相关论文: Steady-state fingering patterns for a periodic Mus…

The stability of a horizontal interface between two viscous fluids, one of which is conducting and the other is dielectric, acted upon by a vertical time-periodic electric field is considered. The two fluids are bounded by electrodes…

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are…

Metastatic tumors often invade healthy neighboring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model…

We analytically investigate the stability of {\it splay states} in networks of $N$ pulse-coupled phase-like models of neurons. By developing a perturbative technique, we find that, in the limit of large $N$, the Floquet spectrum scales as…

The onset of frictional motion is mediated by rupture-like slip fronts, which nucleate locally and propagate eventually along the entire interface causing global sliding. The static friction coefficient is a macroscopic measure of the…

A free boundary problem modeling a microelectromechanical system (MEMS) consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at different electrostatic potentials. It couples a second order…

We consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by…

When twisting a strip of paper or acetate under high longitudinal tension, one observes, at some critical load, a buckling of the strip into a regular triangular pattern. Very similar triangular facets have recently been observed in…

Euler buckling epitomises mechanical instabilities: An inextensible straight elastic line buckles under compression when the compressive force reaches a critical value $F_\ast>0$. Here, we extend this classical, planar instability to the…

We prove the existence of global, smooth solutions to the 2D Muskat problem in the stable regime whenever the product of the maximal and minimal slopes is strictly less than 1. The curvature of these solutions solutions decays to 0 as $t$…

Analytical solutions for both a finite assembly and a periodic array of bubbles steadily moving in a Hele-Shaw channel are presented. The particular case of multiple fingers penetrating into the channel and moving jointly with an assembly…

We solve numerically the nonlinear differential equation for the Hele-Shaw, Saffman-Taylor problem derived in the preceding work. Stationary solutions with no free phenomenological parameters are found to fit the measured patterns. The…

A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural…

The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…

The spot model has been developed by Bazant and co-workers to describe quasistatic granular flows. It assumes that granular flow is caused by the opposing flow of so-called spots of excess free volume, with spots moving along the slip lines…

Fingering instabilities akin to the Rayleigh-Taylor (RT) instability in fluids have been observed in a binary granular system consisting of dense and small particles layered on top of lighter and larger particles, when the system is…

We consider the totally asymmetric simple exclusion process on a ring with stationary initial conditions. The crossover between KPZ dynamics and equilibrium dynamics occurs when time is proportional to the $3/2$ power of the ring size. We…

When a flexible plate is peeled off a thin and soft elastic film bonded to a rigid support, uniformly spaced fingering patterns develop along their line of contact. While, the wavelength of these patterns depends only on the thickness of…

Using renormalized field theory, we examine the dynamics of a growing surface, driven by an obliquely incident particle beam. Its projection on the reference (substrate) plane selects a ``parallel'' direction, so that the evolution equation…

Snapping mechanisms are investigated for an elastic strip with ends imposed to move and rotate in time. Attacking the problem analytically via Euler's elastica and the second variation of the total potential energy, the number of stable…