A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IV: FROM BERNOULLI SHIFT TO 1/f SPECTRUM

2005 ◽  
Vol 15 (04) ◽  
pp. 1045-1183 ◽  
Author(s):  
LEON O. CHUA ◽  
VALERY I. SBITNEV ◽  
SOOK YOON
Keyword(s):  
Bernoulli Shift ◽  
Dynamical Evolution ◽  
Complete Characterization ◽  
Characteristic Functions ◽  
One Dimensional ◽  
New Concepts ◽  
The Right ◽  
Science Part

By exploiting the new concepts of CA characteristic functions and their associated attractor time-τ maps, a complete characterization of the long-term time-asymptotic behaviors of all 256 one-dimensional CA rules are achieved via a single "probing" random input signal. In particular, the graphs of the time-1 maps of the 256 CA rules represent, in some sense, the generalized Green's functions for Cellular Automata. The asymptotic dynamical evolution on any CA attractor, or invariant orbit, of 206 (out of 256) CA rules can be predicted precisely, by inspection. In particular, a total of 112 CA rules are shown to obey a generalized Bernoulli στ-shift rule, which involves the shifting of any binary string on an attractor, or invariant orbit, either to the left, or to the right, by up to 3 pixels, and followed possibly by a complementation of the resulting bit string. The most intriguing result reported in this paper is the discovery that the four Turing-universal rules [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], and only these rules, exhibit a 1/f power spectrum.

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IX: QUASI-ERGODICITY

2008 ◽  
Vol 18 (09) ◽  
pp. 2487-2642 ◽  
Author(s):  
LEON O. CHUA ◽  
GIOVANNI EGIDIO PAZIENZA ◽  
LASZLO ORZO ◽  
VALERY I. SBITNEV ◽  
JINWOOK SHIN
Keyword(s):  
Bernoulli Shift ◽  
Modular Arithmetic ◽  
Characteristic Functions ◽  
Scale Free ◽  
Return Maps ◽  
Definition Of ◽  
Empirical Property ◽  
Science Part

Our scientific odyssey through the theory of 1-D cellular automata is enriched by the definition of quasi-ergodicity, a new empirical property discovered by analyzing the time-1 return maps of local rules. Quasi-ergodicity plays a key role in the classification of rules into six groups: in fact, it is an exclusive characteristic of complex and hyper Bernoulli-shift rules. Besides introducing quasi-ergodicity, this paper answers several questions posed in the previous chapters of our quest. To start with, we offer a rigorous explanation of the fractal behavior of the time-1 characteristic functions, finding the equations that describe this phenomenon. Then, we propose a classification of rules according to the presence of Isles of Eden, and prove that only 28 local rules out of 256 do not have any of them; this result sheds light on the importance of Isles of Eden. A section of this paper is devoted to the characterization of Bernoulli basin-tree diagrams through modular arithmetic; the formulas obtained allow us to shorten drastically the number of cases to take into consideration during numerical simulations. Last but not least, we present some theorems about additive rules, including an analytical explanation of their scale-free property.

scholarly journals (M,β)-Stability of Positive Linear Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Octavian Pastravanu ◽  
Mihaela-Hanako Matcovschi
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Transient Behavior ◽  
Short Term ◽  
Time Dynamics ◽  
The Right ◽  
Long Term Behavior ◽  
Stability Concept

The main purpose of this work is to show that the Perron-Frobenius eigenstructure of a positive linear system is involved not only in the characterization of long-term behavior (for which well-known results are available) but also in the characterization of short-term or transient behavior. We address the analysis of the short-term behavior by the help of the “(M,β)-stability” concept introduced in literature for general classes of dynamics. Our paper exploits this concept relative to Hölder vectorp-norms,1≤p≤∞, adequately weighted by scaling operators, focusing on positive linear systems. Given an asymptotically stable positive linear system, for each1≤p≤∞, we prove the existence of a scaling operator (built from the right and left Perron-Frobenius eigenvectors, with concrete expressions depending onp) that ensures the best possible values for the parametersMandβ, corresponding to an “ideal” short-term (transient) behavior. We provide results that cover both discrete- and continuous-time dynamics. Our analysis also captures the differences between the cases where the system dynamics is defined by matrices irreducible and reducible, respectively. The theoretical developments are applied to the practical study of the short-term behavior for two positive linear systems already discussed in literature by other authors.

