Related papers: Directed percolation depinning models: Evolution e…
In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\mathcal{O} \subset \mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective…
Particle coarsening and grain growth take place to minimize the total interfacial energy. The classical mean-field treatments by Lifshitz, Slyozov, [1] Wagner [2] and Hillert [3] predicted cubic growth law under bulk-diffusion controlled…
In this work, we study the extended viscous dark energy models in the context of matter perturbations. To do this, we assume an alternative interpretation of the flat Friedmann-Lema\^itre-Robertson-Walker Universe, through the nonadditive…
We present results of numerical simulations of kinetic roughening for a growth model with surface diffusion (the Wolf-Villain model) in 3+1 and 4+1~dimensions using lattices of a linear size up to $L=64$ in 3+1~D and $L=32$ in 4+1~D. The…
We study the interface representation of the contact process (CP) at its directed-percolation critical point, where the scaling properties of the interface can be related to those of the original particle model. Interestingly, such a…
Building on an analogy between the ageing behaviour of magnetic systems and growing interfaces, the Arcetri model, a new exactly solvable model for growing interfaces is introduced, which shares many properties with the kinetic spherical…
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 consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…
In this paper, we characterize a degenerate PDE as the gradient flow in the space of nonnegative measures endowed with an optimal transport-growth metric. The PDE of concern, of Hele-Shaw type, was introduced by Perthame et. al. as a…
In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the…
Recent literature shows that hypocoercivity properties of linear evolution equations (in particular their exponential decay and the sharp short time decay of their propagator norm) carry over to their discretization via the midpoint rule.…
We consider a random interface model on the discrete torus with $2n$ sites, obtained from the classical corner flip dynamics but with a weak global perturbation, namely an asymmetry of order $n^{-\gamma}$ of the direction of growth that…
When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied trough Langevin equations or discrete growth models. In the first case, the…
In this paper, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for a…
We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can…
In this work we generalize the etching model (Mello et al 2001 Phys. Rev. E 63 041113) to d + 1 dimensions. The dynamic exponents of this model are compatible with those of the Kardar-Parisi-Zhang universality class. We investigate the…
A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum…
Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a…
We study the dynamical exponent $z$ for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that $z$ for $(d+1)$ dimensions is equal to the exponent $d_{\rm min}$…
The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and…