ON THE PRESENCE OF NORMALLY ATTRACTING MANIFOLDS CONTAINING PERIODIC OR QUASIPERIODIC ORBITS IN COUPLED MAP LATTICES

1993 ◽  
Vol 03 (06) ◽  
pp. 1503-1514 ◽  
Author(s):  
CLAUDIO GIBERTI ◽  
CECILIA VERNIA
Keyword(s):  
Invariant Manifolds ◽  
Chaotic Maps ◽  
Period Doubling ◽  
Coupled Map Lattices ◽  
Saddle Node Bifurcation ◽  
Closed Curves ◽  
One Dimensional ◽  
Weak Hyperbolicity ◽  
Long Time ◽  
Almost All

The significant presence of normally attracting invariant manifolds, formed by closed curves or two-tori, is investigated in two-dimensional lattices of coupled chaotic maps. In the case of a manifold formed by closed curves, it contains symmetrically placed periodic orbits, with the property of a very weak hyperbolicity along the manifold itself. The resulting dynamics is an extremely slow relaxation to periodic behavior. Analogously, a manifold consisting of two-tori includes very weakly hyperbolic periodic (or quasiperiodic) orbits, which in this case also implies quite a long time before any solution approaches periodicity or quasiperiodicity. The normally attracting manifolds and the contained weak attractors can undergo several global bifurcations. Some of them, including saddle-node bifurcation, period-doubling and Hopf bifurcation, are illustrated. Almost all the asymptotic solutions that we discuss have flat rows or flat columns, which means that they can occur also in one-dimensional lattices.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

scholarly journals Multifaceted phase ordering kinetics of an antiferromagnetic spin-1 condensate

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Joanna Pietraszewicz ◽  
Aleksandra Seweryn ◽  
Emilia Witkowska
Keyword(s):  
Scaling Laws ◽  
Study Phase ◽  
One Dimensional ◽  
Phase Domain ◽  
Ordering Kinetics ◽  
Domain Coarsening ◽  
Long Time ◽  
Phase Ordering ◽  
Kinetics Of ◽  
Antiferromagnetic Spin

AbstractWe study phase domain coarsening in the long time limit after a quench of magnetic field in a quasi one-dimensional spin-1 antiferromagnetic condensate. We observe that the growth of correlation length obeys scaling laws predicted by the two different models of phase ordering kinetics, namely the binary mixture and vector field. We derive regimes of clear realization for both of them. We demonstrate appearance of atypical scaling laws, which emerge in intermediate regions.

A WEIGHTED CHAOTIC BLOCK ENCRYPTION ALGORITHM USING MULTIPLE ONE-DIMENSIONAL CHAOTIC MAPS

2011 ◽  
Vol 25 (29) ◽  
pp. 3987-3996
Author(s):  
XING-YUAN WANG ◽  
XIAO-JUAN WANG
Keyword(s):  
Chaotic Maps ◽  
Encryption Algorithm ◽  
One Dimensional ◽  
Chaotic Iterations ◽  
Block Encryption

This paper proposes a new block encryption algorithm. The chaotic trajectories are computed by weighting. Then the result is used to mask the plaintext. Multiple blocks of plaintext are encrypted at the same time and this decreases the chaotic iterations. So the encryption speed is improved to some extent. The proposed algorithm is flexible. When the number of weights is increased, the number of the encrypted plaintext block at the same time is increased and the encryption speed is improved. The simulation result shows that the proposed algorithm has fast encryption speed and fine security.

scholarly journals Chaotic period doubling

2009 ◽  
Vol 29 (2) ◽  
pp. 381-418 ◽  
Author(s):  
V. V. M. S. CHANDRAMOULI ◽  
M. MARTENS ◽  
W. DE MELO ◽  
C. P. TRESSER
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Chaotic Dynamics ◽  
A Priori ◽  
Period Doubling ◽  
Small Scale ◽  
Unimodal Maps ◽  
One Dimensional ◽  
Renormalization Operator ◽  
Renormalization Theory

