Related papers: Growth Models And The Question Of Universality Cla…
The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive…
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 study the link between the degree growth of integrable birational mappings of order higher than two and their singularity structures. The higher order mappings we use in this study are all obtained by coupling mappings that are…
We present numerical evidence that there are two distinct universality classes characterizing driven interface roughening in the presence of quenched disorder. The evidence is based on the behavior of $\lambda$, the coefficient of the…
The emergent spatial patterns generated by growing bacterial colonies have been the focus of intense study in physics during the last twenty years. Both experimental and theoretical investigations have made possible a clear qualitative…
We investigate a class of Young diagrams growing via the addition of unit cells and satisfying the constraint that the height difference between adjacent columns $\geq r$. In the long time limit, appropriately re-scaled Young diagrams…
We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails…
The MBE grown Si$_{1-x}$Ge$_x$ islands on reconstructed high index surfaces, such as, Si(5 5 12), Si(5 5 7) and Si(5 5 3) show a universality in the shape evaluation and the growth exponent parameters, \emph{irrespective} of the substrate…
In this article we study the existence of solutions to a fourth-order nonlinear PDE related to crystal surface growth. The key difficulty in the equations comes from the mobility matrix, which depends on the gradient of the solution. When…
In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…
In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical…
We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…
We investigate sandpile models where the updating of unstable columns is done according to a stochastic rule. We examine the effect of introducing nonlocal relaxation mechanisms. We find that the models self-organize into critical states…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
Several network growth models have been proposed in the literature that attempt to incorporate properties of citation networks. Generally, these models aim at retaining the degree distribution observed in real-world networks. In this work,…
In many growth processes particles are highly mobile in an active layer at the surface, but are relatively immobile once incorporated in the bulk. We study models in which atoms are allowed to interact, equilibrate, and order on the…
We study the critical behavior at the ordinary surface universality class of the three-dimensional O($N$) model, bounded by a two-dimensional surface. Using high-precision Monte Carlo simulations of an improved lattice model, where the…
While general relativity ties together the cosmic expansion history and growth history of large scale structure, beyond the standard model these can have independent behaviors. We derive expressions for cosmologies with identical growth…
Function diversity, the range of tasks individuals perform, and specialization, the distribution of function abundances, are fundamental to complex adaptive systems. In the absence of overarching principles, these properties have appeared…