Related papers: Kardar-Parisi-Zhang growth on one-dimensional decr…
Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that can not be derived from a potential…
Flat surface phases are unstable during growth and known to become rough. This does not exclude the possibility that surface reconstruction order persists in rough growing surfaces, in analogy with so-called equilibrium reconstructed rough…
Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been…
Recently, a variational approach has been introduced for the paradigmatic Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits.…
We investigate an off-lattice Eden model where the growth of new cells is performed with a probability dependent on the availability of resources coming externally towards the growing aggregate. Concentration of nutrients necessary for…
In this article we will present a study of the well-known Kardar-Parisi-Zhang(KPZ) model. Under certain conditions we have found analytic self-similar solutions for the underlying equation. The results are strongly related to the error…
Stochastic growth processes in dimension $(2+1)$ were conjectured by D. Wolf, on the basis of renormalization-group arguments, to fall into two distinct universality classes, according to whether the Hessian $H_\rho$ of the speed of growth…
We consider the relaxation (noise-free) statistics of the one-point height $H=h(x=0,t)$ where $h(x,t)$ is the evolving height of a one-dimensional Kardar-Parisi-Zhang (KPZ) interface, starting from a Brownian (random) initial condition. We…
The investigation of the dynamical universality classes of quantum systems is an important, and rather less explored, aspect of non-equilibrium physics. In this work, considering the out-of-equilibrium dynamics of spinless fermions in a…
Universality of interfacial roughness in growing epithelial tissue has remained a controversial issue. Kardar-Parisi-Zhang (KPZ) and Molecular Beam Epitaxy (MBE) universality classes have been reported among other behaviors including total…
We consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq0$ with the reflecting boundary at $x=0$. The interface is initially flat, $h(x,t=0)=0$. We focus on the…
We present large-scale simulations of radial Eden clusters in three-dimensions and show that the growth exponent is in agreement with the value $\beta=0.242$ accepted for the Kardar-Parisi-Zhang (KPZ) universality class. Our results refute…
Recently, Newman and Swift[T. J. Newman and M. R. Swift, Phys. Rev. Lett. {\bf 79}, 2261 (1997)] made an interesting suggestion that the strong-coupling exponents of the Kardar-Parisi-Zhang (KPZ) equation may not be universal, but rather…
In this work, an approach to generate radial interfaces is presented. A radial network recursively obtained is used to implement discrete model rules designed originally for the investigation in flat substrates. In order to test the…
We present a directed unloading sand box type avalanche model, driven by slowly lowering the retaining wall at the bottom of the slope. The avalanche propagation in the two dimensional surface is related to the space-time configurations of…
A nonperturbative weak noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the growth morphology can be interpreted in terms of a dynamically evolving texture of localized…
We determine the exact short-time distribution $-\ln \mathcal{P}_{\text{f}}\left(H,t\right)= S_{\text{f}} \left(H\right)/\sqrt{t}$ of the one-point height $H=h(x=0,t)$ of an evolving 1+1 Kardar-Parisi-Zhang (KPZ) interface for flat initial…
We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties…
Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a…
We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Freedericksz…