AbstractThe period doubling renormalization operator was introduced by Feigenbaum and by Coullet and Tresser in the 1970s to study the asymptotic small-scale geometry of the attractor of one-dimensional systems that are at the transition from simple to chaotic dynamics. This geometry turns out not to depend on the choice of the map under rather mild smoothness conditions. The existence of a unique renormalization fixed point that is also hyperbolic among generic smooth-enough maps plays a crucial role in the corresponding renormalization theory. The uniqueness and hyperbolicity of the renormalization fixed point were first shown in the holomorphic context, by means that generalize to other renormalization operators. It was then proved that, in the space ofC2+αunimodal maps, forα>0, the period doubling renormalization fixed point is hyperbolic as well. In this paper we study what happens when one approaches from below the minimal smoothness thresholds for the uniqueness and for the hyperbolicity of the period doubling renormalization generic fixed point. Indeed, our main result states that in the space ofC2unimodal maps the analytic fixed point is not hyperbolic and that the same remains true when adding enough smoothness to geta prioribounds. In this smoother class, calledC2+∣⋅∣, the failure of hyperbolicity is tamer than inC2. Things get much worse with just a bit less smoothness thanC2, as then even the uniqueness is lost and other asymptotic behavior becomes possible. We show that the period doubling renormalization operator acting on the space ofC1+Lipunimodal maps has infinite topological entropy.

scholarly journals Women and Gender in 1917

Slavic Review ◽  
2017 ◽  
Vol 76 (3) ◽  
pp. 694-702 ◽  
Author(s):  
Rochelle Goldberg Ruthchild
Keyword(s):  
Political Parties ◽  
Significant Issue ◽  
Women And Gender ◽  
One Dimensional ◽  
History Of ◽  
Key Issues ◽  
And Gender ◽  
Almost All ◽  
The Revolution

This paper argues for greater integration of considerations of women and gender in the history of the 1917 Russian Revolutions. Two key issues have long been discussed by historians: the spontaneity/consciousness paradigm, and the role of class in the revolution. Neither has been adequately analyzed in relation to gender. Women's suffrage has been largely neglected despite the fact that it was a significant issue throughout the year and represented a pioneering advance won by a countrywide coalition of women and men from the working class and intelligentsia, and from almost all political parties. In this centennial year, accounts of the Revolution remain one-dimensional; women remain the other.

Long-time behavior for the full one-dimensional Frémond model for shape memory alloys

2000 ◽  
Vol 12 (6) ◽  
pp. 423-433 ◽  
Author(s):  
Pierluigi Colli ◽  
Philippe Laurençot ◽  
Ulisse Stefanelli
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Time Behavior ◽  
Long Time Behavior ◽  
One Dimensional ◽  
Long Time

Missing Value Imputation Using ANN Optimized by Genetic Algorithm

2018 ◽  
Vol 5 (2) ◽  
pp. 41-57 ◽  
Author(s):  
Anjana Mishra ◽  
Bighnaraj Naik ◽  
Suresh Kumar Srichandan
Keyword(s):  
Genetic Algorithm ◽  
Missing Data ◽  
Data Entry ◽  
Missing Information ◽  
Missing Value ◽  
Need Analysis ◽  
Processing Data ◽  
Real World Applications ◽  
Long Time ◽  
Almost All

Missing value arises in almost all serious statistical analyses and creates numerous problems in processing data in databases. In real world applications, information may be missing due to instrumental errors, optional fields and non-response to some questions in surveys, data entry errors, etc. Most of the data mining techniques need analysis of complete data without any missing information and this induces researchers to develop efficient methods to handle them. It is one of the most important areas where research is being carried out for a long time in various domains. The objective of this article is to handle missing data, using an evolutionary (genetic) algorithm including some relatively simple methodologies that can often yield reasonable results. The proposed method uses genetic algorithm and multi-layer perceptron (MLP) for accurately predicting missing data with higher accuracy.

Sign in / Sign up

Export Citation Format

Share Document