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The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…
We study the creep rupture of fiber composites in the framework of fiber bundle models. Two novel fiber bundle models are introduced based on different microscopic mechanisms responsible for the macroscopic creep behavior. Analytical and…
Numerous urban indicators scale with population in a power law across cities, but whether the cross-sectional scaling law is applicable to the temporal growth of individual cities is unclear. Here we first find two paradoxical scaling…
Neural scaling laws aim to characterize how out-of-sample error behaves as a function of model and training dataset size. Such scaling laws guide allocation of a computational resources between model and data processing to minimize error.…
What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained…
A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution $\mathrm{d} N/\mathrm{d} M\propto M^{-2}$ which (to first order) describes stars, protostellar…
The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its…
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…
A simple, physically motivated, scaling hypothesis, which becomes exact in important limits, yields estimates for the ground-state energy of large, composed, systems in terms of the ground-state energy of its building blocks. The concept is…
In this paper, we study the phase field models with fractional-order in time. The phase field models have been widely used to study coarsening dynamics of material systems with microstructures. It is known that phase field models are…
Logarithmic finite-size scaling of the O($n$) universality class at the upper critical dimensionality ($d_c=4$) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems.…
The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for…
We discuss the properties of a self--organized critical forest--fire model which has been introduced recently. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer…
The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of…
As huge complex systems consisting of geographic regions, natural resources, people and economic entities, countries follow the allometric scaling law which is ubiquitous in ecological, urban systems. We systematically investigated the…
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…
Scaling and hyperscaling laws provide exact relations among critical exponents describing the behavior of a system at criticality. For nonequilibrium growth models with a conserved drift there exist few of them. One such relation is $\alpha…
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…
We have investigated scaling properties of the Aubry-Andr\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground…
The shape of buildings plays a critical role in the energy efficiency, lifestyles, land use and infrastructure systems of cities. Thus, as most of the world's cities continue to grow and develop, understanding the interplay between the…