Related papers: Feedback control of surface roughness in a one-dim…
We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface,…
We study the surface dynamics of silica films grown by low pressure chemical vapor deposition. Atomic force microscopy measurements show that the surface reaches a scale invariant stationary state compatible with the Kardar-Parisi-Zhang…
We study a stochastic PDE model for an evolving set $\mathbb{M}(t)\subseteq\mathbb{R}^{\mathrm{d}+1}$ that resembles a continuum version of origin-excited or reinforced random walk. We show that long-time fluctuations of an associated…
We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence.…
We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface dynamics is unstable at early times, but asymptotically…
We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y(t)= h(t)-< h(t)>, which is depicted as being subordinated to a standard…
We present a recently introduced real space renormalization group (RG) approach to the study of surface growth. The method permits us to obtain the properties of the KPZ strong coupling fixed point, which is not accessible to standard…
We introduce a self-organized surface growth model in 2+1 dimensions with anisotropic avalanche process, which is expected to be in the universality class of the anisotropic quenched Kardar-Parisi-Zhang equation with alternative signs of…
We study a restricted solid-on-solid (RSOS) model involving deposition and evaporation with probabilities p and 1-p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang…
A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the…
We describe a directed avalanche model; a slowly unloading sandbox driven by lowering a retaining wall. The directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower…
Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy$_2$ spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as…
We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the…
We study (2+1)-dimensional single step model (SSM) for crystal growth including both deposition and evaporation processes parametrized by a single control parameter $p$. Using extensive numerical simulations with a relatively high…
We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson…
We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J.~Sci.\ Comput.~{\bf 1}, 3 (1986)]. Hence we calculate the…
We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho and the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the…
We discuss the universal behavior linked to the Goldstone mode associated with the spontaneous breaking of time-translation symmetry in many-body systems, in which the order parameter traces out a limit cycle. We show that this universal…
We explore the Kardar-Parisi-Zhang (KPZ) scaling in the one-dimensional Hubbard model, which exhibits global $SU_c(2)\otimes SU_s(2)$ symmetry at half-filling, for the pseudo-charge and the total spin. We analyze dynamical scaling…
The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent…