Related papers: An exactly solvable lattice model for inhomogeneou…
We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…
We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
The self-affinity of growing systems with radial symmetry, from tumors to grain-grain displacement, has devoted increasing interest in the last decade. In this work, we analyzed features about the interface scaling of these clusters through…
The real area of contact of a frictional interface changes rapidly when the normal load is altered, and evolves slowly when normal load is held constant, aging over time. Traditionally, the total area of contact is considered a proxy for…
We study a moving boundary model of non-conserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin film production by…
Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance…
When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the…
Motivated by a recently synthesizable class of active interfaces formed by linked self--propelled colloids, we investigate the dynamics and fluctuations of a phoretically (chemically) interacting active interface with roto--translational…
The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (A. Lema\^\i tre & H. Chat\'e, {\em Phys. Rev. Lett.} {\bf 82}, 1140 (1999)) are revisited with the help of detailed investigations of interface…
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely…
The domino-shuffling algorithm can be seen as a stochastic process describing the irreversible growth of a $(2+1)$-dimensional discrete interface. Its stationary speed of growth $v_{\mathtt w}(\rho)$ depends on the average interface slope…
A general theory of thermodynamically consistent biomechanical--biochemical growth in a body, considering mass addition in the bulk and at an incoherent interface, is developed. The incoherency arises due to incompatibility of growth and…
We consider a discretized version of the quenched Edwards-Wilkinson model for the propagation of a driven interface through a random field of obstacles. Our model consists of a system of ordinary differential equations on a $d$-dimensional…
Experimental realizations of a 1D interface always exhibit a finite microscopic width $\xi>0$; its influence is erased by thermal fluctuations at sufficiently high temperatures, but turns out to be a crucial ingredient for the description…
The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…
We consider the asymptotic limit of a diffuse interface model for tumor-growth when a parameter $\varepsilon$ proportional to the thickness of the diffuse interface goes to zero. An approximate solution which shows explicitly the behavior…
In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter $\epsilon$, representing the interface thickness between the tumorous and non tumorous cells,…
We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [L. H. Tang and H. Leschhorn, Phys. Rev. A {\bf 45}, R8309 (1992)]. The evolution equation for the height, the mean height, and…
We study the structure and dynamics of the interface separating a passive fluid from a microtubule-based active fluid. Turbulent-like active flows power giant interfacial fluctuations, which exhibit pronounced asymmetry between regions of…