Related papers: Kinetic roughening in active interfaces
We give a brief overview of the seminal paper which introduced the Kardar-Parisi-Zhang equation as a paradigmatic model for random growth in 1986. We describe some of the developments to which it gave rise in mathematics and physics over…
Nonequilibrium dynamics of biomembranes with active inclusions is considered. The inclusions represent protein molecules which perform cyclic internal conformational motions driven by the energy brought with ATP ligands. As protein…
A living cell actively generates traction forces on its environment with its actin cytoskeleton. These forces deform the cell elastic substrate which, in turn, affects the traction forces exerted by the cell and can consequently modify the…
We define a new model of interface roughening which has the property that the minimum of interface height is conserved locally during the growth. This model corresponds to the limit $q \to \infty$ of the q-color dimer deposition-evaporation…
We study pattern formation, fluctuations and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy consuming proteins embedded in the plasma…
Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but…
The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the…
Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at…
Cell membrane tension directly influences various cellular functions. In this study, we developed a method to estimate surface tension from time-series data. We obtained the curvature-velocity relationship from time-series of binarized cell…
We study the influence of the bulk dynamics of a growing cluster of particles on the properties of its interface. First, we define a {\it general bulk growth model} by means of a continuum Master equation for the evolution of the bulk…
In its original version the KPZ equation models the dynamics of an interface bordering a stable phase against a metastable one. Over past years the corresponding two-dimensional field theory has been applied to models with different…
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 introduce the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any…
Interfaces in three-dimensional many-body systems can exhibit rich phenomena beyond the corresponding bulk properties. In particular, they can fluctuate and give rise to massless low energy degrees of freedom even in the presence of a…
We theoretically explore fluidization of epithelial tissues by active T1 neighbor exchanges. We show that the geometry of cell-cell junctions encodes important information about the local features of the energy landscape, which we support…
Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The…
We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid…
The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent…
Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a…
This paper has two main goals. The first is universality of the KPZ equation for fluctuations of dynamic interfaces associated to interacting particle systems in the presence of open boundary. We consider generalizations on the open-ASEP…