Related papers: Finite-size effects in roughness distribution scal…
We reexamine the range of validity of finite-size scaling in the $\phi^4$ lattice model and the $\phi^4$ field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the $\phi^4$…
A new surface-rupture-length ($SRL$) relationship as a function of magnitude ($\mathbf{M}$), fault thickness, and fault dip angle is presented in this paper. The objective of this study is to model the change in scaling between unbounded…
Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
We present a comprehensive analysis of a linear growth model, which combines the characteristic features of the Edwards--Wilkinson and noisy Mullins equations. This model can be derived from microscopics and it describes the relaxation and…
Using a two dimensional lattice model we investigate the crack growth under the influence of remote tensile forces as well as due to an internally applied pressure (hydraulic fracturing). For homogeneous elastic properties we present…
Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, while the metabolic scaling…
Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis…
From a recently found family of analytic, finite and accelerating 1+1-dimensional solutions to perfect fluid relativistic hydrodynamics, we derive simple and powerful formulae to describe the rapidity and pseudorapidity density…
Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities.…
We study the impact of finite-size effect on continuous variable source-independent quantum random number generation. The central-limit theorem and maximum likelihood estimation theorem are used to derive the formula which could output the…
Finite-size scaling arguments naturally lead us to introduce a coordinate-dependent diffusion coefficient in a Fokker-Planck description of the late stage dynamics of unbiased polymer translocation through a membrane pore. The solution for…
We investigate finite size scaling in percolating widthless stick systems with variable aspect ratios in an extensive Monte Carlo simulation study. A generalized scaling function is introduced to describe the scaling behavior of the…
Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of…
In this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness, or height-height correlation function. By studying the power spectrum of the surface and its relation to the…
Traditional computational approaches in simulating crack propagation in perfectly brittle materials rely on the estimate of stress intensity factors along the rupture front. This proves highly challenging in 3D when the crack geometry…
We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
Motivated in part by quantum criticality in dissipative Kondo systems, we revisit the finite-size scaling of a classical Ising chain with 1/r^{2-epsilon} interactions. For 1/2<epsilon<1, the scaling of the dynamical spin susceptibility is…