collapsible channel. It represents a planar channel with a segment of one of the walls replaced by an elastic membrane under constant pretension and external pressure and containing a high Reynolds number laminar flow of a Newtonian incompressible fluid. We use ideas of interactive boundary layer theory by Smith(1976) and inviscid large amplitude long wavelength analysis by Pedley&Stephanoff(1985) to study the system. F.T. Smith, Quarterly J. Mech. and Appl. Math., 29: 343-376, 1976. T.J. Pedley and K.D. Stephanoff, J. Fluid Mech., 160: 337-367, 1985.
TBA
TBA
Refreshments will be provided in the basement social area of the Schuster Lab. from 3.30pm. If you have any suggestions for future speakers, please contact Dr Mickaël Pailha.