We report electrohydrodynamic instability in nematic liquid crystals found in Hele-Shaw cells. Due to the present cell geometry, the convective structures could be directly visualized as surface or bulk flows. An unexpected structure is observed, which is completely different from the well-known patterns in the standard cells. By using the voltage-frequency jump method, the stability of a conve...

We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the novelty of the present paper. This new ingredient is considered here as a standard diffusion process. The free boundary model is derived from a description at the cell level using the asymptotic of a stiff pressure lim...

In Augustus 1966 het mnr en mev D ’Oliveira medestigters geword van Operation Upgrade o f Southern Africa. Vandag is die organisasie wat vier opleidingsentra oor die hele Suid-Afrika het, besig met ’n veldtog om ongeletterdheid oor die hele Republiek uit te wis — ’n veldtog wat die stigters oor die hele vasteland van Afrika wil voer om brúe van begrip en goedgesindheid tussen die Noorde en Suid...

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution t...

We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between t...

A new general class of exact solutions is presented for the time evolution of a bubble of arbitrary initial shape in a Hele-Shaw cell when surface tension effects are neglected. These solutions are obtained by conformal mapping the viscous flow domain to an annulus in an auxiliary complex plane. It is then demonstrated that the only stable fixed point (attractor) of the nonsingular bubble dynam...

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the e...

This work is motivated by the paper [LP]. In this paper, the authors consider the scaling limits of three discrete aggregation models with multiple sources the internal DLA (diffusion-limited aggregation), the rotor-router, and the divisible sandpile model. They show that for all three models, the scaling limit is the same, and it is a solution of the Hele-Shaw injection problem with multiple s...