Related papers: Scaling law in the Standard Map critical function.…
The Lattice results for the pion and kaon decay constants are analysed within the Resonance Chiral Theory framework in the large NC limit. The approximately linear behaviour of the observable at large light-quark mass is explained through…
Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many…
For the problem of diffraction of harmonic scalar waves by a lossless periodic slab scatterer, we analyze field sensitivity with respect to the material coefficients of the slab. The governing equation is the Helmholtz equation, which…
The self-similarity in space and time (hereafter self-similarity), either deterministic or statistical, is characterized by similarity exponents and a function of scaled variable, called the scaling function. In the present paper, we…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
We generalize Huberman-Rudnick universal scaling law for all periodic windows of the logistic map and show the robustness of $q$-Gaussian probability distributions in the vicinity of chaos threshold. Our scaling relation is universal for…
In dynamical systems theory, there is a lack of a straightforward rule to distinguish exact center solutions from decaying center-like solutions, as both require the damping force function to be zero [1, 2]. By adopting a multi-scale…
It was shown via numerical simulations that geometric phase (GP) and fidelity susceptibility (FS) in some quantum models exhibit universal scaling laws across phase transition points. Here we propose a singular function expansion method to…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
In this paper the scaling law for the relaxation times in thermal phenomena is investigated. It is shown that dependent on the value of the parameter K=E/m(c\alpha)^2,where E is the energy which is delivered to the system, m is the parton…
We revisit the number theoretic division model of self-organized criticality [Phys. Rev. Lett. 101, 158702 (2008)]. The model consists of a pool of $M-1$ ordered integers $\{2, 3, \cdots, M\}$, and the aim is to dynamically form a primitive…
Recently, a novel model to describe ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still differing in…
Under a map T, a point x recurs at rate given by a sequence {r_n} near a point x_0 if d(T^n(x),x_0)< r_n infinitely often. Let us fix x_0, and consider the set of those x's. In this paper, we study the size of this set for expanding maps…
Volume fluctuations are introduced in a statistical modelling of relativistic particle collisions. The micro-canonical ensemble is used, and the volume fluctuations are assumed to have the specific scaling properties. This leads to the KNO…
This work deals with the computation of the power spectrum of large-scale structure using the dynamical system approach for a multi-fluid universe in scalar-tensor theory of gravity. We use the $1+3$ covariant approach to obtain evolution…
We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least…
The scaling behavior of cyclical surface growth (e.g. deposition/desorption), with the number of cycles n, is investigated. The roughness of surfaces grown by two linear primary processes follows a scaling behavior with asymptotic exponents…
We calculate the lowest-order non-linear contributions to the power spectrum, two-point correlation function, and smoothed variance of the density field, for Gaussian initial conditions and scale-free initial power spectra, $P(k) \sim k^n$.…
There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…
Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although, recent years have seen the extension of traditional stochastic partial differential equations…