Related papers: Diffusion-Induced Oscillations of Extended Defects
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the…
We develop an effective theory of pulse propagation in a nonlinear {\it and} disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
It is shown that any three-dimensional periodic configuration that is strictly stable for the area functional is exponentially stable for the surface diffusion flow and for the Mullins-Sekerka or Hele-Shaw flow. The same result holds for…
Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…
Our recent work identifies material surfaces in incompressible flows that extremize the transport of an arbitrary, weakly diffusive scalar field relative to neighboring surfaces. Such barriers and enhancers of transport can be located…
We study a disordered network of bistable bonds subjected to periodic strain. The model is inspired by experiments on crumpled sheets and it features behaviors associated with glasses, including a complex energy landscape, memories, and…
When a liquid slams into a solid, the intermediate gas is squeezed out at a speed that diverges when approaching the moment of impact. Although there is mounting experimental evidence that instabilities form on the liquid interface during…
Zero-point fluctuations of surface plasmon modes near the interface between metal and nonlinear dielectric are shown to produce a thin layer of altered dielectric constant near the interface. This effect may be sufficiently large to produce…
We show how multiplexing influences propagating fronts in multilayer networks of coupled bistable oscillators. Using numerical simulation, we investigate both deterministic and noise-sustained propagation. In particular, we demonstrate that…
It was shown previously that the current-carrying state of a Field Effect Transistor with asymmetric source and drain boundary conditions may become unstable against spontaneous generation of plasma waves [1]. By extending the analysis to…
We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action…
A continuum (Mullins-type) model is formulated for the isotropic evolution of a solid surface on which the mass transport occurs by oscillatory surface diffusion. The time-space oscillations of diffusivity are assumed to be induced by…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
Mechanical metamaterials can be designed to exhibit unique mechanical properties, including tunable auxetic behavior as well as multi-stability, which arise from the geometry and configuration of the constituent building blocks.…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
Freezing of polymer solutions has been extensively investigated from many aspects, especially the complex pattern formation. The cell/dendrite micro-structures are believed to be in the type of diffusion-induced M-S instability. However,…
In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects…