Related papers: Scale properties as a basis of power law relaxatio…

Starting from a simple definition of stationary regime in first-order relaxation processes, we obtain that experimental results are to be fitted to a power-law when approaching the stationary limit. On the basis of this result we propose a…

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…

We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…

Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables…

We investigate scaling phenomena at first-order quantum transitions, when the boundary conditions favor one of the two phases. We show that the corresponding finite-size scaling behavior, arising from the interplay between the driving…

We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a…

Many self-gravitating systems often show scaling properties in their mass density, system size, velocities and so on. In order to clarify the origin of these scaling properties, we consider the stationary state of N-body system with inverse…

We study samples of natural images for which a set of statistical characteristics is computed and scale-invariant properties of samples are demonstrated computationally. Computations of the power spectrum are carried out and a power-law…

A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…

Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar…

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…

In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…

We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the…

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time…

We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory…

We study the condensation phenomenon in a zero range process on scale-free networks. We show that the stationary state property depends only on the degree distribution of underlying networks. The model displays a stationary state phase…

The process of relaxation of a system of particles interacting with long-range forces is relevant to many areas of Physics. For obvious reasons, in Stellar Dynamics much attention has been paid to the case of 1/r^2 force law. However,…

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…