2,957 research outputs found
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
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