A simple microscopic model for the dynamics of adhesive failure

We consider a microscopic model for the failure of soft adhesives in tension based on ideas of bond rupture under dynamic loading. Focusing on adhesive failure under loading at constant velocity, we demonstrate that bi-modal curves of stress against strain may occur due to effects of finite polymer chain or bond length and characterise the loading conditions under which such bi-modal behaviour is observed. The results of this analysis are in qualitative agreement with experiments performed on unconfined adhesives in which failure does not occur by cavitation.Comment: 11 pages, 5 figure

The 'Cheerios effect'

Objects that float at the interface between a liquid and a gas interact because of interfacial deformation and the effect of gravity. We highlight the crucial role of buoyancy in this interaction, which, for small particles, prevails over the capillary suction that is often assumed to be the dominant effect. We emphasize this point using a simple classroom demonstration, and then derive the physical conditions leading to mutual attraction or repulsion. We also quantify the force of interaction in some particular instances and present a simple dynamical model of this interaction. The results obtained from this model are then validated by comparison to experimental results for the mutual attraction of two identical spherical particles. We conclude by looking at some of the applications of the effect that can be found in the natural and manmade worlds.Comment: 10 pages, 12 figures. (Typos in eqs 7 and 8 corrected

Optimal strategies for throwing accurately

Accuracy of throwing in games and sports is governed by how errors at projectile release are propagated by flight dynamics. To address the question of what governs the choice of throwing strategy, we use a simple model of throwing with an arm modelled as a hinged bar of fixed length that can release a projectile at any angle and angular velocity. We show that the amplification of deviations in launch parameters from a one parameter family of solution curves is quantified by the largest singular value of an appropriate Jacobian. This allows us to predict a preferred throwing style in terms of this singular value, which itself depends on target location and the target shape. Our analysis also allows us to characterize the trade-off between speed and accuracy despite not including any effects of signal-dependent noise. Using nonlinear calculations for propagating finite input-noise, we find that an underarm throw to a target leads to an undershoot, but an overarm throw does not. Finally, we consider the limit of the arm-length vanishing, i.e. shooting a projectile, and find that the most accurate shooting angle bifurcates as the ratio of the relative noisiness of the initial conditions crosses a threshold.Comment: 18 pages, 8 figure