Related papers: Growth Models And The Question Of Universality Cla…
In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
We introduce a model in which cells belonging to two species proliferate with volume exclusion on an expanding surface. If the surface expands uniformly, we show that the domains formed by the two species present a critical behavior. We…
We use deposition models of kinetic roughening of a growing surface to introduce the concepts of universality and scaling and to analyze the qualitative and quantitative role of different parameters. In particular, we focus on two classes…
Since publication of the main contributions on the theory of kinetic roughening more than fifteen years ago, many works have been reported on surface growth or erosion that employ the framework of dynamic scaling. This interest was mainly…
We show that in the construction of continuum equations for competitive growth processes that are a mixture of random deposition and a correlation process, a distinction must be made within a \textit{single universality class} between…
It had been conjectured that Diffusion Limited Aggregates and Laplacian Growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a 1-parameter family of fractal growth…
Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with non-equilibrium problems, however, the distinction in…
We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic…
We present simulation results of deposition growth of surfaces in 2, 3 and 4 dimensions for ballistic deposition where overhangs are present, and for restricted solid on solid deposition where there are no overhangs. The values of the…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
A classification in universality classes of broad categories of phenomenologies, belonging to different disciplines, may be very useful for a crossfertilization among them and for the purpose of pattern recognition. We present here a simple…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the…
We show that the mapping class group of an orientable finite type surface has uniformly exponential growth, as well as various closely related groups. This provides further evidence that mapping class groups may be linear.
We construct the complete set of orders of growth and we define on it the generalized entropy of a dynamical systems. With this object we provide a framework where we can study the separation of orbits of a map beyond the scope of…
Comment on "Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences" by P. Castorina, P. P. Delsanto and C. Guiot, Phys. Rev. Lett. {\bf 96}, 188701 (2006) is presented. It has been proved…
We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique…
The growth of cities has traditionally been studied from a population perspective, while urban expansion-its spatial growth-has often been approached qualitatively. However, characterizing and modeling this spatial expansion is crucial,…
Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…