Related papers: Pattern formation in fast-growing sandpiles
A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequence of qualitatively different patterned states, "gaps -> labyrinth -> spots", that occurs as a parameter representing precipitation…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
The local Universe displays a rich hierarchical pattern of galaxy clusters and superclusters. The early Universe, however, was almost smooth, with only slight 'ripples' seen in the cosmic microwave background radiation. Models of the…
Recently, unusual and strikingly beautiful seahorse-like growth patterns have been observed under conditions of quasi-two-dimensional growth. These `S'-shaped patterns strongly break two-dimensional inversion symmetry; however such broken…
Metastable vaterite crystals were synthesized by increasing the pH and consequently the saturation states of Ca and CO3 containing solutions using an ammonia diffusion method. SEM and TEM analyses indicate that vaterite grains produced by…
We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket ($SG$) when particles are launched from the corner vertex. In particular, the abelian sandpile…
We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope $\sigma_c\/$, a parameter $\alpha\/$, governing the local current-slope relation (beyond…
With the present paper we conclude the presentation of a semianalytical model of hierarchical clustering of bound virialized objects formed by gravitational instability from a random Gaussian field of density fluctuations. In paper I, we…
When a solid object or wheel is repeatedly dragged on a dry sandy surface, ripple patterns are formed. Although the conditions to form ripple patterns have been studied well, methods to eliminate the developed ripple patterns have not been…
We discuss some features of a boundary value problem for a system of PDEs that describes the growth of a sandpile in a container under the action of a vertical source. In particular, we characterize the long-term behavior of the profiles,…
In a critically self--organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes,…
Stars are commonly formed in binary systems, which provide a natural laboratory for studying planet formation in extreme conditions. In our first paper (Paper I) of a series Xie et al. (2011), we have shown that the intermediate stage -…
We present in this paper a simplification of the dune model proposed by Sauermann et al. which keeps the basic mechanisms but allows analytical and parametric studies. Two kinds of purely propagative two dimensional solutions are exhibited:…
The evolution of occupied volume under progressive fragmentation of granular matter is studied using a purely geometric model. Rather than modelling disorder directly, properties are investigated by analysing highly ordered reference…
We consider a family of growth models defined using conformal maps in which the local growth rate is determined by $|\Phi_n'|^{-\eta}$, where $\Phi_n$ is the aggregate map for $n$ particles. We establish a scaling limit result in which…
In this thesis we present few theoretical studies of the models of self-organized criticality. Following a brief introduction of self-organized criticality, we discuss three main problems. The first problem is about growing patterns formed…
We compute the correlations of two height variables in the two-dimensional Abelian sandpile model. We extend the known result for two minimal heights to the case when one of the heights is bigger than one. We find that the most dominant…
A first-principles statistical theory is constructed for the evolution of two dimensional interfaces in Laplacian fields. The aim is to predict the pattern that the growth evolves into, whether it becomes fractal and if so the…