Related papers: Growth Models And The Question Of Universality Cla…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
Recently, a hypothesis on the complexity growth of unitarily evolving operators was presented. This hypothesis states that in generic, non-integrable many-body systems the so-called Lanczos coefficients associated with an autocorrelation…
A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide.…
We analyze the growth statistics of Swedish trade unions and find a universal functional form for the probability distribution of growth rates of union size, and a power law dependence of the standard deviation of this distribution on the…
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…
In this paper we give an explanation of a number of observations relating to degree growth of birational mappings of the plane and their deautonomisation by singularity confinement. These observations are of a link between two a priori…
Extensive dynamical simulations of Restricted Solid on Solid models in $D=2+1$ dimensions have been done using parallel multisurface algorithms implemented on graphics cards. Numerical evidence is presented that these models exhibit KPZ…
In this paper, we define a class of slice mappings of several Clifford variables, and the corresponding slice regular mappings. Furthermore, we establish the growth theorem for slice regular starlike or convex mappings on the unit ball of…
Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the…
Recently, West et al. claimed to derive a general quantitative model based on fundamental principles for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass, and in addition claimed to…
Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth…
Motivated by recent experimental studies in microbiology, we suggest a modification of the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…
Recently a number of empirical "universal" scaling law papers have been published, most notably by OpenAI. `Scaling laws' refers to power-law decreases of training or test error w.r.t. more data, larger neural networks, and/or more compute.…
Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…
This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…