Tensor function analysis of quantized chaotic piecewise-affine pseudo-Markov systems. I. Second-order correlations and self similarity

2002 ◽  
Vol 49 (2) ◽  
pp. 137-149 ◽  
Author(s):  
R. Rovatti ◽  
G. Mazzini
Keyword(s):  
Function Analysis ◽  
Second Order ◽  
Tensor Function ◽  
Self Similarity ◽  
Markov Systems ◽  
Piecewise Affine

scholarly journals Integrity basis for a second-order and a fourth-order tensor

1982 ◽  
Vol 5 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Josef Betten
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Tensor Function ◽  
Order Tensor ◽  
Isotropic Tensor ◽  
Anisotropic Properties ◽  
Isotropic Tensor Function ◽  
Fourth Order Tensor

In this paper a scalar-valued isotropic tensor function is considered, the variables of which are constitutive tensors of orders two and four, for instance, characterizing the anisotropic properties of a material. Therefore, the system of irreducible invariants of a fourth-order tensor is constructed. Furthermore, the joint or simultaneous invariants of a second-order and a fourth-order tensor are found. In a similar way one can construct an integrity basis for a tensor of order greater than four, as shown in the paper, for instance, for a tensor of order six.

The nature of discrete second-order self-similarity

2003 ◽  
Vol 35 (02) ◽  
pp. 395-416 ◽  
Author(s):  
A. Gefferth ◽  
D. Veitch ◽  
I. Maricza ◽  
S. Molnár ◽  
I. Ruzsa
Keyword(s):  
Fixed Points ◽  
Long Range ◽  
Power Laws ◽  
Complete Classification ◽  
Second Order ◽  
General Definition ◽  
Long Range Dependence ◽  
Self Similarity ◽  
New Treatment ◽  
Definition Of

A new treatment of second-order self-similarity and asymptotic self-similarity for stationary discrete time series is given, based on the fixed points of a renormalisation operator with normalisation factors which are not assumed to be power laws. A complete classification of fixed points is provided, consisting of the fractional noise and one other class. A convenient variance time function approach to process characterisation is used to exhibit large explicit families of processes asymptotic to particular fixed points. A natural, general definition of discrete long-range dependence is provided and contrasted with common alternatives. The closely related discrete form of regular variation is defined, its main properties given, and its connection to discrete self-similarity explained. Folkloric results on long-range dependence are proved or disproved rigorously.

Structure function analysis of plasma density fluctuations during total loss of lock of GPS signal events

2020 ◽  
Author(s):  
Hossein Ghadjari ◽  
David Knudsen ◽  
Susan Skone
Keyword(s):  
Structure Function ◽  
Plasma Density ◽  
Large Scale ◽  
Function Analysis ◽  
Density Fluctuations ◽  
Total Loss ◽  
Small Scale ◽  
Self Similarity ◽  
Radio Signals ◽  
Swarm Mission

<p>Ionospheric irregularities are fluctuations or structures of plasma density that affect the propagation of radio signals. Whenever large-scale irregularities break up into meso and small-scale irregularities, these processes become similar to a turbulence cascade. In order to have a better comparison between this and plasma density irregularities, we study different orders of structure functions of plasma density of total loss of lock events measured with the faceplate measurements of plasma density and the GPS measurements from the Swarm mission. Total loss of lock of GPS signal is a physical proxy for severe degradation of GPS signals. In addition to different orders of structure-function, we study the existence of self-similarity or multifractality of plasma density of total loss of lock events to investigate any possible intermittent fluctuations. </p>

scholarly journals Poisson random balls: self-similarity and X-ray images

2006 ◽  
Vol 38 (4) ◽  
pp. 853-872 ◽  
Author(s):  
Hermine Biermé ◽  
Anne Estrade
Keyword(s):  
Porous Media ◽  
Random Field ◽  
Random Measure ◽  
Second Order ◽  
Poisson Random Measure ◽  
Media Images ◽  
Self Similarity ◽  
X Ray ◽  
Ray Transform

We study a random field obtained by counting the number of balls containing a given point when overlapping balls are thrown at random according to a Poisson random measure. We describe a microscopic process which exhibits multifractional behavior. We are particularly interested in the local asymptotic self-similarity (LASS) properties of the field, as well as in its X-ray transform. We obtain two different LASS properties when considering the asymptotics either in law or in the sense of second-order moments, and prove a relationship between the LASS behavior of the field and the LASS behavior of its X-ray transform. These results can be used to model and analyze porous media, images, or connection networks.

