Related papers: Interface growth in the channel geometry and tripo…
The motion of interfaces is an essential feature of microstructure evolution in crystalline materials. While atomic-scale descriptions provide mechanistic clarity, continuum descriptions are important for understanding microstructural…
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 consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional…
In this article we study two classical linear water wave problems, i) normal modes of infinite straight channels of bounded constant cross-section, and ii) trapped longitudinal modes in domains with unbounded constant cross-section. Both…
We derive interface models for 3D Rayleigh-Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are derived for the purpose of studying universal features…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…
In this article we investigate a system of geometric evolution equations describing a curvature driven motion of a family of 3D curves in the normal and binormal directions. Evolving curves may be subject of mutual interactions having both…
Topological interfaces of two-dimensional conformal field theories contain information about symmetries of the theory and exhibit striking spectral and entanglement characteristics. While lattice realizations of these interfaces have been…
Roughening of interfaces implies the divergence of the interface width $w$ with the system size $L$. For two-dimensional systems the divergence of $w^2$ is linear in $L$. In the framework of a detailed capillary wave approximation and of…
We consider a Markovian growth process on a partially ordered set $\Lambda$, equivalent to last passage percolation (LPP) with independent (not necessarily identical) exponentially distributed weights on the elements of $\Lambda$. Such a…
The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…
Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of…
Loewner chains with Levy drivers have been proposed as models for random dendritic growth in two dimensions, and as candidates for finding extremal multifractal spectra in problems in classical function theory. These processes are not…
In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations.…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
An improved wetting boundary implementation strategy is proposed based on lattice Boltzmann color-gradient model in this paper. In this strategy, an extra interface force condition is demonstrated based on the diffuse interface assumption…
Developing an evolution model of the Internet has been a long standing research challenge. Such a model can improve the design and placement of communication infrastructure, reducing costs and improving users' quality of experience. While…
Instabilities of fluid-fluid interfaces are ubiquitous in passive soft matter. Adding activity to the interface or either fluid can dramatically change the stability of the interface. Using experiment and theory, we investigate the…
The fundamental properties of 2-dimensional (2D) Ising system were formulated using the Loewner theory. We focus on the role of the complexity measure of the 2D geometry, referred to as the Loewner entropy, to derive the…
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The…