Related papers: Steady-state fingering patterns for a periodic Mus…
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it…
The three-layer Saffman-Taylor problem introduces two coupled moving interfaces separating the three fluids. A very recent weakly nonlinear analysis of this problem in a radial Hele-Shaw cell setup has shown that the morphologies of the…
We study the surface tension and the phenomenon of phase coexistence for the Ising model on $\mathbbm{Z}^d$ ($d \geqslant 2$) with ferromagnetic but random couplings. We prove the convergence in probability (with respect to random…
A fluid droplet suspended in an extensional flow of moderate intensity may break into pieces, depending on the amplitude of the initial droplet deformation. In subcritical uniaxial extensional flow the non-breaking base state is linearly…
Impact of a droplet on an undercooled surface is a complex phenomenon as it simultaneously instigates several physical processes that cover a broad spectrum of transport phenomena and phase-transition. Here, we report and explain an…
Pattern-forming processes, such as electrodeposition, dielectric breakdown or viscous fingering are often driven by instabilities. Accordingly, the resulting growth patterns are usually highly branched, fractal structures. However, in some…
We consider a finite system of interacting point processes with memory of variable length modeling a finite but large network of spiking neurons with two different leakage mechanisms. Associated to each neuron there are two point processes,…
To find the regularities of formed fingers in gravity driven coating flows on upper cylinder and sphere, the mathematical formulation to model the fingering instability on cylindrical or spherical surface which consists of a capillary wave…
We study viscous fingering of an air-nematic interface in a radial Hele-Shaw cell when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its…
We study the surface fluctuations of a tissue with a dynamics dictated by cell-rearrangement, cell-division, and cell-death processes. Surface fluctuations are calculated in the homeostatic state, where cell division and cell death…
Motivated by studies suggesting that the patterns exhibited by the collectively expanding fronts of thin cells during the closing of a wound [Mark et al., Biophys. J., 98:361-370, 2010] and the shapes of single cells crawling on surfaces…
We consider the Muskat problem describing the viscous displacement in a two-phase fluid system located in an unbounded two-dimensional porous medium or Hele-Shaw cell. After formulating the mathematical model as an evolution problem for the…
A new solution for general half-plane contact problems subject to a constant normal load together with alternating shear loads and tension in the steady state is presented. The method uses a formulation where a displacement correction is…
We study pattern formation during tensile deformation of confined viscoelastic layers. The use of a model system (PDMS with different degrees of crosslinking) allows us to go continuously from a viscous liquid to an elastic solid. We…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…
We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the…
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the…
Wetting phenomena, molecular protrusions of lipid bilayers and membrane stacks under lateral tension provide physical examples for interacting surfaces with tension. Such surfaces are studied theoretically using functional renormalization…
We use analytical calculations and Monte Carlo simulations to determine the thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in size, whose corners are located at a fixed distance $d$ above a plane rigid surface.…
Axisymmetric steady solutions of Taylor-Couette flow at high Taylor numbers are studied numerically and theoretically. As the axial period of the solution shortens from about one gap length, the Nusselt number goes through two peaks before…