Related papers: Kardar-Parisi-Zhang model for the fractal structur…
In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the Fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that…
Growth in crystals can be { usually } described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics…
The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and…
We show that the emergence of different surface patterns (ripples, dots) can be well understood by a suitable mapping onto the simplest nonequilibrium lattice gases and cellular automata.Using this efficient approach difficult, unanswered…
The Kardar-Parisi-Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height…
We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the…
We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar-Parisi-Zhang (KPZ) dynamics. We find that particles tend to cluster together…
Understanding of clouds is instrumental in interpreting current and future spectroscopic observations of exoplanets. Modelling clouds consistently is complex, since it involves many facets of chemistry, nucleation theory, condensation…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
A cumulus cloud model which can explain the observed characteristics of warm rain formation in monsoon clouds is presented. The model is based on classical statistical physical concepts and satisfies the principle of maximum entropy…
We consider generalizations of the Kardar--Parisi--Zhang equation that accomodate spatial anisotropies and the coupled evolution of several fields, and focus on their symmetries and non-perturbative properties. In particular, we derive…
Recently it was shown that self-organized criticality is an important ingredient of the dynamics of cumulus clouds (Physical Review E, 103(5), p.052106, 2021). Here we introduce a new algorithm to simulate cumulus clouds in two-dimensional…
We report on the growth dynamic of CdTe thin films for deposition temperatures ($T$) in the range of $150\,^{\circ}\mathrm{C}$ to $300\,^{\circ}\mathrm{C}$. A relation between mound evolution and large-wavelength fluctuations at CdTe…
We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in…
We study the influence of the bulk dynamics of a growing cluster of particles on the properties of its interface. First, we define a {\it general bulk growth model} by means of a continuum Master equation for the evolution of the bulk…
The Kardar-Parisi-Zhang (KPZ) equation with infinitesimal surface tension, dynamically develops sharply connected valley structures within which the height derivative is not continuous. We discuss the intermittency issue in the problem of…
We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the…
We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the…
Atmospheric flows exhibit cantorian fractal space-time fluctuations signifying long-range spatiotemporal correlations. A recently developed cell dynamical system model shows that such non-local connections are intrinsic to quantum-like…
The fractal cosmological model which accounts for observable fractal properties of the Universe's large-scale structure is constructed. In this framework these properties are consequences of the rotary symmetry of charged scalar meson…