Related papers: Finite-time scaling in local bifurcations
Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour…
In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
We present analytical results for the finite-size scaling in d--dimensional O(N) systems with strong anisotropy where the critical exponents (e.g. \nu_{||} and \nu_{\perp}) depend on the direction. Prominent examples are systems with…
Systems brought out of equilibrium through a rapid quench from a disordered initial state into an ordered phase undergo physical aging in the form of phase-ordering kinetics, with characteristic dynamical scaling. In many systems, notably…
We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic…
We develop the finite-size scaling (FSS) theory at quantum transitions, considering generic boundary conditions, such as open and periodic boundary conditions, and also the corrections to the leading FSS behaviors. Using…
We analyze the scaling parameter, extracted from the fidelity for two different ground states, for the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
We investigate how the scaling behavior of finite systems at magnetic first-order transitions (FOTs) with relaxational dynamics changes in correspondence of various boundary conditions. As a theoretical laboratory we consider the…
There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals…
Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…
The analysis of the radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. This approach from classical statistical mechanics has…
We perform molecular dynamics simulations in order to examine the rheological transition of fluids confined in a small space. By performing finite-size scaling analysis, we demonstrate that this rheological transition results from the…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Freedericksz…
Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
Based on quasi-stationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as,…
Phase transitions, sharp in the thermodynamic limit, get smeared in finite systems where macroscopic order-parameter fluctuations dominate. Achieving a coherent and complete theoretical description of these fluctuations is a central…