scholarly journals Characterization of morphology and function of the ‘neo-atria’ after a modified Mustard operation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Mohamed Nagy ◽  
Hatem Hosny ◽  
Amr El Sawy ◽  
Ahmed Mahgoub ◽  
Magdi H Yacoub
Keyword(s):  
Contractile Function ◽  
Postoperative Recovery ◽  
Long Term Results ◽  
3D Segmentation ◽  
Mustard Operation ◽  
The Right ◽  
And Function ◽  
Atrial Systole

Background: There is a pressing need to improve early and long-term results of the Mustard operation. A modification of the operation was introduced at the Aswan Heart Centre for this purpose which relies on creating new functional atria rather than the two rigid channels in the classical Mustard operation.Objectives: To evaluate the morphology and function of the neo-atria, shortly after modified mustard operation for a ‘neglected’ patient with TGA, VSD and severe pulmonary hypertension.Methods: A 6-year-old with neglected TGA, VSD and pulmonary hypertension presented with severe cyanosis, clubbing and haemoconcentration (Hb 22 g/dL), underwent the modified Aswan-Mustard operation (MAM) with rapid smooth postoperative recovery. Repeated 2D echograms and multi-slice CT scans, followed by 3D segmentation, were performed after the operation. The size, shape, and morphology of the neo-atria were measured and measurements of the patterns of instantaneous filling and emptying of the right and left ventricles were quantified.Results: The neo-systemic venous atrium consisted of three components with a combined volume of 78 mL/m2, all of which contributed to the reservoir, conduit, and importantly contractile function of the neo-atrium. The pulmonary venous atrium consisted of two components with a combined volume of 66 mL/m2. These measurements were made at atrial end diastole. The volumes of the systemic venous and the pulmonary venous diminished to 51 and 54 mL/m2, respectively, at the end atrial systole - indicating relatively preserved contractile functions.

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE. PART X: PERIOD-1 RULES

2009 ◽  
Vol 19 (05) ◽  
pp. 1425-1654 ◽  
Author(s):  
LEON O. CHUA ◽  
GIOVANNI E. PAZIENZA ◽  
JINWOOK SHIN
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Characteristic Functions ◽  
Theoretical Treatment ◽  
String Length ◽  
Nonlinear Dynamical ◽  
One Dimensional ◽  
First Time ◽  
The Universe ◽  
Science Part ◽  
Group 1

This stage of our journey through the universe of one-dimensional binary Cellular Automata is devoted to period-1 rules, constituting the first of the six groups in which we systematized the 88 globally-independent CA rules. The first part of this article is mainly dedicated to reviewing the terminology and the empirical results found in the previous papers of our quest. We also introduce the concept of the ω-limit orbit with the purpose of linking our work to the classical theory of nonlinear dynamical systems. Moreover, we present the basin tree diagrams of all period-1 rules — except for rule [Formula: see text], which is trivial — along with their Boolean cubes and time-1 characteristic functions. In the second part, we prove a theorem demonstrating that all rules belonging to group 1 have robust period-1 rules for any finite, and infinite, bit-string length L. This is the first time we give analytical results on the behavior of CA local rules for large values of L and, consequently, for bi-infinite bit strings. The theoretical treatment is complemented by two remarkable practical results: an explicit formula for generating isomorphic basin trees, and an algorithm for creating new periodic orbits by concatenation. We also provide several examples of both of them, showing how they help to avoid tedious simulations.

