Related papers: Time Invariant Scaling in Discrete Fragmentation M…

We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters…

We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…

Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the…

The exit time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments (Inverse Structure Functions) it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out…

We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group…

We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A self-similar scaling regime is detected when the…

We derive the time evolution of the density contrast to all orders of perturbation theory, by solving the Einstein equation for scale-invariant fluctuations. These fluctuations are represented by an infinite series in inverse powers of the…

A recently proposed scaling law for the decay time of alpha particles is generalized for cluster decay. It is shown that for the decay of even-even parents, $logT_{1/2}$ depends linearly on the scaling variable…

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies…

Decaying turbulence is studied numerically using as initial condition a random flow whose shell-integrated energy spectrum increases with wavenumber k like k^q. Alternatively, initial conditions are generated from a driven turbulence…

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially…

The nonlinear evolution equation for the scattering amplitude of colour dipole off the heavy nucleus is solved in the double logarithmic approximation. It is found that if the initial parton density in a nucleus is smaller then some…

Dislocation systems exhibit well known scaling properties such as the Taylor relationship between flow stress and dislocation density, and the "law of similitude" linking the flow stress to the characteristic wavelength of dislocation…

We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents…

Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack…

We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…

The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a rearrangement of the low-frequency vibrational spectrum. In this letter, we derive scaling forms for the singular…

We investigate the fragmentation of ring-like brittle structures under explosive loading using a discrete element model. By systematically varying ring thickness and strain rate, we uncover a transition from one-dimensional (1D)…

Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two…

Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…