Michael Wilkinson

There is a dimensionless parameter which enters into the equation for the evolution of supersaturation in Ostwald ripening processes. This parameter is typically a large number. Here it is argued that the consequent stiffness of the equation results in the evolution of the supersaturation being unstable. The instability is evident in numerical simulations of Ostwald ripening.

If a body of inviscid fluid is disturbed, it will typically eject a jet of fluid. If the effects of gravity and surface tension are negligible, these jets travel in straight lines, with the tips approaching a constant velocity. Earlier works have concentrated upon jets which result from the occurrence of shocks or singularities in the fluid flow. In this paper, by contrast, we describe the simplest case, in two dimensions: an infinitely deep body of inviscid fluid, with no surface tension or gravitational forces acting, responds to a generic impulsive disturbance. We find that, contrary to some earlier suggestions, the jet has a hyperbolic profile (away from its tip and its base).

This paper considers an Ostwald ripening process in which new droplets are injected at a constant rate, with a fixed distribution of radii, and in which droplets are removed when they grow to a specified maximum radius. This process exhibits a transition from a steady state to a limit cycle as a parameter is varied. The instability is shown to be related to the roots of the Laplace transform of a response kernel. A model is described which gives a good approximation of the period of the limit cycle. The system may also exhibit chaotic behaviour. The relevance of the model to atmospheric precipitation is discussed.

This paper considers an Ostwald ripening process in which new droplets are injected at a constant rate, with a fixed distribution of radii, and in which droplets are removed when they grow to a specified maximum radius. This process exhibits a transition from a steady state to a limit cycle as a parameter is varied. The instability is shown to be related to the roots of the Laplace transform of a response kernel. A model is described which gives a good approximation of the period of the limit cycle. The model may also exhibit chaotic behaviour. The relevance of the model to atmospheric precipitation is discussed.

If a body of inviscid fluid is disturbed, it will typically eject a jet of fluid. If the effects of gravity and surface tension are negligible, these jets travel in straight lines, with the tips approaching a constant velocity. It has been observed that these jets can have a broad base, tapering progressively toward the tip, but the mathematical form of their profile has not been successfully analysed in earlier works. In this paper, we describe the simplest case, in two dimensions: an infinitely deep body of inviscid fluid, with no surface tension or gravitational forces acting, responds to an impulsive disturbance. We find that, contrary to some earlier suggestions, the jet has a hyperbolic profile (away from its tip and its base).

We obtain the full equations of motion for a wide, pivoted, slider bearing. These are used to review the choice of the optimal position for the pivot point, to discuss its response to time-dependent sliding velocity, and to determine the stability of the motion. The case of an abrupt acceleration of the slider, which results in a large transient increase in the resistive force, is surprisingly complicated. We also discuss a general transversion formula for changing the dependent variables in Stokes flow problems.

We discuss a model for directed percolation in which the flux of material along each bond is a dynamical variable. The model includes a physically significant limiting case where the total flux of material is conserved. We show that the distribution of fluxes is asymptotic to a power law at small fluxes. We give an implicit equation for the exponent, in terms of probabilities characterising site occupations. In one dimension the site occupations are exactly independent, and the model is exactly solvable. In two dimensions, the independent-occupation assumption gives a good approximation. We explore the relationship between this model and traditional models for directed percolation.

We obtain the full equations of motion for a wide, pivoted, slider bearing. These are used to review the choice of the optimal position for the pivot point, to discuss its response to time-dependent sliding velocity, and to determine the stability of the motion. The case of an abrupt acceleration of the slider, which results in a large transient increase of the resistive force, is surprisingly complicated. We also discuss a general \emph{transversion} formula for changing the dependent variables in Stokes flow problems.