Related papers: 1/f Noise in Fractal Quaternionic Structures
In this paper we study the radial and orthogonal projections and the distance sets of the random Cantor sets $E\subset \mathbb{R}^2 $ which are called Mandelbrot percolation or percolation fractals. We prove that the following assertion…
\emph{Fractal percolation} or \emph{Mandelbrot percolation} is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theoretical properties (dimension of projections and structure of…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. In this Letter we show that the level fluctuations of experimental realizations of the Sinai billiard exhibit…
Simple analytically solvable model of 1/f noise is proposed. The model consists of one or few particles moving in the closed contour. The drift period of the particle round the contour fluctuates about some average value, e.g. due to the…
1/f noise is very common but is difficult to handle in a metrological way. After having recalled the main characteristics of stongly correlated noise, this paper will determine relationships giving confidence intervals over the arithmetic…
This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split…
We investigate a problem of the necessary and sufficient conditions for appearance of the 1/f fluctuations in the simple systems affected by the external random perturbations, i.e. the power spectral density of the flux of particles moving…
Multiplicative processes and multifractals have earned increased popularity in applications ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. We analyse the multifractality of the recently…
It is generally assumed that stochastic processes exhibiting 1/f noise are affected with the so-called infrared catastrophe. We present an intermittent stochastic process generating 1/f noise which avoids this problem.
The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's…
Quasicrystals are fractal due to their self similar property. In this paper, a new cycloidal fractal signature possessing the cardioid shape in the Mandelbrot set is presented in the Fourier space of a Fibonacci chain with two lengths, L…
We analyze recent data on the complex inductance of dc SQUIDs that show 1/f inductance noise highly correlated with conventional 1/f flux noise. We argue that these data imply a formation of long range order in fractal spin structures. We…
A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost…
We consider the concept of fractons as particles or quasiparticles which obey a specific fractal statistics in connection with a one-dimensional Luttinger liquid theory. We obtain a dual statistics parameter ${\tilde{\nu}}=\nu+1$ which is…
We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection, in particular, we obtain recurrence relations for them. We also make…
Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model…
The performance of superconducting devices like qubits, SQUIDs, and particle detectors is often limited by finite coherence times and 1/f noise. Various types of slow fluctuators in the Josephson junctions and the passive parts of these…
The contribution emphasizes the geometric modeling point of view on Minkowski point set operations. In this paper, the Minkowski product is specified as the quaternionic product. Selected point sets are visualized using double orthogonal…
In this article we study an exact analogue of the cross-ratio for the algebra of quaternions H and use it to derive several interesting properties of quaternionic fractional linear transformations. In particular, we show that there exists a…
In this paper, we generalize the Mandelbrot set using quaternions and spherical coordinates. In particular, we use pure quaternions to define a spherical product. This product, which is inspired by the product of complex numbers, add the…