BORDER COLLISION BIFURCATIONS IN 1D PWL MAP WITH ONE DISCONTINUITY AND NEGATIVE JUMP: USE OF THE FIRST RETURN MAP

2010 ◽  
Vol 20 (11) ◽  
pp. 3529-3547 ◽  
Author(s):  
LAURA GARDINI ◽  
FABIO TRAMONTANA
Keyword(s):  
Parameter Space ◽  
Complete Characterization ◽  
One Dimensional ◽  
Return Map ◽  
Border Collision Bifurcations ◽  
One Dimensional Maps ◽  
Negative Jump

The aim of this work is to study discontinuous one-dimensional maps in the case of slopes and offsets having opposite signs. Such models represent the dynamics of applied systems in several disciplines. We analyze in particular attracting cycles, their border collision bifurcations and the properties of the periodicity regions in the parameter space. The peculiarity of this family is that we can make use of the technical instrument of the first return map. With this, we can rigorously prove properties which were known numerically, as well as prove new ones, giving a complete characterization of the overlapping periodicity regions.

scholarly journals Regional improvement of global reanalyses by means of a new long-term Mediterranean hindcasted precipitation dataset: a first study over the Iberian Peninsula

2006 ◽  
Vol 7 ◽  
pp. 307-311
Author(s):  
M. G. Sotillo ◽  
M. L. Martín ◽  
F. Valero ◽  
M. Y. Luna
Keyword(s):  
Iberian Peninsula ◽  
Complete Characterization ◽  
Balearic Islands ◽  
Important Improvement ◽  
Complete Study ◽  
In Situ Observations ◽  
Global Reanalysis

Abstract. Generation of a Mediterranean long-term (1958-2001) homogeneous high resolution environmental database constituted the main objective whitin the HIPOCAS Project. The high number of parameters included in this database allows a complete characterization of Mediterranean storms. In this paper, the HIPOCAS precipitation reliability over the Iberian Peninsula and the Balearic Islands is evaluated against long-term in-situ observations from Iberia. In order to provide a more complete study, comparisons of the HIPOCAS field with NCEP/NCAR and ERA global reanalysis show the important improvement in the characterisation of the observed precipitation introduced by the HIPOCAS hindcast.

Equilibrium Distribution of Alloyed Nanowires

2011 ◽  
Vol 172-174 ◽  
pp. 676-681 ◽  
Author(s):  
Emile Maras ◽  
Isabelle Braems ◽  
Fabienne Berthier
Keyword(s):  
Size Distribution ◽  
Equilibrium Distribution ◽  
Canonical Ensemble ◽  
Complete Characterization ◽  
Total Density ◽  
Alloying Effect ◽  
One Dimensional ◽  
Analytical Formulae ◽  
Grand Canonical

The size distribution and the total density of clusters of a one-dimensional pure deposit can be expressed analytically from the Ising model. For a codeposit, the alloying effect and the presence of broken bonds at the cluster edges lead to inhomogeneities of the chemical composition of the clusters. We investigate the influence of codeposition on the size distribution of clusters in the case of an alloy that forms an ideal solution. We obtain the exact solution for the size distribution of clusters while the complete characterization of the system results from coupled analytical formulae in the grand-canonical ensemble. The results of this analytical model are successfully compared with those obtained by Monte Carlo simulations.

Stability of a thermoelastic mixture with second sound

2018 ◽  
Vol 24 (6) ◽  
pp. 1692-1706 ◽  
Author(s):  
Margareth S. Alves ◽  
Marcio V. Ferreira ◽  
Jaime E. Muñoz Rivera ◽  
O. Vera Villagrán
Keyword(s):  
Initial Data ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Second Sound ◽  
Dimensional Model ◽  
One Dimensional ◽  
The One ◽  
Necessary And Sufficient

We consider the one-dimensional model of a thermoelastic mixture with second sound. We give a complete characterization of the asymptotic properties of the model in terms of the coefficients of the model. We establish the necessary and sufficient conditions for the model to be exponential or polynomial stable and also the conditions for which there exist initial data for where the energy is conserved.

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