One-dimensional reduction of viscous jets. I. Theory

On the One-dimensional Stability of Viscous Strong Detonation Waves

Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following [1, 17], is the calculation of a stability index whose sign determines a necessary condition for spectral stability. We show that for an ideal gas this index can be ev...

Delayed capillary breakup of falling viscous jets.

Thin jets of viscous fluid like honey falling from capillary nozzles can attain lengths exceeding 10 m before breaking up into droplets via the Rayleigh-Plateau (surface tension) instability. Using a combination of laboratory experiments and WKB analysis of the growth of shape perturbations on a jet being stretched by gravity, we determine how the jet's intact length l(b) depends on the flow ra...

Falling jets of particles in viscous fluids

We have investigated the time evolution of a jet of non-Brownian particles falling under the action of gravity in a viscous liquid at low Reynolds number. Different regimes have been observed depending on volume fraction and particle-to-jet diameter ratio. In particular, the jet has been found to be unstable and to develop varicose modulation of its diameter at low volume fractions. The dominan...

One-Dimensional Reduction of Multidimensional Persistent Homology

A recent result on size functions is extended to higher homology modules: the persistent homology based on a multidimensional measuring function is reduced to a 1-dimensional one. This leads to a stable distance for multidimensional persistent homology. Some reflections on i-essentiality of homological critical values conclude the paper.

The Mathematical Theory of Three- Dimensional Cavities and Jets