The nature of discrete second-order self-similarity

2003 ◽  
Vol 35 (2) ◽  
pp. 395-416 ◽  
Author(s):  
A. Gefferth ◽  
D. Veitch ◽  
I. Maricza ◽  
S. Molnár ◽  
I. Ruzsa
Keyword(s):  
Fixed Points ◽  
Long Range ◽  
Power Laws ◽  
Complete Classification ◽  
Second Order ◽  
General Definition ◽  
Long Range Dependence ◽  
Self Similarity ◽  
New Treatment ◽  
Definition Of

A new treatment of second-order self-similarity and asymptotic self-similarity for stationary discrete time series is given, based on the fixed points of a renormalisation operator with normalisation factors which are not assumed to be power laws. A complete classification of fixed points is provided, consisting of the fractional noise and one other class. A convenient variance time function approach to process characterisation is used to exhibit large explicit families of processes asymptotic to particular fixed points. A natural, general definition of discrete long-range dependence is provided and contrasted with common alternatives. The closely related discrete form of regular variation is defined, its main properties given, and its connection to discrete self-similarity explained. Folkloric results on long-range dependence are proved or disproved rigorously.

Synchronous and Asynchronous Reversible Markov Systems(1)

1975 ◽  
Vol 17 (5) ◽  
pp. 633-649 ◽  
Author(s):  
D. A. Dawson
Keyword(s):  
Invariant Measure ◽  
Random Field ◽  
Markov Random Field ◽  
Second Order ◽  
Markov Systems ◽  
First Order ◽  
Markov Random

AbstractThe relationships between synchronous and asynchronous reversible Markov systems are investigated. It is shown that the invariant measure of such systems is a second order Markov random field. The conditions under which the invariant measure is a first order Markov random field are obtained.

Scaling Analysis of the China France Oceanography Satellite Along Track Wave and Wind Data

2020 ◽  
Author(s):  
Yang Gao ◽  
Francois G Schmitt ◽  
Jianyu Hu ◽  
Yongxiang Huang
Keyword(s):  
Power Spectrum ◽  
Power Law ◽  
Function Analysis ◽  
Second Order ◽  
Order Structure ◽  
Scaling Analysis ◽  
Scaling Exponents ◽  
Fourier Power Spectrum ◽  
Along Track ◽  
Dual Power

<p>Turbulence or turbulence-like phenomena are ubiquitous in nature, often showing a power-law behavior of the Fourier power spectrum in either spatial or temporal domains. This power-law behavior is due to interactions among different scales of motion, and to the absence of characteristic scale among several scale ranges. It can be further interpreted in the framework of turbulent cascade with movements on continuous range of scales. The power-law feature and the associate cascade picture are vitally important to our understanding of the ocean and atmosphere dynamics. In this work, we consider the China France Oceanography SATellite (CFOSAT) data in the general framework of ocean and atmosphere multi-scale dynamics. We apply both Fourier power spectrum analysis and second-order structure-function analysis, used in the fields of turbulence, to extract multiscale information from the wind speed (WS) and significant wave-height (Hs) data provided by CFOSAT project. The data analyzed here are along track data spatially collected from 29<sup>th</sup> July to 31<sup>th</sup> December 2019. The measured Fourier power spectrums for both WS and Hs illustrate a dual power-law behavior respectively from 5 to 25 km, and 30 to 500 km with measured scaling exponents β close to 2 and 5/3. The measured second-order structure-functions confirm the existence of the dual power-law behavior. The corresponding measured scaling exponents  ζ(2) close to 1 and 2/3 for the spatial scales mentioned above. Our preliminary results confirm the relevance of using multiscale statistical tools and turbulent theory to characterize the large-scale movements of both ocean and atmosphere.</p>

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