Related papers: Interface dynamics in discrete forward-backward di…
We study a reversible continuous-time Markov dynamics of a discrete $(2+1)$-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the $L\times L$ torus, or as a conservative dynamics for a…
Hypothesis: Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular…
Hysteresis, with rich dynamical behaviors-especially in interacting systems-has drawn broad research interest. Yet its dynamic scalings across time scales lack a unified description, and their transitions remain unclear. Here, we study the…
Phase field models are powerful tools to tackle free boundary problems. For phase transformations involving diffusion, the evolution of the non conserved phase field is coupled to the evolution of the conserved diffusion field. Introducing…
We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional…
We consider the free boundary problem for relativistic plasma--vacuum interfaces in two and three spatial dimensions. The plasma flow is governed by the equations of ideal relativistic magnetohydrodynamics, while the vacuum magnetic and…
It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling…
We investigate dynamics of large scale and slow deformations of layered structures. Starting from the respective model equations for a non-conserved system, a conserved system and a binary fluid, we derive the interface equations which are…
We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact…
The steady state structure of an interface in an Ising system on a square lattice placed in a {\em non-uniform} external field, shows a commensurate -incommensurate transition driven by the velocity of the interface. The non-uniform field…
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
We propose a generalized diffusion equation for a flat Euclidean space subjected to a continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent scale…
We consider interface fluctuations on a two-dimensional layered lattice where the couplings follow a hierarchical sequence. This problem is equivalent to the diffusion process of a quantum particle in the presence of a one-dimensional…
In an effort to study the stability of contact lines in fluids, we consider the dynamics of a drop of incompressible viscous Stokes fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary…
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…
We investigate some unstable behavior of the interface given by two incompressible fluids of different densities evolving by the regular Stokes law with gravity force. In the unstable scenario, where the denser fluid lies above the lighter…
We derive the hydrodynamic limit of Glauber-Kawasaki dynamics. The Kawasaki part is simple and describes independent movement of the particles with hard core exclusive interactions. It is speeded up in a diffusive space-time scaling. The…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…
We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation…